# ABSTRACT

Lettuce (Lactuca sativa) is the main leafy vegetable produced in Brazil. Since its production is widespread all over the country, lettuce traceability and quality assurance is hampered. In this study, we propose a new method to identify the geographical origin of Brazilian lettuce. The method uses a powerful data mining technique called support vector machines (SVM) applied to elemental composition and soil properties of samples analyzed. We investigated lettuce produced in São Paulo and Pernambuco, two states in the southeastern and northeastern regions in Brazil, respectively. We investigated efficiency of the SVM model by comparing its results with those achieved by traditional linear discriminant analysis (LDA). The SVM models outperformed the LDA models in the two scenarios investigated, achieving an average of 98 % prediction accuracy to discriminate lettuce from both states. A feature evaluation formula, called F–score, was used to measure the discriminative power of the variables analyzed. The soil exchangeable cation capacity, soil contents of low crystalized Al and Zn content in lettuce samples were the most relevant components for differentiation. Our results reinforce the potential of data mining and machine learning techniques to support traceability strategies and authentication of leafy vegetables.

ICP–OES; traceability; tropical soils; heavy metals; feature selection

# Introduction

Lettuce is among the most consumed vegetables worldwide and is considered the most produced and consumed leafy vegetable in Brazil. Lettuce is low in calories, fat, and Na, while being a good source of fibers, Fe, folate, vitamins and several other bioactive compounds that are beneficial to human health (Kim et al., 2016Kim, M.J.; Moon, Y.; Tou, J.C.; Mou, B.; Waterland, N.L. 2016. Nutritional value, bioactive compounds and health benefits of lettuce (Lactuca sativa L.). Journal of Food Composition and Analysis 49: 19–34.). Since the consumption per capita of fruits and vegetables is about 40 kg per yr1in Brazil, much less than 143 kg per yr1 consumed in a developed country, such as the United States (Mainville and Peterson, 2005Mainville, D.Y.; Peterson, H.C. 2005. Fresh Produce Procurement Strategies in a Constrained Supply Environment: Case Study of Companhia Brasileira de Distribuicao. Applied Economic Perspectives and Policy 27: 130–138.), lettuce is an important source of vegetable–based nutrients for the Brazilian population.

According to the most recent research conducted by IBGE (Brazilian Institute of Geography and Statistics) in 2006, the states of São Paulo (SP) and Pernambuco (PE) are the main lettuce producers in the southeastern and northeastern regions of Brazil, respectively. Growers can sell to a diversity of buyers, including intermediaries (purchase at farm gate), small supermarkets, large supermarket chains, wholesale markets, processors, and directly to consumers. This fragmented production chain makes the traceability and quality assurance of lettuce a difficult task. Moreover, most farmers neglect to use methods and techniques that add value to the product, such as food safety, traceability of inputs, improvements of handling and planting, among others (Carvalho et al., 2014Carvalho, K.L.; Costa, R.P.; Souza, R.C. 2014. Strategic management of relationships in lettuce supply chain. Production 24: 271–282.).

## This study has the following main objectives:

1. We propose the use of support vector machines (SVM) and feature selection to determine the geographical origin of lettuce samples based on their elemental composition and soil properties. We discriminate lettuce samples from São Paulo and Pernambuco, major lettuce producers in Brazil (Figure 1).

Figure 1
– Map of administrative divisions of Brazil. Pernambuco and São Paulo States are highlighted in green and blue colors, respectively.

2. In order to ascertain the efficiency of the SVM model, we developed simple linear discriminant models for the same data and compared the results and performance measurements.

3. We also investigated the discriminative power of each variable and identified a subset of variables that mostly impact differentiation through the use of a feature selection technique, called F–score, a novel approach to lettuce discrimination.

4. We expect to show the potential of data mining and machine learning techniques to support traceability strategies and authentication of leafy vegetables.

# Materials and Methods

## Lettuce and soil samples analyzed

We collected 194 lettuce samples and soil samples from farms in São Paulo (n = 72) and Pernambuco (n = 122), Brazil. Coordinates of the sampling sites are shown in Table 1. Soil samples were dried in the shade and then sieved (2 mm mesh). Lettuce leaves were washed in running water to remove impurities, dried (45 – 60 oC) and ground in a stainless–steel mill (< 1 mm).

Table 1
– Approximated geographical coordinates of cities where the analyzed lettuce samples were collected. Column # is the number of samples collected from the location.

Soil texture was obtained by the densimeter method (Gee and Or, 2002Gee, G.W.; Or, D. 2002. Particle–size analysis. p. 241–254. In: Dane, J.H.; Topp, G.C., eds. Methods of soil analysis. Part 4. Physical methods. Soil Science Society of America, Madison, WI, USA.) and the pH was obtained by potentiometry using a combined electrode immersed in the soil: water suspension (1:2.5) and soil: 1 mol L1 KCl solution (1:2.5). Potential acidity (H + Al) was obtained by extraction with 1 mol L1 calcium acetate (pH 7.0) and titration with NaOH using phenolphthalein as indicator. The organic carbon (OC) content of soils was obtained by dry combustion in an elemental analyzer. A 1 mol L1 KCl solution extracted the levels of exchangeable Ca, Mg and Al. Levels of available K and P were extracted with a double acid solution (Mehlich–1), following the protocol of Anderson and Ingram (1992)Anderson, J.M.; Ingram, J.S.I. 1992. Tropical Soil Biology and Fertility: A Handbook of Methods. CAB International, Wallingford, UK.. Based on these extractions, we obtained the following values: ΔpH = pHKCl – pHH2O; CECT (Ca2 + Mg2 + K+ + H+Al); CECe (Ca2 + Mg2 + K+ + Al3); SB (Ca2 + Mg2 + K+); V % ([SB × 100]/CECT); and m % ([Al3 × 100]/CECe). Levels of well–crystallized Fe and Al (Fe2O3DCB and Al2O3DCB) were extracted with Na dithionite–citrate–bicarbonate (DCB) (Inda Junior and Kämpf, 2003; Mehra and Jackson, 1960Mehra, J.P.; Jackson, M.L. 1960. Iron oxides removal from soils and clays by a dithionite–citrate–bicarbonate system buffered with bicarbonate sodium. Clays and Clay Minerals 7: 317–327.), while amorphous Fe and Al were extracted with acidic ammonium oxalate (Fe2O3OXA and Al2O3OXA) (McKeague and Day, 1966McKeague, J.A.; Day, J.H. 1966. Dithionite and oxalate extractable fe and al as aids in differentiating various classes of soils. Canadian Journal of Soil Science 46: 13–22.).

The pseudo-total concentrations of Cu, Ni, and Zn in the soil were extracted by acid extraction in a microwave oven using the EPA 3051A method (1:3 HCl:HNO3, v/v). Plant material digestion followed Araújo et al. (2002)Araújo, C.L.; Nogueira, A.R.A.; Nobrega, J.A. 2002. Effect of acid concentration on closed–vessel microwave–assisted digestion of plant materials. Spectrochimica Acta Part B: Atomic Spectroscopy 57: 2121–2132., using HNO3 and H2O2 in microwave assisted digestion. Contents of Cu, Ni and Zn were determined by inductively coupled plasma / optical emission spectroscopy (ICP OES) using the conventional sample introduction system. Data quality control was measured using standard reference material (SRM 2709a – San Joaquin Soil) from the National Institute of Standards and Technology (NIST, USA) and an analytical blank in triplicate. The concentrations of analytical blanks were below the quantification limit (0.01 mg L1 for Cu and Ni; 0.05 mg L1 for Zn). Precision (n = 3), expressed as relative standard deviation (RSD), was < 10 % for all elements. More details can be found at Santos–Araujo and Alleoni (2016)Santos–Araujo, S.N.; Alleoni, L.R.F. 2016. Concentrations of potentially toxic elements in soils and vegetables from the macroregion of São Paulo, Brazil: availability for plant uptake. Environmental Monitoring and Assessment 188: 1–17..

## Data mining for prediction of food origin

In the past decade, authenticity and traceability of foodstuffs became a desirable feature for consumers and producers worldwide (Baroni et al., 2015Baroni, M.V.; Podio, N.S.; Badini, R.G;, Inga, M.; Ostera, H.A.; Cagnoni, M.; Gautier, E.A.; García, P.P.; Hoogewerff, J.; Wunderlin, D.A. 2015. Linking soil, water, and honey composition to assess the geographical origin of Argentinean honey by multielemental and isotopic analyses. Journal of Agricultural and Food Chemistry 63: 4638–4645.) and the search for methods that ensure authenticity of food has received great attention from researchers. A strategy that emerged in recent literature was the use of data mining and multivariate data analysis to discriminate the geographical origin of foodstuffs and vegetables based on their chemical components. Successful applications of this methodology and other similar were reported for rice (Maione et al., 2018), honey (Maione et al., 2019Maione, C.; Barbosa, F.; Barbosa, R.M. 2019. Predicting the botanical and geographical origin of honey with multivariate data analysis and machine learning techniques: a review. Computers and Electronics in Agriculture 157: 436–446. https://doi.org/10.1016/j.compag.2019.01.020
https://doi.org/10.1016/j.compag.2019.01...
), Italian and Turkish lemon (Potortì et al., 2018Potortì, A.G.; Bella, G. Di; Mottese, A.F.; Bua, G.D.; Fede, M.R.; Sabatino, G.; Salvo, A.; Somma, R.; Dugo, G.; Turco, V.L. 2018. Traceability of protected geographical indication (PGI) Interdonato lemon pulps by chemometric analysis of the mineral composition. Journal of Food Composition and Analysis 69: 122–128.), tea (Moreda–Piñeiro et al., 2003Moreda–Piñeiro, A.; Fisher, A.; Hill, S.J. 2003. The classification of tea according to region of origin using pattern recognition techniques and trace metal data. Journal of Food Composition and Analysis 16: 195–211.), chocolate (Cambrai et al., 2010Cambrai, A.; Marcic, C.; Morville, S.; Sae Houer, P.; Bindler, F.; Marchioni, E. 2010. Differentiation of chocolates according to the cocoa’s geographical origin using chemometrics. Journal of Agricultural and Food Chemistry 58: 1478–1483.), alcoholic beverages (Alcázar et al., 2012Alcázar, Á.; Jurado, J.M.; Palacios–Morillo, A.; Pablos, F.; Martín, M.J. 2012. Recognition of the geographical origin of beer based on support vector machines applied to chemical descriptors. Food Control 23: 258–262.; Ceballos–Magaña et al., 2012Ceballos–Magaña, S.G.; Jurado, J.M.; Muñiz–Valencia, R.; Alcázar, A.; Pablos, F.; Martín, M.J. 2012. Geographical authentication of tequila according to its mineral content by means of support vector machines. Food Analytical Methods 5: 260–265.; Coetzee et al., 2005Coetzee, P.P.; Steffens, F.E.; Eiselen, R.J.; Augustyn, O.P.; Balcaen, L.; Vanhaecke, F. 2005. Multi–element analysis of South African wines by icp−ms and their classification according to geographical origin. Journal of Agricultural and Food Chemistry 53: 5060–5066.), coffee (Oliveira et al., 2015Oliveira, M.; Ramos, S.; Delerue–Matos, C.; Morais, S. 2015. Espresso beverages of pure origin coffee: mineral characterization, contribution for mineral intake and geographical discrimination. Food Chemistry 177: 330–338.; Serra et al., 2005Serra, F.; Guillou, C.G.; Reniero, F.; Ballarin, L.; Cantagallo, M.I.; Wieser, M.; Iyer, S.S.; Héberger, K.; Vanhaecke, F. 2005. Determination of the geographical origin of green coffee by principal component analysis of carbon, nitrogen and boron stable isotope ratios. Rapid Communications in Mass Spectrometry 19: 2111–2115.), tomato (Mahne Opatić et al., 2018Mahne Opatić, A.; Nečemer, M.; Lojen, S.; Masten, J.; Zlatić, E.; Šircelj, H.; Stopar, D.; Vidrih, R. 2018. Determination of geographical origin of commercial tomato through analysis of stable isotopes, elemental composition and chemical markers. Food Control 89: 133–141.), and others. Therefore, we proposed the use of data mining techniques, namely SVM and feature selection algorithms, to determine the geographical origin of lettuce samples based on their chemical composition.

