A reproducing kernel Hilbert space framework for functional data classification

by   Peijun Sang, et al.

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied directly or have poor performance due to the curse of dimensionality. To address this concern, we propose to project functional data onto one specific direction, and then a distance-weighted discrimination DWD classifier is built upon the projection score. The projection direction is identified through minimizing an empirical risk function that contains the particular loss function in a DWD classifier, over a reproducing kernel Hilbert space. Hence our proposed classifier can avoid overfitting and enjoy appealing properties of DWD classifiers. This framework is further extended to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate. In finite sample case, we demonstrate that the proposed classifiers compare favorably with some commonly used functional classifiers in terms of prediction accuracy through simulation studies and a real-world application.



There are no comments yet.


page 1

page 2

page 3

page 4


Continuum centroid classifier for functional data

Aiming at the binary classification of functional data, we propose the c...

Fast Convergence on Perfect Classification for Functional Data

In this study, we investigate the availability of approaching to perfect...

On Mahalanobis distance in functional settings

Mahalanobis distance is a classical tool in multivariate analysis. We su...

Non-asymptotic Optimal Prediction Error for RKHS-based Partially Functional Linear Models

Under the framework of reproducing kernel Hilbert space (RKHS), we consi...

A nonlinear aggregation type classifier

We introduce a nonlinear aggregation type classifier for functional data...

Neural Networks as Functional Classifiers

In recent years, there has been considerable innovation in the world of ...

Optimal Imperfect Classification for Gaussian Functional Data

Existing works on functional data classification focus on the constructi...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.