Support vector machine for functional data classification

Abstract

In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional Data Analysis (FDA). In this paper, we investigate the use of Support Vector Machines (SVMs) for functional data analysis and we focus on the problem of curves discrimination. SVMs are large margin classifier tools based on implicit non linear mappings of the considered data into high dimensional spaces thanks to kernels. We show how to define simple kernels that take into account the unctional nature of the data and lead to consistent classification. Experiments conducted on real world data emphasize the benefit of taking into account some functional aspects of the problems.

13 pages

References in corpus (3)

• Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis
• Representation of Functional Data in Neural Networks
• Multilayer Perceptron with Functional Inputs: an Inverse Regression Approach

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• A Fourier representation of kernel Stein discrepancy with application to Goodness-of-Fit tests for measures on infinite dimensional Hilbert spaces
• Continuum centroid classifier for functional data
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• Stability for Inference with Persistent Homology Rank Functions
• A Novel Statistical Method Based on Dynamic Models for Classification
• Semi-supervised logistic discrimination for functional data