Data mining is an efficient process to find hidden patterns and information in large and complex data sets where simple multivariate data analysis techniques and statistical methods are often unable to model efficiently, such as the principal component analysis and the discriminant analysis. Data mining techniques combine concepts and methods from artificial intelligence, mathematical optimization, linear algebra, and statistical analysis in order to perform either predictive or exploratory analysis on labeled or unlabeled data (Kotsiantis et al., 2006Kotsiantis, S.B.; Zaharakis, I.D.; Pintelas, P.E. 2006. Machine learning: a review of classification and combining techniques. Artificial Intelligence Review 26: 159–190.). Although data mining processes emerged from the multivariate data analysis and statistical techniques to handle larger and more complex data sets (Izenman, 2008Izenman, A.J. 2008. Modern Multivariate Statistical Techniques. Springer Science, New York, NY, USA.), these processes can be applied to smaller data sets to extract meaningful information, often preferred due to their sophisticated algorithms that are capable of performing probabilistic reasoning. Furthermore, these algorithms are constantly evolving.

Classification models can be described as data mining tools that can predict information, represented by a categorical variable, in data samples. These models observe similar and previously labeled samples and use the information learned from this observation to build a function or model that is capable of generalizing the learned information in new and unknown data samples, as long as they are described by the same set of variables as the observed samples. This learning process is known as supervised learning in the field of artificial intelligence. Support vector machines, created by Cortes and Vapnik (1995)Cortes, C.; Vapnik, V. 1995. Support–vector networks. Machine Learning 20: 273–297., are an example a popular classification model in the recent data mining literature and are successfully employed to discriminate and classify data from different fields for various purposes.

Our previous literature search revealed that this is the first attempt to discriminate the geographical origin of Brazilian lettuce samples based on the machine learning technique for data mining, such as support vector machines, also applied to chemical composition and soil parameters. In order to ascertain the efficiency of the SVM model, we developed simple linear discriminant models for the same data and compared the results and performance measurements. We also investigated the discriminative power of each variable and identified a subset of variables that mostly impact differentiation through the use of a feature selection technique called F–score, a novel approach to the discrimination of lettuce.

## Support vector machines (SVM)

SVM is described as an optimization function to find the decision boundary with the largest margin possible to separate the data, minimizing the risk of overfitting and improving the generalization performance. The decision boundary is computed by the following Eq. 1:

$w\cdot x+b=0$ (1)

where: x is the values obtained from the variables of the training samples, w refers to weights whose linear combination computes the class label, and b is a model parameter, the decision boundary with the largest margin possible is achieved by the minimization Eq. 2:

$\underset{w}{min}\frac{\parallel W{\parallel }^{2}}{2}$ (2)

Classification models based on SVM are widely used in the literature to perform the predictive analyses on data from several problems and fields. Only in the last two years, SVM has been successfully employed to solve problems in domains, such as geology (García–Nieto et al., 2019García–Nieto, P.J.; García–Gonzalo, E.; Fernández, J.R.A.; Muñiz, C.D. 2019. Modeling of the algal atypical increase in La Barca reservoir using the DE optimized least square support vector machine approach with feature selection. Mathematics and Computers in Simulation 166: 461–480.; Huang et al., 2017Huang, G.; Qiu, W.; Zhang, J. 2017. Modelling seismic fragility of a rock mountain tunnel based on support vector machine. Soil Dynamics and Earthquake Engineering 102: 160–171.; Jung et al., 2018Jung, H.; Jo, H.; Kim, S.; Lee, K.; Choe, J. 2018. Geological model sampling using PCA–assisted support vector machine for reliable channel reservoir characterization. Journal of Petroleum Science and Engineering 167: 396–405.; Kumar et al., 2017Kumar, D.; Thakur, M.; Dubey, C.S.; Shukla, D.P. 2017. Landslide susceptibility mapping and prediction using support vector machine for Mandakini River Basin, Garhwal Himalaya, India. Geomorphology 295: 115–125.; Mahvash and Hezarkhani, 2018Mahvash, N.M.; Hezarkhani, A. 2018. Application of support vector machine for the separation of mineralised zones in the Takht–e–Gonbad porphyry deposit, SE Iran. Journal of African Earth Sciences 143: 301–308.; Pu et al., 2019Pu, Y.; Apel, D.B.; Liu, V.; Mitri, H. 2019. Machine learning methods for rockburst prediction–state–of–the–art review. International Journal of Mining Science and Technology 29: 565–570. https://doi.org/10.1016/j.ijmst.2019.06.009
https://doi.org/10.1016/j.ijmst.2019.06....
), hydrological sciences (Choubin et al., 2019b, 2018; Kisi et al., 2019Kisi, O.; Choubin, B.; Deo, R.C.; Yaseen, Z.M. 2019. Incorporating synoptic–scale climate signals for streamflow modelling over the Mediterranean region using machine learning models. Hydrological Sciences Journal 64: 1240–1252.; Rahmati et al., 2019Rahmati, O.; Choubin, B.; Fathabadi, A.; Coulon, F.; Soltani, E.; Shahabi, H.; Mollaefar, E.; Tiefenbacher, J.; Cipullo, S.; Ahmad, B.B.; Bui, D.T. 2019. Predicting uncertainty of machine learning models for modelling nitrate pollution of groundwater using quantile regression and UNEEC methods. Science of the Total Environment 688: 855–866. https://doi.org/10.1016/j.scitotenv.2019.06.320
https://doi.org/10.1016/j.scitotenv.2019...
; Sajedi–Hosseini et al., 2018Sajedi–Hosseini, F.; Malekian, A.; Choubin, B.; Rahmati, O.; Cipullo, S.; Coulon, F.; Pradhan, B. 2018. A novel machine learning–based approach for the risk assessment of nitrate groundwater contamination. Science of the Total Environment 644: 954–962.), climate and weather (Fan et al., 2018Fan, J.; Wang, X.; Wu, L.; Zhou, H.; Zhang, F.; Yu, X.; Lu, X.; Xiang, Y. 2018. Comparison of Support vector machine and extreme gradient boosting for predicting daily global solar radiation using temperature and precipitation in humid subtropical climates: a case study in China. Energy Conservation and Managment 164: 102–111. https://doi.org/10.1016/j.enconman.2018.02.087
https://doi.org/10.1016/j.enconman.2018....
; Kundu et al., 2017Kundu, S.; Khare, D.; Mondal, A. 2017. Future changes in rainfall, temperature and reference evapotranspiration in the central India by least square support vector machine. Geoscience Frontiers 8: 583–596. https://doi.org/10.1016/j.gsf.2016.06.002
https://doi.org/10.1016/j.gsf.2016.06.00...
; Yu et al., 2018Yu, C.; Li, Y.; Bao, Y.; Tang, H.; Zhai, G. 2018. A novel framework for wind speed prediction based on recurrent neural networks and support vector machine. Energy Conversion and Management 178: 137–145., 2017Yu, P.S.; Yang, T.C.; Chen, S.Y.; Kuo, C.M.; Tseng, H.W. 2017. Comparison of random forests and support vector machine for real–time radar–derived rainfall forecasting. Journal of Hydrology 552: 92–104. https://doi.org/10.1016/j.jhydrol.2017.06.020
https://doi.org/10.1016/j.jhydrol.2017.0...
), fault detection in various systems and processes (Ali et al., 2018Ali, S.M.; Hui, K.H.; Hee, L.M.; Leong, M.S. 2018. Automated valve fault detection based on acoustic emission parameters and support vector machine. Alexandria Engeineering Journal 57: 491–498.; Fazai et al., 2019Fazai, R.; Abodayeh, K.; Mansouri, M.; Trabelsi, M.; Nounou, H.; Nounou, M.; Georghiou, G.E. 2019. Machine learning–based statistical testing hypothesis for fault detection in photovoltaic systems. Solar Energy 190: 405–413.; Ghalyani and Mazinan, 2019Ghalyani, P.; Mazinan, A.H. 2019. Performance–based fault detection approach for the dew point process through a fuzzy multi–label support vector machine. Measurement: Journal of the International Measurement Confederation 144: 214–224.; Han et al., 2019Han, H.; Cui, X.; Fan, Y.; Qing, H. 2019. Least squares support vector machine (LS–SVM)–based chiller fault diagnosis using fault indicative features. Applied Thermal Engineering 154: 540–547.; Liu and Zio, 2018Liu, J.; Zio, E. 2018. A scalable fuzzy support vector machine for fault detection in transportation systems. Expert Systems with Applications 102: 36–43.; Manjurul Islam and Kim, 2019Manjurul Islam, M.M.; Kim, J.M. 2019. Reliable multiple combined fault diagnosis of bearings using heterogeneous feature models and multiclass support vector machines. Reliabilty Engineering & System Safety 184: 55–66.; Saari et al., 2019Saari, J.; Strömbergsson, D.; Lundberg, J.; Thomson, A. 2019. Detection and identification of windmill bearing faults using a one–class support vector machine (SVM). Measurement: Journal of the International Measurement Confederation 137: 287–301.; Xi et al., 2019Xi, P.P.; Zhao, Y.P.; Wang, P.X.; Li, Z.Q.; Pan, Y.T.; Song, F.Q. 2019. Least squares support vector machine for class imbalance learning and their applications to fault detection of aircraft engine. Aerospace Science and Technology 84: 56–74.), health and medicine (Battineni et al., 2019Battineni, G.; Chintalapudi, N.; Amenta, F. 2019. Machine learning in medicine: performance calculation of dementia prediction by support vector machines (SVM). Informatics in Medicine Unlocked 16: 100200.; Di et al., 2019Di, Z.; Gong, X.; Shi, J.; Ahmed, H.O.A.; Nandi, A.K. 2019. Internet addiction disorderdetection of Chinese college students using several personality questionnaire data and support vector machine. Addictive Behaviors Reports 10: 100200.; Liu et al., 2019Liu, J.; Xu, H.; Chen, Q.; Zhang, T.; Sheng, W.; Huang, Q.; Song, J.; Huang, D.; Lan, L.; Li, Y.; Chen, W.; Yang, Y. 2019. Prediction of hematoma expansion in spontaneous intracerebral hemorrhage using support vector machine. EBioMedicine 43: 454–459.; Lukmanto et al., 2019Lukmanto, R.B.; Suharjito, Nugroho, A.; Akbar, H. 2019. Early detection of diabetes mellitus using feature selection and fuzzy support vector machine. Procedia Computer Science 157: 46–54.; Vougas et al., 2019Vougas, K.; Sakellaropoulos, T.; Kotsinas, A.; Foukas, G.R.P.; Ntargaras, A.; Koinis, F.; Polyzos, A.; Myrianthopoulos, V.; Zhou, H.; Narang, S.; Georgoulias, V.; Alexopoulos, L.; Aifantis, I.; Townsend, P.A.; Sfikakis, P.; Fitzgerald, R.; Thanos, D.; Bartek, J.; Petty, R.; Tsirigos, A.; Gorgoulis, V.G. 2019. Machine learning and data mining frameworks for predicting drug response in cancer: an overview and a novel in silico screening process based on association rule mining. Pharmacology and Therapeutics 203: 107395.), agriculture (Akbarzadeh et al., 2018Akbarzadeh, S.; Paap, A.; Ahderom, S.; Apopei, B.; Alameh, K. 2018. Plant discrimination by Support Vector Machine classifier based on spectral reflectance. Computers and Electronics in Agriculture 148: 250–258.; Feng et al., 2019Feng, P.; Wang, B.; Liu, D.L.; Yu, Q. 2019. Machine learning–based integration of remotely–sensed drought factors can improve the estimation of agricultural drought in South–Eastern, Australia. Agricultural Systems 173: 303–316. https://doi.org/10.1016/j.agsy.2019.03.015
https://doi.org/10.1016/j.agsy.2019.03.0...
; Fernandes et al., 2019Fernandes, A.M.; Utkin, A.B.; Eiras–Dias, J.; Cunha, J.; Silvestre, J.; Melo–Pinto, P. 2019. Grapevine variety identification using “Big Data” collected with miniaturized spectrometer combined with support vector machines and convolutional neural networks. Computers and Electronics in Agriculture 163: 104855. https://doi.org/10.1016/j.compag.2019.104855
https://doi.org/10.1016/j.compag.2019.10...
; Griffel et al., 2018Griffel, L.M.; Delparte, D.; Edwards, J. 2018. Using support vector machines classification to differentiate spectral signatures of potato plants infected with potato virus Y. Computers and Electronics in Agriculture 153: 318–324. https://doi.org/10.1016/j.compag.2018.08.027
https://doi.org/10.1016/j.compag.2018.08...
; Leena and Saju, 2019Leena, N.; Saju, K.K. 2019. Classification of macronutrient deficiencies in maize plants using optimized multi class support vector machines. Engineering in Agriculture, Environment and Food 12: 126–139. https://doi.org/10.1016/j.eaef.2018.11.002
https://doi.org/10.1016/j.eaef.2018.11.0...
; Radhakrishnan and Ramanathan, 2018Radhakrishnan, S.; Ramanathan, R., 2018. A support vector machine with Gabor features for animal intrusion detection in agriculture fields. Procedia Computer Science 143: 493–501.; Zhou et al., 2019Zhou, Z.; Morel, J.; Parsons, D.; Kucheryavskiy, S.V.; Gustavsson, A.M. 2019. Estimation of yield and quality of legume and grass mixtures using partial least squares and support vector machine analysis of spectral data. Computers and Electronics in Agriculture 162: 246–253.) power and energy systems (Ma et al., 2018Ma, Z.; Ye, C.; Li, H.; Ma, W. 2018. Applying support vector machines to predict building energy consumption in China. Energy Procedia 152: 780–786.; Wang et al., 2018Wang, X.; Luo, D.; Zhao, X.; Sun, Z. 2018. Estimates of energy consumption in China using a self–adaptive multi–verse optimizer–based support vector machine with rolling cross–validation. Energy 152: 539–548.; Zendehboudi et al., 2018Zendehboudi, A.; Baseer, M.A.; Saidur, R. 2018. Application of support vector machine models for forecasting solar and wind energy resources: a review. Journal of Cleaner Production 199: 272-285.), urban wastes and infrastructure (Karimi et al., 2019Karimi, F.; Sultana, S.; Shirzadi Babakan, A.; Suthaharan, S. 2019. An enhanced support vector machine model for urban expansion prediction. Comput. Environment and Urban Systems 75: 61–75.; Solano Meza et al., 2019Solano Meza, J.K.; Orjuela Yepes, D.; Rodrigo–Ilarri, J.; Cassiraga, E. 2019. Predictive analysis of urban waste generation for the city of Bogotá, Colombia, through the implementation of decision trees–based machine learning, support vector machines and artificial neural networks. Heliyon 5: e02810.; Tang et al., 2019Tang, J.; Chen, X.; Hu, Z.; Zong, F.; Han, C.; Li, L. 2019. Traffic flow prediction based on combination of support vector machine and data denoising schemes. Physica A: Statistical Mechanics and its Applications 534: 120642.; Xiao et al., 2019Xiao, R.; Hu, Q.; Li, J. 2019. Leak detection of gas pipelines using acoustic signals based on wavelet transform and Support Vector Machine. Measurement: Journal of the International Measurement Confederation 146: 479–489.; Zhu et al., 2019Zhu, S.; Chen, H.; Wang, M.; Guo, X.; Lei, Y.; Jin, G. 2019. Plastic solid waste identification system based on near infrared spectroscopy in combination with support vector machine. Advanced Industrial and Engineering Polymer Research 2: 77–81.), speech recognition (Bhavan et al., 2019Bhavan, A.; Chauhan, P.; Hitkul, Shah, R.R. 2019. Bagged support vector machines for emotion recognition from speech. Knowledge–Based Systems 184: 104886.; Braga et al., 2019Braga, D.; Madureira, A.M.; Coelho, L.; Ajith, R. 2019. Automatic detection of Parkinson’s disease based on acoustic analysis of speech. Engineering Applications of Artificial Intelligence 77: 148–158. https://doi.org/10.1016/j.engappai.2018.09.018
https://doi.org/10.1016/j.engappai.2018....
; Rahmeni et al., 2019Rahmeni, R.; Aicha, A.B.; Ayed, Y.B. 2019. Speech spoofing countermeasures based on source voice analysis and machine learning techniques. Procedia Computer Science 159: 668–675. https://doi.org/10.1016/j.procs.2019.09.222
https://doi.org/10.1016/j.procs.2019.09....
; Wang et al., 2019Wang, J.; Shan, Y.; Xie, X.; Kuang, J. 2019. Output–based speech quality assessment using autoencoder and support vector regression. Speech Communication 110: 13–20. https://doi.org/10.1016/j.specom.2019.04.002
https://doi.org/10.1016/j.specom.2019.04...
), and many others. In addition, we chose to work with the SVM models in this project due to two main advantages. First, the models are capable of performing kernel trick and project the data into higher dimensions to better classify non–linearly separable data such as ours. Second, because the SVM models are known to perform relatively better on small data sets in comparison to other machine learning algorithms, such as neural networks, which are heavily dependent on the amount of data available for training.

