Nonlinear Discriminative Dimensionality Reduction of Multiple Datasets

Jia Chen, Gang Wang, Georgios B. Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Dimensionality reduction (DR) is critical to many machine learning and signal processing tasks involving high-dimensional large-scale data. Standard DR tools such as principal component analysis (PCA) deal with a single dataset at a time. In diverse practical settings however, one is often tasked with learning the discriminant subspace such that one dataset of particular interest (a.k.a., target data) lies on, whereas the other dataset(s) (a.k.a., control data) do not. This is what is known as discriminative DR. Building on but considerably generalizing existing linear variants, this contribution puts forth a novel nonlinear approach for discriminative DR of multiple datasets through kernel-based learning. Interestingly, its solution can be provided analytically in terms of a generalized eigenvalue decomposition problem, for which various efficient solvers are available. Numerical experiments using synthetic and real data showcase the merits of the proposed nonlinear discriminative DR approach relative to state-of-the-art alternatives.

Original languageEnglish (US)
Title of host publicationConference Record of the 52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1993-1997
Number of pages5
ISBN (Electronic)9781538692189
DOIs
StatePublished - Feb 19 2019
Event52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018 - Pacific Grove, United States
Duration: Oct 28 2018Oct 31 2018

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
Volume2018-October
ISSN (Print)1058-6393

Conference

Conference52nd Asilomar Conference on Signals, Systems and Computers, ACSSC 2018
CountryUnited States
CityPacific Grove
Period10/28/1810/31/18

Bibliographical note

Funding Information:
This work was supported by NSF grants 1711471, 1500713, 1514056, and the NIH grant no. 1R01GM104975-01.

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