Bayesian Fisher's Discriminant for Functional Data

TL;DR

This paper introduces a Bayesian Gaussian process framework to extend Fisher's discriminant for classifying functional data, leveraging smoothness priors and outperforming existing methods in simulations and real applications.

Contribution

It presents a novel Bayesian approach that explicitly formulates the probability structure for functional data classification, unifying and improving upon existing smoothness-based methods.

Findings

Significantly outperforms existing Fisher's discriminant methods in simulations.

Provides a unified Bayesian framework for functional data classification.

Demonstrates effectiveness on real-world spectral and image data.

Abstract

We propose a Bayesian framework of Gaussian process in order to extend Fisher's discriminant to classify functional data such as spectra and images. The probability structure for our extended Fisher's discriminant is explicitly formulated, and we utilize the smoothness assumptions of functional data as prior probabilities. Existing methods which directly employ the smoothness assumption of functional data can be shown as special cases within this framework given corresponding priors while their estimates of the unknowns are one-step approximations to the proposed MAP estimates. Empirical results on various simulation studies and different real applications show that the proposed method significantly outperforms the other Fisher's discriminant methods for functional data.