In this study, we employed SVM with the radial basis (RBF) kernel function. The use of kernel functions allows SVM to project the original data into a new dimensional space and find a linear decision boundary to separate the transformed samples when they cannot be linearly separated in the original dimensional space. In addition to the required parameter C, which can be described as the cost imposed by the SVM model on a misclassification, the RBF kernel also requires a γ parameter, namely the value used by the kernel to perform the kernel trick and handle non–linear classification. Both parameters must be chosen carefully, since increasing their value indiscriminately potentially results in overfitting, high variance, and low biases, while very restrictive values lead to an under-fitted model that cannot capture patterns in the data. We determine these values through a grid search on values C = {0.25, 0.5, 1, 1,5, 2, 3} and γ = {3, 2, 1, 0.5, 0.1, 0.01, 0,02, 0.03, 0.05, 0.06} for each SVM model developed. The model with the best performance was selected.

## Linear discriminant analysis (LDA)

The linear discriminant analysis (LDA) is a classification technique to maximize the ratio of between-class variance to within-class variance to achieve maximal separability. The LDA creates a decision boundary called discriminant function (DF), which is a linear combination of the variables that describe the data and that best separates the classes. Considering a problem for classes y1 and y2, the linear DF is defined as Eq. 3 (Duda et al., 2001Duda, R.O.; Hart, P.E.; Stork, D.G. 2001. Pattern Classification, 2ed. Willey–Interscience, Hoboken, NJ, USA.):

$g\left(x\right)={w}^{\prime }V+{w}_{0}$ (3)

where: x is an arbitrary sample, V is the variable set values for sample x, w is the weight vector, and w0 is a bias value. We aimed to find w and w0 values for g(x) > 0, otherwise, the class label associated to x is y1, and y2.

The LDA has been widely used recently in several classification problems and, despite traditional, it is still a well–known and popular method to discriminate food data, largely reported in literature reviews (Abbas et al., 2018Abbas, O.; Zadravec, M.; Baeten, V.; Mikuš, T.; Lešić, T., Vulić, A., Prpić, J., Jemeršić, L., Pleadin, J. 2018. Analytical methods used for the authentication of food of animal origin. Food Chemistry 246: 6-17.; Berrueta et al., 2007Berrueta, L.A.; Alonso–Salces, R.M.; Héberger, K. 2007. Supervised pattern recognition in food analysis. Journal of Chromatography A 1158: 196-214.; Callao and Ruisánchez, 2018Callao, M.P.; Ruisánchez, I. 2018. An overview of multivariate qualitative methods for food fraud detection. Food Control 86: 283-293.; Cavanna et al., 2018Cavanna, D.; Righetti, L.; Elliott, C.; Suman, M. 2018. The scientific challenges in moving from targeted to non–targeted mass spectrometric methods for food fraud analysis: A proposed validation workflow to bring about a harmonized approach. Trends Food Science and Technology 80: 223-241.; Esteki et al., 2019Esteki, M.; Shahsavari, Z.; Simal–Gandara, J. 2019. Food identification by high performance liquid chromatography fingerprinting and mathematical processing. Food Research International 122: 303-317., 2018aEsteki, M.; Shahsavari, Z.; Simal–Gandara, J. 2018a. Use of spectroscopic methods in combination with linear discriminant analysis for authentication of food products. Food Control 91: 100-112., 2018bEsteki, M.; Simal–Gandara, J.; Shahsavari, Z.; Zandbaaf, S.; Dashtaki, E.; Vander Heyden, Y. 2018b. A review on the application of chromatographic methods, coupled to chemometrics, for food authentication. Food Control 93: 165-182.; Granato et al., 2018Granato, D.; Santos, J.S.; Escher, G.B.; Ferreira, B.L.; Maggio, R.M. 2018. Use of principal component analysis (PCA) and hierarchical cluster analysis (HCA) for multivariate association between bioactive compounds and functional properties in foods: A critical perspective. Trends in Food Science and Technology 72: 83-90.; Jiménez–Carvelo et al., 2019Jiménez–Carvelo, A.M.; González–Casado, A.; Bagur–González, M.G.; Cuadros–Rodríguez, L. 2019. Alternative data mining/machine learning methods for the analytical evaluation of food quality and authenticity: a review. Food Research International 122: 25-39.; Kemsley et al., 2019Kemsley, E.K.; Defernez, M.; Marini, F. 2019. Multivariate statistics: considerations and confidences in food authenticity problems. Food Control 105: 102-112.; Medina et al., 2019a, 2019b; Oliveri, 2017Oliveri, P. 2017. Class–modelling in food analytical chemistry: development, sampling, optimisation and validation issues: a tutorial. Analytica Chimica Acta 982: 9-19.; Peris and Escuder–Gilabert, 2016Peris, M.: Escuder–Gilabert, L. 2016. Electronic noses and tongues to assess food authenticity and adulteration. Trends in Food Science and Technology 58: 40-54.; Ropodi et al., 2016Ropodi, A.I.; Panagou, E.Z.; Nychas, G.J.E. 2016. Data mining derived from food analyses using non–invasive/non–destructive analytical techniques; determination of food authenticity, quality & safety in tandem with computer science disciplines. Trends in Food Science and Technology 50: 11-25.; Valdés et al., 2018Valdés, A.; Beltrán, A.; Mellinas, C.; Jiménez, A.; Garrigós, M.C. 2018. Analytical methods combined with multivariate analysis for authentication of animal and vegetable food products with high fat content. Trends in Food Science and Technolology 77: 120-130.; Wadood et al., 2020Wadood, S.A.; Boli, G.; Xiaowen, Z.; Hussain, I.; Yimin, W. 2020. Recent development in the application of analytical techniques for the traceability and authenticity of food of plant origin. Microchemical Journal 152: 104295.). Therefore, we expect this model to perform well in our data set and that its use certify the efficiency of the SVM model by comparing the results obtained by both methods.

