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Discriminant feature extraction by generalized difference subspace

Fukui, Kazuhiro; Sogi, Naoya; Kobayashi, Takumi; Xue, Jing-Hao; Maki, Atsuto; (2022) Discriminant feature extraction by generalized difference subspace. IEEE Transactions on Pattern Analysis and Machine Intelligence 10.1109/tpami.2022.3168557. (In press). Green open access

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Abstract

This paper reveals the discriminant ability of the orthogonal projection of data onto a generalized difference subspace (GDS) both theoretically and experimentally. In our previous work, we have demonstrated that GDS projection works as the quasi-orthogonalization of class subspaces. Interestingly, GDS projection also works as a discriminant feature extraction through a similar mechanism to the Fisher discriminant analysis (FDA). A direct proof of the connection between GDS projection and FDA is difficult due to the significant difference in their formulations. To avoid the difficulty, we first introduce geometrical Fisher discriminant analysis (gFDA) based on a simplified Fisher criterion. gFDA can work stably even under few samples, bypassing the small sample size (SSS) problem of FDA. Next, we prove that gFDA is equivalent to GDS projection with a small correction term. This equivalence ensures GDS projection to inherit the discriminant ability from FDA via gFDA. Furthermore, we discuss two useful extensions of these methods, 1) nonlinear extension by kernel trick, 2) the combination of convolutional neural network (CNN) features. The equivalence and the effectiveness of the extensions have been verified through extensive experiments on the extended Yale B+, CMU face database, ALOI, ETH80, MNIST and CIFAR10, focusing on the SSS problem.

Type: Article
Title: Discriminant feature extraction by generalized difference subspace
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/tpami.2022.3168557
Publisher version: https://doi.org/10.1109/TPAMI.2022.3168557
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Principal component analysis , Image recognition , Feature extraction , Kernel , Lighting , Face recognition , Task analysis
UCL classification: UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10147192
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