Interpretable support vector machines for functional data

Abstract

Support Vector Machines (SVM) has been shown to be a powerful nonparametric classification technique even for high-dimensional data. Although predictive ability is important, obtaining an easy-to-interpret classifier is also crucial in many applications. Linear SVM provides a classifier based on a linear score. In the case of functional data, the coefficient function that defines such linear score usually has many irregular oscillations, making it difficult to interpret. This paper presents a new method, called Interpretable Support Vector Machines for Functional Data, that provides an interpretable classifier with high predictive power. Interpretability might be understood in different ways. The proposed method is flexible enough to cope with different notions of interpretability chosen by the user, so the obtained coefficient function can be sparse, linear-wise, smooth, etc. The usefulness of the proposed method is shown in real applications getting interpretable classifiers with comparable, sometimes better, predictive ability versus classical SVM.

CRM in social media: Predicting increases in Facebook usage frequency

“…An important parameter in Support Vector Machines (SVM) is the kernel function (Martin- Barragan et al, 2014). The most popular choices are the linear, polynomial, and radial basis (RBF) kernel (Ballings and Van den Poel, 2013a).…”

Methodologies for assessing costs of rail transit systems based on small sample data

“…Hwang et al [35] developed a novel Lagrangian SVM to address multiclass problems. Lillo and Martin-Barragan [36] presented interpretable SVMs for functional data that provide an interpretable classifier with high predictive power. Milad and Morteza [37,38] presented a multilevel SVM that enhanced the original SVM.…”

The Mahalanobis Distance for Functional Data With Applications to Classification

“…Next, the classification procedures are applied to the Tecator dataset previously considered by Ferraty and Vieu (2003), Rossi and Villa (2006), Li and Yu (2008), Alonso et al (2012) and Martin-Barragan et al (2013), among others. The dataset that consists of 215 nearinfrared absorbance spectra of meat samples, recorded on a Tecator Infracted Food Analyzer is available at http://lib.stat.cmu.edu/datasets/tecator.…”

“…Alternatively, Preda et al (2007) used functional PLS regression to obtain the discriminant functions while Shin (2008) considered an approach based on reproducing kernel Hilbert spaces. Finally, Ferraty and Vieu (2003) have proposed a method based on estimating nonparametrically the posterior probability that the new function χ 0 is of a given class, López-Pintado and Romo (2006), Cuevas et al (2007) and Sguera et al (2012) have proposed classifiers based on the notion of data depth that are well suited for datasets containing outliers, Rossi and Villa (2006) and Martin-Barragan et al (2013) have investigated the use of support vector machines (SVMs) for functional data, Wang et al (2007) have considered classification for functional data by Bayesian modeling with wavelet basis functions, Epifanio (2008) has developed classifiers based on shape descriptors, Araki et al (2009) have considered functional logistic classification, and, finally, Alonso et al (2012) have proposed a weighted distance approach. Note that, when a distance is required, these papers use the L 1 , L 2 and L ∞ distances which are well defined in Hilbert spaces.…”