## Performance measures

The data available for analysis must be divided into a training set to build the classification model and as a test set to verify the model prediction performance, also called the holdout method.

The default holdout method has two main disadvantages. First, it requires the data set to be divided into two subsets for training and testing the model, respectively. When the available data set is relatively small, similar to that analyzed in this study, dividing the data set can be unfeasible, as the resulting subsets can be too small to effectively train a reliable classification model (Varma and Simon, 2006Varma, S.; Simon, R. 2006. Bias in error estimation when using cross–validation for model selection. BMC Bioinformatics 7: 91.). Moreover, since only a single subset is used for training the model and this subset is commonly generated by random selection, meaningful information possibly contained in data samples assigned to the test set is not considered and is thus wasted. In order to tackle these issues, we used a training and validation method called the k–fold cross validation, a solution to the lack of sufficiently large training and testing sets (Duda et al., 2001Duda, R.O.; Hart, P.E.; Stork, D.G. 2001. Pattern Classification, 2ed. Willey–Interscience, Hoboken, NJ, USA.). This method divides the data set into k mutually exclusive subsets (folds) of similar size. The classification model is trained and tested for k iterations. In each iteration, one subset, different from the subsets previously used, is selected to test the model while the others are used for training. Therefore, all the data samples available for analysis are eventually considered in the construction of the classification model. The final accuracy of the model is computed as the average of the accuracies obtained in each iteration.

After the test phase, the tested samples can be categorized as true positives, true negatives, false positives or false negatives. True positives (TP) and true negatives (TN) are the number of positive and negative samples correctly classified, respectively. False positives (FP) refer to the number of negative samples incorrectly classified as positives and false negative (FN) is the number of positive samples incorrectly classified as negative. Performance measurements of accuracy, sensitivity and specificity (Tan et al., 2005Tan, P.–N.; Steinbach, M.; Kumar, V. 2005. Introduction to data mining. Addison Wesley, Boston, MA, USA.) are computed based on these values. Accuracy refers to the overall probability of the model to correctly classify an arbitrary sample (Choubin et al., 2019a). Sensitivity refers to the overall probability of the model to correctly classify an arbitrary sample, which originally belongs to the positive class. Specificity is the overall probability of the model to correctly classify an arbitrary sample, which originally belongs to the negative class. Therefore, the three performance measurements are computed with Eq. 4–6 :

$\text{Accuracy}\left(%\right)=\frac{TP+TN}{TP+TN+FP+FN}×100$ (4)
$\text{Sensitivity}\left(%\right)=\frac{TP}{TP+FN}×100$ (5)
$\text{Specificity}\left(%\right)=\frac{TN}{FP+TN}×100$ (6)

## Estimating the relevance of the parameters analyzed

One of our objectives was to evaluate the discriminative power of the descriptive variables and try to build classification models capable of discriminating lettuce from two distinct locations with high performance using only variables considered relevant for the decision–making of the classifier. Disregarding variables with low or null influence on the information mapped by the class label could also provide advantages, such as improvement of prediction accuracy, dimensionality reduction, reduction of time to build and run classification models, among others.

Filter methods are variable selection methods applied to the training data prior to the learning phase of the models, allowing irrelevant variables to be identified and discarded before training occurs. Filter methods evaluate variables by computing the intercorrelation between each other and the correlation between the variables and the class label. The best rated variables are present little dependence from other variables while presenting the highest dependence as possible from the class label. Since filter methods are algorithmically simple and operate with low computational cost, a common strategy is to use them to evaluate all the variables individually, to set up subsets with combinations of the best ranked variables, to apply them to a classification model and to check the final prediction accuracy obtained to attest their discriminative power. There are several examples of popular filter methods for the multivariate data analysis, such as information gain, chi–square, random forest importance (Izenman, 2008Izenman, A.J. 2008. Modern Multivariate Statistical Techniques. Springer Science, New York, NY, USA.), mutual information, Correlation–based Feature Selection (CFS), and others (Bommert et al., 2020Bommert, A.; Sun, X.; Bischl, B.; Rahnenführer, J.; Lang, M. 2020. Benchmark for filter methods for feature selection in high–dimensional classification data. Computational Statistics & Data Analysis 143: 106839.).

In this study, we used a variable selection algorithm called F–score. This function presented by Chen and Lin (2006)Chen, Y.–W.; Lin, C.–J. 2006. Combining SVMs with various feature selection strategies, p. 315–324. In: Guyon, I.; Gunn, S.; Nikravesh, M.; Zadeh, L.A. eds. Feature extraction. Springer, Berlin, Germany. measures the discrimination of two sets of real numbers. For a single descriptive variable from our data set, we can divide its measurements into two distinct sets called positive and negative sets, which hold the variable measurements for lettuce samples from SP and PE, respectively. The value produced from this function, when applied to a variable to measure the discrimination between its positive and negative sets, can be used as a score for measuring the variable contribution to the class label. Given the training samples xk, k = {1, ..., m}, if the number of samples belonging to the SP and PE classes are nSP and nPE, respectively, the F-score value of the i–th variable, which reflects the discrimination between positive and negative samples, is calculated by the Eq. 7:

$F\left(i\right)=\frac{{\left({\overline{X}}_{i}^{\left(SP\right)}-{\overline{X}}_{i}\right)}^{2}+{\left({\overline{X}}_{i}^{\left(PE\right)}-{\overline{X}}_{i}\right)}^{2}}{\frac{1}{{n}_{SP}-1}\sum _{k=1}^{{n}_{SP}}{\left({X}_{k,i}^{\left(SP\right)}-{\overline{X}}_{i}^{\left(SP\right)}\right)}^{2}+\frac{1}{{n}_{PE}-1}\sum _{k=1}^{{n}_{PB}}{\left({X}_{k,i}^{\left(PE\right)}-{\overline{X}}_{i}^{\left(PE\right)}\right)}^{2}}$ (7)

where: ${\overline{X}}_{i}$, ${\overline{X}}_{i}^{⟨SP\right)}$, ${\overline{X}}_{i}^{\left(PE\right)}$ are the average of the i–th variable of the whole, positive, and negative data sets, respectively; ${\overline{X}}_{k,i}^{\left(SP\right)}$ is the i–th variable of the k–th positive sample, and ${\overline{X}}_{k,i}^{\left(PE\right)}$ is the i–th variable of the k–th negative sample. The numerator indicates the discrimination between the positive and negative sets, and the denominator indicates the discrimination within each set. The larger the F–score, the more discriminative this variable.

## Balancing the data set with the K–means clustering algorithm

Imbalanced data sets are inconvenient and present various challenges for data mining and the multivariate data analysis (Chawla, 2005Chawla, N.V. 2005. Data mining for imbalanced datasets: an overview. p. 853–867. In: Maimon O.; Rokach L., eds. Data mining and knowledge discovery handbook. Springer, New York, NY, USA.; Haixiang et al., 2017Haixiang, G.; Yijing, L.; Shang, J.; Mingyun, G.; Yuanyue, H.; Bing, G. 2017. Learning from class–imbalanced data: review of methods and applications. Expert Systems with Applications 73: 220–239. https://doi.org/10.1016/j.eswa.2016.12.035
https://doi.org/10.1016/j.eswa.2016.12.0...
; He and Garcia, 2009He, H.; Garcia, E.A. 2009. Learning from Imbalanced data. IEEE Transactions on Knowledge and Data Engineerng 21: 1263–1284. https://doi.org/10.1109/TKDE.2008.239
https://doi.org/10.1109/TKDE.2008.239...
; Jo and Japkowicz, 2004Jo, T.; Japkowicz, N. 2004. Class imbalances versus small disjuncts. ACM SIGKDD Exploration Newsletters 6: 40. https://doi.org/10.1145/1007730.1007737
https://doi.org/10.1145/1007730.1007737...
; López et al., 2013López, V.; Fernández, A.; García, S.; Palade, V.; Herrera, F. 2013. An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Information Sciences 250: 113–141. https://doi.org/10.1016/j.ins.2013.07.007
https://doi.org/10.1016/j.ins.2013.07.00...
; Prati et al., 2004Prati, R.C.; Batista, G.E.A.P.A.; Monard, M.C. 2004. Class imbalances versus class overlapping: an analysis of a learning system behavior. p. 312–321. In: Monroy R.; Arroyo–Figueroa, G.; Sucar, L.E.; Sossa, H., eds. MICAI 2004: advances in artificial intelligence. Springer, Berlin, Germany.). Overall, classification models trained on imbalanced data tend to express a good prediction performance for samples of the majority class and a lower performance for samples of the minority class. This decrease occurs not necessarily due to the difference in the class proportion, but due to other natural factors of imbalanced data, such as the presence of small disjuncts, low density of data, data overlapping and others (He and Garcia, 2009He, H.; Garcia, E.A. 2009. Learning from Imbalanced data. IEEE Transactions on Knowledge and Data Engineerng 21: 1263–1284. https://doi.org/10.1109/TKDE.2008.239
https://doi.org/10.1109/TKDE.2008.239...
; López et al., 2013López, V.; Fernández, A.; García, S.; Palade, V.; Herrera, F. 2013. An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Information Sciences 250: 113–141. https://doi.org/10.1016/j.ins.2013.07.007
https://doi.org/10.1016/j.ins.2013.07.00...
). In this study, we tackled the imbalanced data issue with the aid of a clustering algorithm called K–means.

Clustering algorithms are considered a branch of unsupervised learning and are basically employed in exploratory data analyses, where no hypothesis about the data nor previously known class labels existed. These techniques are useful to aid the identification of natural groupings existing within the data based on a similarity (or dissimilarity) pattern. Partitional clustering algorithms, such as K–means, divide the data set into mutually exclusive clusters in a way that samples assigned to a same cluster must be as similar as possible and as different as possible from samples associated to other clusters.

The K–means algorithm could be summarized in the following steps (Jain, 2010Jain, A.K. 2010. Data clustering: 50 years beyond K–means, pattern recognition letters. Pattern Recognition Letters 31: 651-666. https://doi.org/10.1016/j.patrec.2009.09.011
https://doi.org/10.1016/j.patrec.2009.09...
): (i) randomly selects k data samples and names their centroids. Each centroid is associated to a different cluster label; (ii) for each non–centroid sample in the data set, it find its nearest centroid and associates this sample to the same cluster as the centroid found; (iii) for each cluster formed, it updates the centroid to be the center of cluster mass; and (iv) repeats the previous steps until no new changes are made to the clusters, or a stopping criterion is reached.

