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On using derivatives and multiple kernel methods for clustering and classifying functional data
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DOI：10.1016/j.neucom.2024.129231.png)
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Abstract
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In this paper, we propose a framework for rich representation of smooth functional data, leveraging a multiview approach that considers functions and their derivatives as complementary sources of information. Additionally, motivated by the non-linear nature of functional data, we advocate for kernel methods as a suitable modeling approach. We extend existing multiple kernel learning techniques for multivariate data to handle functional data. In particular, we introduce a general procedure for linearly combining different kernel functions. We apply this framework to both clustering and classification tasks, extending multiple kernel kmeans and multiple kernel SVM methods to Sobolev functions in H q . Our experiments involve both simulated and real-world data, demonstrating the effectiveness of our proposed methods.
Keywords:
Functional data analysis
Functional data clustering
Functional data classification
Derivative functions
Multiple kernel learning
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