The K–means algorithm is not new and is still highly reported in the literature due to its simplicity, low computational cost, and good performance (Jain, 2010Jain, A.K. 2010. Data clustering: 50 years beyond K–means, pattern recognition letters. Pattern Recognition Letters 31: 651-666. https://doi.org/10.1016/j.patrec.2009.09.011
https://doi.org/10.1016/j.patrec.2009.09...
). In this study, we used the K–means algorithm to aid data balancing due to under sampling. Considering that we want to discard m samples of a certain class from the data set, we divide the data labeled as this class into (n – m) clusters with the K–means algorithm and keep only the determined centroids as data samples. Because the centroids found for each cluster could be considered the most representative samples in a data partition, this strategy reduces the information loss that naturally occurs under sampling.

## Analysis strategy

The entire statistical and predictive analysis was conducted on the RStudio software, version 1.1.463. Our analysis methodology is presented in Figure 2 and summarized in the following steps:

Figure 2
– Methodology for construction of the SVM (support vector machines) and LDA (linear discriminant analysis) models and performance measure estimation.

1. Data samples obtained from Pernambuco (PE) state are under sampled in order to match the number of available samples from São Paulo (SP) state. The goal of this step is to create a balanced data set that could be reliably used to develop classification models without biases. The K–means clustering algorithm is applied only to the samples obtained from PE and 36 clusters were determined. The centroids computed for each cluster were retained in the data set, while the other samples from PE were discarded from analysis. Therefore, the final data set comprised all 36 originally samples collected in SP and 36 samples from PE retained as centroids from the clustering algorithm.

2. In order to perform five–fold cross validation, the balanced data set is randomly divided into five mutually exclusive subsets (folds), properly keeping the original proportion of the two states (50 % – 50 %) in each set.

3. For each validation:
1. The selected validation is used as a test set while the remaining folds are merged and used as a training set;

2. The training and test sets are standardized to avoid potential biases caused by the different unit measurements and ranges of values of the variables. The variables are centered by subtracting their means from theirs values, and then the centered variables are divided by their standard deviations;

3. F–score values are computed for each variable of the training set. The selection threshold is set as the maximum F–score value obtained by the variables divided by 3;

4. The SVM and LDA models are developed using the entire training data and the training data with only the variables that received F–score values higher than the threshold, resulting in a total of four models developed;

5. Accuracy, sensitivity, and specificity values are computed for the four models.

4. The average accuracy, sensitivity, and specificity obtained by the models are determined and presented as final performance measurements.

# Results and Discussion

## Properties and micronutrients in lettuce and soil samples

Metal uptake by plants is influenced by several soil properties (Kumpiene et al., 2017Kumpiene, J.; Giagnoni, L.; Marschner, B.; Denys, S.; Mench, M.; Adriaensen, K.; Vangronsveld, J.; Puschenreiter, M.; Renella, G. 2017. Assessment of methods for determining bioavailability of trace elements in soils: a review. Pedosphere 27: 389–406.). Therefore, we evaluated 25 soil variables (Table 2). We designated letters to represent the variables analyzed in lettuce and soil samples to simplify visualization in our graphics and specific mentions throughout the rest of the paper. Soil samples collected from lettuce farms in SP had fairly higher amount of nutrients and other beneficial traits than soil samples obtained from PE.

Table 2
– Analyzed variables in the determination of the geographical origin of lettuce samples and their respective mean and standard deviation values for each state, São Paulo (SP) and Pernambuco (PE).

Soil samples from SP farms presented mean values for pseudo-total concentrations of Ni, Cu and Zn of 9.45, 41.34 and 72.81 mg kg1, respectively, while samples from PE presented 2.95, 14.43 and 38.43 mg kg1, respectively. Ni, Cu, and Zi are essential metals for plants. Biondi et al. (2011)Biondi, C.M.; Nascimento, C.W.A.; Fabrício Neta, A.B.; Ribeiro, M.R. 2011. Concentrations of Fe, Mn, Zn, Cu, Ni and Co in benchmark soils of Pernambuco, Brazil. Revista Brasileira de Ciência do Solo 35: 1057–1066. demonstrated that soils from PE have low capacity to release Cu and Ni to plants. Their study also indicated a significant association of most metals to clayey soils. Considering that the soil samples from PE are mostly composed of sand (approximately 70 %), the low clay content of these soils may help explain the relatively low metal concentration in the pseudototal fraction of soils from PE.

Amorphous and crystalline Al and Fe oxide minerals play a major role in stabilizing soil structure, and their presence in soils has a favorable effect on soil physical properties (Goldberg, 1989Goldberg, S. 1989. Interaction of aluminum and iron oxides and clay minerals and their effect on soil physical properties: a review. Communications in Soil Science and Plant Analysis 20: 1181–1207.). Furthermore, kaolinite, Fe and Al oxides compose the dominant mineralogy in the clay fraction of most Brazilian soils (Fink et al., 2014Fink, J.R.; Inda, A.V.; Bayer, C.; Torrent, J.; Barrón, V. 2014. Mineralogy and phosphorus adsorption in soils of south and central–west Brazil under conventional and no–tillage systems. Acta Scientiarum. Agronomy 36: 379–387.), responsible for chemical reactions that control the availability of essential and non–essential elements.

Phytoavailable metal forms are sorbed to amorphous metal oxides (Rodrigues et al., 2010Rodrigues, S.M.; Henriques, B.; Silva, E.F.; Pereira, M.E.; Duarte, A.C.; Römkens, P.F.A.M. 2010. Evaluation of an approach for the characterization of reactive and available pools of twenty potentially toxic elements in soils. Part I. The role of key soil properties in the variation of contaminants’ reactivity. Chemosphere 81: 1549–1559.). Levels of well–crystallized Fe and Al were higher in soil samples from SP than for those from PE, presenting mean values of 22.13 g kg1 and 10.77 g kg1 respectively, against 7.94 g kg1 and 5.04 g kg1 respectively for soils from PE. Soil samples from SP also showed fairly higher numbers of amorphous Al than soil samples from PE, with mean values of 14.66 mg kg1and 1.21 mg kg1 for soils of both states, respectively. As for amorphous Fe, mean values were 4.82 mg kg1and 1.28 mg kg1for soils from SP and PE, respectively.

Mean levels of available P in soil samples from SP and PE states were 530.82 mg kg1and 311.67 mg kg1, respectively. Although samples from PE presented higher levels of exchangeable Ca and Mg, the soil samples from SP state showed higher CEC (for both CECT and CECe), which depends on the levels of Ca, Mg, K, Al and potential acidity in the soil samples. Mean values of CECT were 104 mmolc dm3and 29.17 mmolc dm3for soils from SP and PE states, respectively, while mean values of CECe were 80.67 mmolc dm3and 17.68 mmolc dm3for soils from SP and PE states, respectively. Finally, values for the sum of bases were also considerably higher in soils from SP (mean 79.53 mmolc dm3) than in soils from PE (mean 17.07 mmolc dm3). Maybe soils in SP farms are better fertilized than in PE.

## Statistical and predictive analysis

Using the standardized measurements of all variables shown in Table 2 as input values, the SVM models reached an average value of 98.67 % for accuracy, 97.14 % for sensitivity, and 100 % for specificity. The LDA models trained with the same input values performed fairly lower than SVM for all performance measurements, presenting 66 % average accuracy, 71.43 % average sensitivity, and 60.71 % average specificity. Although more complex to build than linear discriminant models and designed to handle large and complex data bases, SVM models are excellent tools to determine the geographical origin of lettuce, even when trained on a relatively small amount of data.

In order to determine the individual importance of each component for the discrimination of the lettuce samples from both regions, we applied the F–score equation to each training set during the cross–validation process. The F–score values achieved by each variable in each iteration are presented in descending order in Figure 3. The variables referring to the sum of bases obtained by (Ca2 + Mg2 + K+) and soil cation exchangeable capability (CECT and CECe) were retained in all training sets with very high F–score values. Levels of exchangeable Ca, well–crystallized Al, amorphous Al, sand and pseudo-total concentration of Ni measured from the soil plus the Zn levels in the plant were retained by four of five considered training sets. Overall, we conclude that these eight factors were the most relevant variables for the discrimination of lettuce samples from both states according to the F–score metric.

Figure 3
– Relative importance of each variable to determine the lettuce geographical origin, computed according to the F–score equation.

To ascertain the real relevance of the best rated components, we also built SVM and LDA models using only values for variables that achieved F–score values higher than the determined threshold (Table 3), while the others were discarded. The average performance measurements, namely accuracy, sensitivity and specificity, achieved by the models with and without variable selection are summarized in Table 4. The SVM model trained with only the best rated variables achieved 95.81 % average accuracy, 94.29 % average sensitivity and 97.14 % average specificity, a very small decrease in performance in comparison to the values achieved when all 28 variables were used for training. On the other hand, the LDA model experienced a slight decrease in performance, presenting 86.29 % average accuracy, 94.29 % average sensitivity, and 78.57 % average specificity when only the five best rated variables were used for training. Although the SVM and LDA models achieved the same average sensitivity values when combined with variable selection, the SVM models still clearly outperformed the LDA models in both scenarios for all other performance measures.

Table 3
– Variables retained by the F–score in the training set in each iteration of the cross–validation process. Variables discarded achieved F–score value below the computed threshold max/3.

Table 4
– Averaged performance measures computed for the SVM (support vector machines) and LDA (linear discriminant analysis) models trained with the whole variable set and with only the best rated variables according to the F–score.

The best classification model achieved was the SVM model trained on all variables available from the data set. The accuracy value achieved is approximately 3 %, 32 % and 12 % higher than the accuracy values obtained from the SVM model with feature selection, the LDA model without feature selection and the LDA model with feature selection, respectively. This slight increase in error for the SVM model is expected since several variables were discarded, the model was possibly deprived from meaningful information contained in them; however, the SVM model with variable selection still presented a high average accuracy value for predicting the geographical origin of lettuce when only approximately eight out of 28 variables were used. This is a substantial decrease in the dimensionality and size of the data set, and consequently reduction of the required effort from researchers to gather and prepare the necessary data.

Mean values of the sum of bases, CECT, CECE, exchangeable Ca, well–crystallized Al, sand, amorphous Al, nickel in soil and Zn in plant for the lettuce samples produced in SP and PE are shown in Figure 4. Samples collected in SP presented relatively higher values for almost all of these components than the samples obtained from PE. França et al. (2017)França, F.C.S.S.; Albuuerque, A.M.A.; Almeida, A.C.; Silveira, P.B.; Silva Filho, C.A.; Hazin, C.A.; Honorato, E.V. 2017. Heavy metals deposited in the culture of lettuce (Lactuca sativa L.) by the influence of vehicular traffic in Pernambuco. Brazilian Food Chemistry 215: 171–176. studied lettuce production in PE, and although the Zn content in their soil samples was higher than those observed by Santos–Araujo and Alleoni (2016)Santos–Araujo, S.N.; Alleoni, L.R.F. 2016. Concentrations of potentially toxic elements in soils and vegetables from the macroregion of São Paulo, Brazil: availability for plant uptake. Environmental Monitoring and Assessment 188: 1–17., the Zn content in the plant was much lower. Because different varieties of lettuce present different Zn uptakes even when cultivated under the same soils conditions (França et al., 2017França, F.C.S.S.; Albuuerque, A.M.A.; Almeida, A.C.; Silveira, P.B.; Silva Filho, C.A.; Hazin, C.A.; Honorato, E.V. 2017. Heavy metals deposited in the culture of lettuce (Lactuca sativa L.) by the influence of vehicular traffic in Pernambuco. Brazilian Food Chemistry 215: 171–176.), lettuce varieties grown in SP may differ from varieties cultivated in PE, resulting in different levels of soil–plant transference.

Figure 4
– Mean values of the sum of bases, CECT, CECe, exchangeable calcium in soil, well–crystallized aluminum in soil, sand, amorphous aluminum in soil, nickel in soil and zinc in plant for the lettuce samples produced in São Paulo (SP) and Pernambuco (PE) state.

The strong effect of soil variables on the plant classification could be explained by relevance of soil properties in plant uptake. A previous study carried out by Santos–Araujo and Alleoni (2016)Santos–Araujo, S.N.; Alleoni, L.R.F. 2016. Concentrations of potentially toxic elements in soils and vegetables from the macroregion of São Paulo, Brazil: availability for plant uptake. Environmental Monitoring and Assessment 188: 1–17. showed that the most important covariates for predicting the Zn content in vegetables sampled in SP were CECe, pH, organic carbon, and the pseudo-total content of Zn and Cu. As production is a result of cultivated area multiplied by yield, it is possible to use soil productivity to infer the incorporation of agricultural technology (Camargo Filho and Camargo, 2017). Therefore, the inclusion of soil parameters in the model for plant classification complements the assortment and may give insights into the geographical origin of lettuce.

# Conclusion

The Sustainable Capitol Hill (SCH) and Michigan State University list several reasons for customers to buy and consume locally produced food (Klavinski, 2013Klavinski, R. 2013. 7 benefits of eating local foods. Available at: https://www.canr.msu.edu/news/7_benefits_of_eating_local_foods [Accessed Nov 4, 2019]
https://www.canr.msu.edu/news/7_benefits...
; SCH, 2019). Because local food involves a shorter time and less transportation effort from harvest to costumer table, it is likely to be safer to consume, fresher, less contaminated, more flavorful, and higher in nutritional value. It is also easier for customers to monitor the food origin and investigate practices and substances used to grow and harvest the crops. Purchasing local food also benefits the local economy as the money is retained within the community and reinvested in local businesses and services, also supporting local farmers, considerable importance in economic and food supply crises.

Verifying the geographic origin of food is a substantial matter to ascertain that this important kind of food was produced by a trusted source that takes quality and safety into account. In this study, we proposed a novel methodology to determine the geographical origin of Brazilian lettuce based on their elemental composition and soil properties through the use of SVM, LDA, and feature selection. We analyzed the contents of several chemical variables and soil properties determined for 72 lettuce samples obtained from São Paulo and Pernambuco Sates in Brazil. Through the use of a filter method for feature selection, we estimated that soil cation exchangeable capacity, exchangeable Ca, well–crystallized Al, sand, amorphous Al and Ni in soil, Zn levels in the plant and the sum of bases obtained by (Ca2 + Mg2 + K+) were generally the most important variables for differentiating lettuce samples produced in both regions. We developed classification models based on SVM, which were capable of discriminating lettuce samples from both regions with a high accuracy level, presenting approximately 98.67 % correct predictions when all 28 chemical variables were used for training, and 95.81 % correct predictions when only the most important variables were used for training. These values surpass those obtained by the LDA model, a well–known, reliable and widely employed model for classification of food samples, which scored 66 % and 86.29 % prediction accuracy when all variables and only the best rated variables were used for training, respectively. The values achieved proved that, when combined with the chemical composition of lettuce samples determined by ICP OES and certain soil properties, classification models based on SVM could successfully determine the geographical origin of lettuce samples with excellent accuracy, at the same time attesting that data mining techniques could powerfully support traceability strategies and ensure vegetable authenticity. Our previous literature search reveals that this is the first attempt to discriminate the geographical origin of Brazilian lettuce samples based on a powerful machine learning technique for data mining, such as SVM, also applied to chemical composition and soil parameters.

# Acknowledgments

The authors would like to thank the São Paulo Research Foundation (FAPESP), Processes number 12/03682–2, 15/19332–9 and 15/25416–0; the National Council for Scientific and Technological Development (CNPq); and the Coordination for the Improvement of Higher Level Personnel (CAPES) for their financial support.

# References

• Abbas, O.; Zadravec, M.; Baeten, V.; Mikuš, T.; Lešić, T., Vulić, A., Prpić, J., Jemeršić, L., Pleadin, J. 2018. Analytical methods used for the authentication of food of animal origin. Food Chemistry 246: 6-17.
• Akbarzadeh, S.; Paap, A.; Ahderom, S.; Apopei, B.; Alameh, K. 2018. Plant discrimination by Support Vector Machine classifier based on spectral reflectance. Computers and Electronics in Agriculture 148: 250–258.
• Alcázar, Á.; Jurado, J.M.; Palacios–Morillo, A.; Pablos, F.; Martín, M.J. 2012. Recognition of the geographical origin of beer based on support vector machines applied to chemical descriptors. Food Control 23: 258–262.
• Ali, S.M.; Hui, K.H.; Hee, L.M.; Leong, M.S. 2018. Automated valve fault detection based on acoustic emission parameters and support vector machine. Alexandria Engeineering Journal 57: 491–498.
• Anderson, J.M.; Ingram, J.S.I. 1992. Tropical Soil Biology and Fertility: A Handbook of Methods. CAB International, Wallingford, UK.
• Araújo, C.L.; Nogueira, A.R.A.; Nobrega, J.A. 2002. Effect of acid concentration on closed–vessel microwave–assisted digestion of plant materials. Spectrochimica Acta Part B: Atomic Spectroscopy 57: 2121–2132.
• Baroni, M.V.; Podio, N.S.; Badini, R.G;, Inga, M.; Ostera, H.A.; Cagnoni, M.; Gautier, E.A.; García, P.P.; Hoogewerff, J.; Wunderlin, D.A. 2015. Linking soil, water, and honey composition to assess the geographical origin of Argentinean honey by multielemental and isotopic analyses. Journal of Agricultural and Food Chemistry 63: 4638–4645.
• Battineni, G.; Chintalapudi, N.; Amenta, F. 2019. Machine learning in medicine: performance calculation of dementia prediction by support vector machines (SVM). Informatics in Medicine Unlocked 16: 100200.
• Berrueta, L.A.; Alonso–Salces, R.M.; Héberger, K. 2007. Supervised pattern recognition in food analysis. Journal of Chromatography A 1158: 196-214.
• Bhavan, A.; Chauhan, P.; Hitkul, Shah, R.R. 2019. Bagged support vector machines for emotion recognition from speech. Knowledge–Based Systems 184: 104886.
• Biondi, C.M.; Nascimento, C.W.A.; Fabrício Neta, A.B.; Ribeiro, M.R. 2011. Concentrations of Fe, Mn, Zn, Cu, Ni and Co in benchmark soils of Pernambuco, Brazil. Revista Brasileira de Ciência do Solo 35: 1057–1066.
• Bommert, A.; Sun, X.; Bischl, B.; Rahnenführer, J.; Lang, M. 2020. Benchmark for filter methods for feature selection in high–dimensional classification data. Computational Statistics & Data Analysis 143: 106839.
• Braga, D.; Madureira, A.M.; Coelho, L.; Ajith, R. 2019. Automatic detection of Parkinson’s disease based on acoustic analysis of speech. Engineering Applications of Artificial Intelligence 77: 148–158. https://doi.org/10.1016/j.engappai.2018.09.018
» https://doi.org/10.1016/j.engappai.2018.09.018
• Callao, M.P.; Ruisánchez, I. 2018. An overview of multivariate qualitative methods for food fraud detection. Food Control 86: 283-293.
• Camargo Filho, W.P.; Camargo, F.P. 2017. A quick review of the production and commercialization of the main vegetables in Brazil and the world from 1970 to 2015. Horticultura Brasileira 35: 160–166.
• Cambrai, A.; Marcic, C.; Morville, S.; Sae Houer, P.; Bindler, F.; Marchioni, E. 2010. Differentiation of chocolates according to the cocoa’s geographical origin using chemometrics. Journal of Agricultural and Food Chemistry 58: 1478–1483.
• Carvalho, K.L.; Costa, R.P.; Souza, R.C. 2014. Strategic management of relationships in lettuce supply chain. Production 24: 271–282.
• Cavanna, D.; Righetti, L.; Elliott, C.; Suman, M. 2018. The scientific challenges in moving from targeted to non–targeted mass spectrometric methods for food fraud analysis: A proposed validation workflow to bring about a harmonized approach. Trends Food Science and Technology 80: 223-241.
• Ceballos–Magaña, S.G.; Jurado, J.M.; Muñiz–Valencia, R.; Alcázar, A.; Pablos, F.; Martín, M.J. 2012. Geographical authentication of tequila according to its mineral content by means of support vector machines. Food Analytical Methods 5: 260–265.
• Chawla, N.V. 2005. Data mining for imbalanced datasets: an overview. p. 853–867. In: Maimon O.; Rokach L., eds. Data mining and knowledge discovery handbook. Springer, New York, NY, USA.
• Chen, Y.–W.; Lin, C.–J. 2006. Combining SVMs with various feature selection strategies, p. 315–324. In: Guyon, I.; Gunn, S.; Nikravesh, M.; Zadeh, L.A. eds. Feature extraction. Springer, Berlin, Germany.
• Choubin, B.; Borji, M.; Mosavi, A.; Sajedi–Hosseini, F.; Singh, V.P.; Shamshirband, S. 2019a. Snow avalanche hazard prediction using machine learning methods. Journal of Hydrolofy 577: 123929. https://doi.org/10.1016/j.jhydrol.2019.123929
» https://doi.org/10.1016/j.jhydrol.2019.123929
• Choubin, B.; Darabi, H.; Rahmati, O.; Sajedi–Hosseini, F.; Kløve, B. 2018. River suspended sediment modelling using the CART model: a comparative study of machine learning techniques. Science of the Total Environment 615: 272–281.
• Choubin, B.; Moradi, E.; Golshan, M.; Adamowski, J.; Sajedi–Hosseini, F.; Mosavi, A. 2019b. An ensemble prediction of flood susceptibility using multivariate discriminant analysis, classification and regression trees, and support vector machines. Science of the Total Environment 651: 2087–2096.
• Coetzee, P.P.; Steffens, F.E.; Eiselen, R.J.; Augustyn, O.P.; Balcaen, L.; Vanhaecke, F. 2005. Multi–element analysis of South African wines by icp−ms and their classification according to geographical origin. Journal of Agricultural and Food Chemistry 53: 5060–5066.
• Cortes, C.; Vapnik, V. 1995. Support–vector networks. Machine Learning 20: 273–297.
• Di, Z.; Gong, X.; Shi, J.; Ahmed, H.O.A.; Nandi, A.K. 2019. Internet addiction disorderdetection of Chinese college students using several personality questionnaire data and support vector machine. Addictive Behaviors Reports 10: 100200.
• Duda, R.O.; Hart, P.E.; Stork, D.G. 2001. Pattern Classification, 2ed. Willey–Interscience, Hoboken, NJ, USA.
• Esteki, M.; Shahsavari, Z.; Simal–Gandara, J. 2019. Food identification by high performance liquid chromatography fingerprinting and mathematical processing. Food Research International 122: 303-317.
• Esteki, M.; Shahsavari, Z.; Simal–Gandara, J. 2018a. Use of spectroscopic methods in combination with linear discriminant analysis for authentication of food products. Food Control 91: 100-112.
• Esteki, M.; Simal–Gandara, J.; Shahsavari, Z.; Zandbaaf, S.; Dashtaki, E.; Vander Heyden, Y. 2018b. A review on the application of chromatographic methods, coupled to chemometrics, for food authentication. Food Control 93: 165-182.
• Fan, J.; Wang, X.; Wu, L.; Zhou, H.; Zhang, F.; Yu, X.; Lu, X.; Xiang, Y. 2018. Comparison of Support vector machine and extreme gradient boosting for predicting daily global solar radiation using temperature and precipitation in humid subtropical climates: a case study in China. Energy Conservation and Managment 164: 102–111. https://doi.org/10.1016/j.enconman.2018.02.087
» https://doi.org/10.1016/j.enconman.2018.02.087
• Fazai, R.; Abodayeh, K.; Mansouri, M.; Trabelsi, M.; Nounou, H.; Nounou, M.; Georghiou, G.E. 2019. Machine learning–based statistical testing hypothesis for fault detection in photovoltaic systems. Solar Energy 190: 405–413.
• Feng, P.; Wang, B.; Liu, D.L.; Yu, Q. 2019. Machine learning–based integration of remotely–sensed drought factors can improve the estimation of agricultural drought in South–Eastern, Australia. Agricultural Systems 173: 303–316. https://doi.org/10.1016/j.agsy.2019.03.015
» https://doi.org/10.1016/j.agsy.2019.03.015
• Fernandes, A.M.; Utkin, A.B.; Eiras–Dias, J.; Cunha, J.; Silvestre, J.; Melo–Pinto, P. 2019. Grapevine variety identification using “Big Data” collected with miniaturized spectrometer combined with support vector machines and convolutional neural networks. Computers and Electronics in Agriculture 163: 104855. https://doi.org/10.1016/j.compag.2019.104855
» https://doi.org/10.1016/j.compag.2019.104855
• Fink, J.R.; Inda, A.V.; Bayer, C.; Torrent, J.; Barrón, V. 2014. Mineralogy and phosphorus adsorption in soils of south and central–west Brazil under conventional and no–tillage systems. Acta Scientiarum. Agronomy 36: 379–387.
• França, F.C.S.S.; Albuuerque, A.M.A.; Almeida, A.C.; Silveira, P.B.; Silva Filho, C.A.; Hazin, C.A.; Honorato, E.V. 2017. Heavy metals deposited in the culture of lettuce (Lactuca sativa L.) by the influence of vehicular traffic in Pernambuco. Brazilian Food Chemistry 215: 171–176.
• García–Nieto, P.J.; García–Gonzalo, E.; Fernández, J.R.A.; Muñiz, C.D. 2019. Modeling of the algal atypical increase in La Barca reservoir using the DE optimized least square support vector machine approach with feature selection. Mathematics and Computers in Simulation 166: 461–480.
• Gee, G.W.; Or, D. 2002. Particle–size analysis. p. 241–254. In: Dane, J.H.; Topp, G.C., eds. Methods of soil analysis. Part 4. Physical methods. Soil Science Society of America, Madison, WI, USA.
• Ghalyani, P.; Mazinan, A.H. 2019. Performance–based fault detection approach for the dew point process through a fuzzy multi–label support vector machine. Measurement: Journal of the International Measurement Confederation 144: 214–224.
• Goldberg, S. 1989. Interaction of aluminum and iron oxides and clay minerals and their effect on soil physical properties: a review. Communications in Soil Science and Plant Analysis 20: 1181–1207.
• Granato, D.; Santos, J.S.; Escher, G.B.; Ferreira, B.L.; Maggio, R.M. 2018. Use of principal component analysis (PCA) and hierarchical cluster analysis (HCA) for multivariate association between bioactive compounds and functional properties in foods: A critical perspective. Trends in Food Science and Technology 72: 83-90.
• Griffel, L.M.; Delparte, D.; Edwards, J. 2018. Using support vector machines classification to differentiate spectral signatures of potato plants infected with potato virus Y. Computers and Electronics in Agriculture 153: 318–324. https://doi.org/10.1016/j.compag.2018.08.027
» https://doi.org/10.1016/j.compag.2018.08.027
• Haixiang, G.; Yijing, L.; Shang, J.; Mingyun, G.; Yuanyue, H.; Bing, G. 2017. Learning from class–imbalanced data: review of methods and applications. Expert Systems with Applications 73: 220–239. https://doi.org/10.1016/j.eswa.2016.12.035
» https://doi.org/10.1016/j.eswa.2016.12.035
• Han, H.; Cui, X.; Fan, Y.; Qing, H. 2019. Least squares support vector machine (LS–SVM)–based chiller fault diagnosis using fault indicative features. Applied Thermal Engineering 154: 540–547.
• He, H.; Garcia, E.A. 2009. Learning from Imbalanced data. IEEE Transactions on Knowledge and Data Engineerng 21: 1263–1284. https://doi.org/10.1109/TKDE.2008.239
» https://doi.org/10.1109/TKDE.2008.239
• Huang, G.; Qiu, W.; Zhang, J. 2017. Modelling seismic fragility of a rock mountain tunnel based on support vector machine. Soil Dynamics and Earthquake Engineering 102: 160–171.
• Inda Junior, A.V.; Kämpf, N. 2003. Evaluation of pedogenic iron oxide extraction procedures with sodium dithionite–citrate–bicarbonate. Revista Brasileira de Ciência do Solo 27: 1139–1147.
• Izenman, A.J. 2008. Modern Multivariate Statistical Techniques. Springer Science, New York, NY, USA.
• Jain, A.K. 2010. Data clustering: 50 years beyond K–means, pattern recognition letters. Pattern Recognition Letters 31: 651-666. https://doi.org/10.1016/j.patrec.2009.09.011
» https://doi.org/10.1016/j.patrec.2009.09.011
• Jiménez–Carvelo, A.M.; González–Casado, A.; Bagur–González, M.G.; Cuadros–Rodríguez, L. 2019. Alternative data mining/machine learning methods for the analytical evaluation of food quality and authenticity: a review. Food Research International 122: 25-39.
• Jo, T.; Japkowicz, N. 2004. Class imbalances versus small disjuncts. ACM SIGKDD Exploration Newsletters 6: 40. https://doi.org/10.1145/1007730.1007737
» https://doi.org/10.1145/1007730.1007737
• Jung, H.; Jo, H.; Kim, S.; Lee, K.; Choe, J. 2018. Geological model sampling using PCA–assisted support vector machine for reliable channel reservoir characterization. Journal of Petroleum Science and Engineering 167: 396–405.
• Karimi, F.; Sultana, S.; Shirzadi Babakan, A.; Suthaharan, S. 2019. An enhanced support vector machine model for urban expansion prediction. Comput. Environment and Urban Systems 75: 61–75.
• Kemsley, E.K.; Defernez, M.; Marini, F. 2019. Multivariate statistics: considerations and confidences in food authenticity problems. Food Control 105: 102-112.
• Kim, M.J.; Moon, Y.; Tou, J.C.; Mou, B.; Waterland, N.L. 2016. Nutritional value, bioactive compounds and health benefits of lettuce (Lactuca sativa L.). Journal of Food Composition and Analysis 49: 19–34.
• Kisi, O.; Choubin, B.; Deo, R.C.; Yaseen, Z.M. 2019. Incorporating synoptic–scale climate signals for streamflow modelling over the Mediterranean region using machine learning models. Hydrological Sciences Journal 64: 1240–1252.
• Klavinski, R. 2013. 7 benefits of eating local foods. Available at: https://www.canr.msu.edu/news/7_benefits_of_eating_local_foods [Accessed Nov 4, 2019]
» https://www.canr.msu.edu/news/7_benefits_of_eating_local_foods
• Kotsiantis, S.B.; Zaharakis, I.D.; Pintelas, P.E. 2006. Machine learning: a review of classification and combining techniques. Artificial Intelligence Review 26: 159–190.
• Kumar, D.; Thakur, M.; Dubey, C.S.; Shukla, D.P. 2017. Landslide susceptibility mapping and prediction using support vector machine for Mandakini River Basin, Garhwal Himalaya, India. Geomorphology 295: 115–125.
• Kumpiene, J.; Giagnoni, L.; Marschner, B.; Denys, S.; Mench, M.; Adriaensen, K.; Vangronsveld, J.; Puschenreiter, M.; Renella, G. 2017. Assessment of methods for determining bioavailability of trace elements in soils: a review. Pedosphere 27: 389–406.
• Kundu, S.; Khare, D.; Mondal, A. 2017. Future changes in rainfall, temperature and reference evapotranspiration in the central India by least square support vector machine. Geoscience Frontiers 8: 583–596. https://doi.org/10.1016/j.gsf.2016.06.002
» https://doi.org/10.1016/j.gsf.2016.06.002
• Leena, N.; Saju, K.K. 2019. Classification of macronutrient deficiencies in maize plants using optimized multi class support vector machines. Engineering in Agriculture, Environment and Food 12: 126–139. https://doi.org/10.1016/j.eaef.2018.11.002
» https://doi.org/10.1016/j.eaef.2018.11.002
• Liu, J.; Xu, H.; Chen, Q.; Zhang, T.; Sheng, W.; Huang, Q.; Song, J.; Huang, D.; Lan, L.; Li, Y.; Chen, W.; Yang, Y. 2019. Prediction of hematoma expansion in spontaneous intracerebral hemorrhage using support vector machine. EBioMedicine 43: 454–459.
• Liu, J.; Zio, E. 2018. A scalable fuzzy support vector machine for fault detection in transportation systems. Expert Systems with Applications 102: 36–43.
• López, V.; Fernández, A.; García, S.; Palade, V.; Herrera, F. 2013. An insight into classification with imbalanced data: Empirical results and current trends on using data intrinsic characteristics. Information Sciences 250: 113–141. https://doi.org/10.1016/j.ins.2013.07.007
» https://doi.org/10.1016/j.ins.2013.07.007
• Lukmanto, R.B.; Suharjito, Nugroho, A.; Akbar, H. 2019. Early detection of diabetes mellitus using feature selection and fuzzy support vector machine. Procedia Computer Science 157: 46–54.
• Ma, Z.; Ye, C.; Li, H.; Ma, W. 2018. Applying support vector machines to predict building energy consumption in China. Energy Procedia 152: 780–786.
• Mahne Opatić, A.; Nečemer, M.; Lojen, S.; Masten, J.; Zlatić, E.; Šircelj, H.; Stopar, D.; Vidrih, R. 2018. Determination of geographical origin of commercial tomato through analysis of stable isotopes, elemental composition and chemical markers. Food Control 89: 133–141.
• Mahvash, N.M.; Hezarkhani, A. 2018. Application of support vector machine for the separation of mineralised zones in the Takht–e–Gonbad porphyry deposit, SE Iran. Journal of African Earth Sciences 143: 301–308.
• Mainville, D.Y.; Peterson, H.C. 2005. Fresh Produce Procurement Strategies in a Constrained Supply Environment: Case Study of Companhia Brasileira de Distribuicao. Applied Economic Perspectives and Policy 27: 130–138.
• Maione, C.; Barbosa, F.; Barbosa, R.M. 2019. Predicting the botanical and geographical origin of honey with multivariate data analysis and machine learning techniques: a review. Computers and Electronics in Agriculture 157: 436–446. https://doi.org/10.1016/j.compag.2019.01.020
» https://doi.org/10.1016/j.compag.2019.01.020
• Maione, C.; Barbosa, R.M. 2018. Recent applications of multivariate data analysis methods in the authentication of rice and the most analyzed parameters: a review. Critical Reviews in Food Science and Nutrition 12: 1868-1879. https://doi.org/10.1080/10408398.2018.1431763
» https://doi.org/10.1080/10408398.2018.1431763
• Manjurul Islam, M.M.; Kim, J.M. 2019. Reliable multiple combined fault diagnosis of bearings using heterogeneous feature models and multiclass support vector machines. Reliabilty Engineering & System Safety 184: 55–66.
• McKeague, J.A.; Day, J.H. 1966. Dithionite and oxalate extractable fe and al as aids in differentiating various classes of soils. Canadian Journal of Soil Science 46: 13–22.
• Medina, S.; Pereira, J.A.; Silva, P.; Perestrelo, R.; Câmara, J.S. 2019a. Food fingerprints: a valuable tool to monitor food authenticity and safety. Food Chemistry 278: 144-162.
• Medina, S.; Perestrelo, R.; Silva, P.; Pereira, J.A.M.; Câmara, J.S. 2019b. Current trends and recent advances on food authenticity technologies and chemometric approaches. Trends in Food Science and Technololy 85: 163-176.
• Mehra, J.P.; Jackson, M.L. 1960. Iron oxides removal from soils and clays by a dithionite–citrate–bicarbonate system buffered with bicarbonate sodium. Clays and Clay Minerals 7: 317–327.
• Moreda–Piñeiro, A.; Fisher, A.; Hill, S.J. 2003. The classification of tea according to region of origin using pattern recognition techniques and trace metal data. Journal of Food Composition and Analysis 16: 195–211.
• Oliveira, M.; Ramos, S.; Delerue–Matos, C.; Morais, S. 2015. Espresso beverages of pure origin coffee: mineral characterization, contribution for mineral intake and geographical discrimination. Food Chemistry 177: 330–338.
• Oliveri, P. 2017. Class–modelling in food analytical chemistry: development, sampling, optimisation and validation issues: a tutorial. Analytica Chimica Acta 982: 9-19.
• Peris, M.: Escuder–Gilabert, L. 2016. Electronic noses and tongues to assess food authenticity and adulteration. Trends in Food Science and Technology 58: 40-54.
• Potortì, A.G.; Bella, G. Di; Mottese, A.F.; Bua, G.D.; Fede, M.R.; Sabatino, G.; Salvo, A.; Somma, R.; Dugo, G.; Turco, V.L. 2018. Traceability of protected geographical indication (PGI) Interdonato lemon pulps by chemometric analysis of the mineral composition. Journal of Food Composition and Analysis 69: 122–128.
• Prati, R.C.; Batista, G.E.A.P.A.; Monard, M.C. 2004. Class imbalances versus class overlapping: an analysis of a learning system behavior. p. 312–321. In: Monroy R.; Arroyo–Figueroa, G.; Sucar, L.E.; Sossa, H., eds. MICAI 2004: advances in artificial intelligence. Springer, Berlin, Germany.
• Pu, Y.; Apel, D.B.; Liu, V.; Mitri, H. 2019. Machine learning methods for rockburst prediction–state–of–the–art review. International Journal of Mining Science and Technology 29: 565–570. https://doi.org/10.1016/j.ijmst.2019.06.009
» https://doi.org/10.1016/j.ijmst.2019.06.009
• Radhakrishnan, S.; Ramanathan, R., 2018. A support vector machine with Gabor features for animal intrusion detection in agriculture fields. Procedia Computer Science 143: 493–501.
• Rahmati, O.; Choubin, B.; Fathabadi, A.; Coulon, F.; Soltani, E.; Shahabi, H.; Mollaefar, E.; Tiefenbacher, J.; Cipullo, S.; Ahmad, B.B.; Bui, D.T. 2019. Predicting uncertainty of machine learning models for modelling nitrate pollution of groundwater using quantile regression and UNEEC methods. Science of the Total Environment 688: 855–866. https://doi.org/10.1016/j.scitotenv.2019.06.320
» https://doi.org/10.1016/j.scitotenv.2019.06.320
• Rahmeni, R.; Aicha, A.B.; Ayed, Y.B. 2019. Speech spoofing countermeasures based on source voice analysis and machine learning techniques. Procedia Computer Science 159: 668–675. https://doi.org/10.1016/j.procs.2019.09.222
» https://doi.org/10.1016/j.procs.2019.09.222
• Rodrigues, S.M.; Henriques, B.; Silva, E.F.; Pereira, M.E.; Duarte, A.C.; Römkens, P.F.A.M. 2010. Evaluation of an approach for the characterization of reactive and available pools of twenty potentially toxic elements in soils. Part I. The role of key soil properties in the variation of contaminants’ reactivity. Chemosphere 81: 1549–1559.
• Ropodi, A.I.; Panagou, E.Z.; Nychas, G.J.E. 2016. Data mining derived from food analyses using non–invasive/non–destructive analytical techniques; determination of food authenticity, quality & safety in tandem with computer science disciplines. Trends in Food Science and Technology 50: 11-25.
• Saari, J.; Strömbergsson, D.; Lundberg, J.; Thomson, A. 2019. Detection and identification of windmill bearing faults using a one–class support vector machine (SVM). Measurement: Journal of the International Measurement Confederation 137: 287–301.
• Sajedi–Hosseini, F.; Malekian, A.; Choubin, B.; Rahmati, O.; Cipullo, S.; Coulon, F.; Pradhan, B. 2018. A novel machine learning–based approach for the risk assessment of nitrate groundwater contamination. Science of the Total Environment 644: 954–962.
• Santos–Araujo, S.N.; Alleoni, L.R.F. 2016. Concentrations of potentially toxic elements in soils and vegetables from the macroregion of São Paulo, Brazil: availability for plant uptake. Environmental Monitoring and Assessment 188: 1–17.
• Serra, F.; Guillou, C.G.; Reniero, F.; Ballarin, L.; Cantagallo, M.I.; Wieser, M.; Iyer, S.S.; Héberger, K.; Vanhaecke, F. 2005. Determination of the geographical origin of green coffee by principal component analysis of carbon, nitrogen and boron stable isotope ratios. Rapid Communications in Mass Spectrometry 19: 2111–2115.
• Solano Meza, J.K.; Orjuela Yepes, D.; Rodrigo–Ilarri, J.; Cassiraga, E. 2019. Predictive analysis of urban waste generation for the city of Bogotá, Colombia, through the implementation of decision trees–based machine learning, support vector machines and artificial neural networks. Heliyon 5: e02810.
• Sustainable Capitol Hill [SCH]. 2019. Top 10 Benefits of eating local, seasonal, organic food. Available at: https://sustainablecapitolhill.org/eating–locally–in–capitol–hill [Accessed Nov 4, 2019]
» https://sustainablecapitolhill.org/eating–locally–in–capitol–hill
• Tan, P.–N.; Steinbach, M.; Kumar, V. 2005. Introduction to data mining. Addison Wesley, Boston, MA, USA.
• Tang, J.; Chen, X.; Hu, Z.; Zong, F.; Han, C.; Li, L. 2019. Traffic flow prediction based on combination of support vector machine and data denoising schemes. Physica A: Statistical Mechanics and its Applications 534: 120642.
• Valdés, A.; Beltrán, A.; Mellinas, C.; Jiménez, A.; Garrigós, M.C. 2018. Analytical methods combined with multivariate analysis for authentication of animal and vegetable food products with high fat content. Trends in Food Science and Technolology 77: 120-130.
• Varma, S.; Simon, R. 2006. Bias in error estimation when using cross–validation for model selection. BMC Bioinformatics 7: 91.
• Vougas, K.; Sakellaropoulos, T.; Kotsinas, A.; Foukas, G.R.P.; Ntargaras, A.; Koinis, F.; Polyzos, A.; Myrianthopoulos, V.; Zhou, H.; Narang, S.; Georgoulias, V.; Alexopoulos, L.; Aifantis, I.; Townsend, P.A.; Sfikakis, P.; Fitzgerald, R.; Thanos, D.; Bartek, J.; Petty, R.; Tsirigos, A.; Gorgoulis, V.G. 2019. Machine learning and data mining frameworks for predicting drug response in cancer: an overview and a novel in silico screening process based on association rule mining. Pharmacology and Therapeutics 203: 107395.
• Wadood, S.A.; Boli, G.; Xiaowen, Z.; Hussain, I.; Yimin, W. 2020. Recent development in the application of analytical techniques for the traceability and authenticity of food of plant origin. Microchemical Journal 152: 104295.
• Wang, J.; Shan, Y.; Xie, X.; Kuang, J. 2019. Output–based speech quality assessment using autoencoder and support vector regression. Speech Communication 110: 13–20. https://doi.org/10.1016/j.specom.2019.04.002
» https://doi.org/10.1016/j.specom.2019.04.002
• Wang, X.; Luo, D.; Zhao, X.; Sun, Z. 2018. Estimates of energy consumption in China using a self–adaptive multi–verse optimizer–based support vector machine with rolling cross–validation. Energy 152: 539–548.
• Xi, P.P.; Zhao, Y.P.; Wang, P.X.; Li, Z.Q.; Pan, Y.T.; Song, F.Q. 2019. Least squares support vector machine for class imbalance learning and their applications to fault detection of aircraft engine. Aerospace Science and Technology 84: 56–74.
• Xiao, R.; Hu, Q.; Li, J. 2019. Leak detection of gas pipelines using acoustic signals based on wavelet transform and Support Vector Machine. Measurement: Journal of the International Measurement Confederation 146: 479–489.
• Yu, C.; Li, Y.; Bao, Y.; Tang, H.; Zhai, G. 2018. A novel framework for wind speed prediction based on recurrent neural networks and support vector machine. Energy Conversion and Management 178: 137–145.
• Yu, P.S.; Yang, T.C.; Chen, S.Y.; Kuo, C.M.; Tseng, H.W. 2017. Comparison of random forests and support vector machine for real–time radar–derived rainfall forecasting. Journal of Hydrology 552: 92–104. https://doi.org/10.1016/j.jhydrol.2017.06.020
» https://doi.org/10.1016/j.jhydrol.2017.06.020
• Zendehboudi, A.; Baseer, M.A.; Saidur, R. 2018. Application of support vector machine models for forecasting solar and wind energy resources: a review. Journal of Cleaner Production 199: 272-285.
• Zhou, Z.; Morel, J.; Parsons, D.; Kucheryavskiy, S.V.; Gustavsson, A.M. 2019. Estimation of yield and quality of legume and grass mixtures using partial least squares and support vector machine analysis of spectral data. Computers and Electronics in Agriculture 162: 246–253.
• Zhu, S.; Chen, H.; Wang, M.; Guo, X.; Lei, Y.; Jin, G. 2019. Plastic solid waste identification system based on near infrared spectroscopy in combination with support vector machine. Advanced Industrial and Engineering Polymer Research 2: 77–81.

# Publication Dates

• Publication in this collection
18 Jan 2021
• Date of issue
2022