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Home / Proceedings / Proceedings of the AAAI Conference on Artificial Intelligence, 30 / No. 1: Thirtieth AAAI Conference On Artificial Intelligence

Discriminative Vanishing Component Analysis

March 8, 2023

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Authors

Chenping Hou

National University of Defense Technology


Feiping Nie

Northwestern Polytechnical University


Dacheng Tao

University of Technology, Sydney


DOI:

10.1609/aaai.v30i1.10223


Abstract:

Vanishing Component Analysis (VCA) is a recently proposed prominent work in machine learning. It narrows the gap between tools and computational algebra: the vanishing ideal and its applications to classification problem. In this paper, we will analyze VCA in the kernel view, which is also another important research direction in machine learning. Under a very weak assumption, we provide a different point of view to VCA and make the kernel trick on VCA become possible. We demonstrate that the projection matrix derived by VCA is located in the same space as that of Kernel Principal Component Analysis (KPCA) with a polynomial kernel. Two groups of projections can express each other by linear transformation. Furthermore, we prove that KPCA and VCA have identical discriminative power, provided that the ratio trace criteria is employed as the measurement. We also show that the kernel formulated by the inner products of VCA's projections can be expressed by the KPCA's kernel linearly. Based on the analysis above, we proposed a novel Discriminative Vanishing Component Analysis (DVCA) approach. Experimental results are provided for demonstration.

Topics: AAAI

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HOW TO CITE:

Chenping Hou|| Feiping Nie|| Dacheng Tao Discriminative Vanishing Component Analysis Proceedings of the AAAI Conference on Artificial Intelligence, 30 (2016) .

Chenping Hou|| Feiping Nie|| Dacheng Tao Discriminative Vanishing Component Analysis AAAI 2016, .

Chenping Hou|| Feiping Nie|| Dacheng Tao (2016). Discriminative Vanishing Component Analysis. Proceedings of the AAAI Conference on Artificial Intelligence, 30, .

Chenping Hou|| Feiping Nie|| Dacheng Tao. Discriminative Vanishing Component Analysis. Proceedings of the AAAI Conference on Artificial Intelligence, 30 2016 p..

Chenping Hou|| Feiping Nie|| Dacheng Tao. 2016. Discriminative Vanishing Component Analysis. "Proceedings of the AAAI Conference on Artificial Intelligence, 30". .

Chenping Hou|| Feiping Nie|| Dacheng Tao. (2016) "Discriminative Vanishing Component Analysis", Proceedings of the AAAI Conference on Artificial Intelligence, 30, p.

Chenping Hou|| Feiping Nie|| Dacheng Tao, "Discriminative Vanishing Component Analysis", AAAI, p., 2016.

Chenping Hou|| Feiping Nie|| Dacheng Tao. "Discriminative Vanishing Component Analysis". Proceedings of the AAAI Conference on Artificial Intelligence, 30, 2016, p..

Chenping Hou|| Feiping Nie|| Dacheng Tao. "Discriminative Vanishing Component Analysis". Proceedings of the AAAI Conference on Artificial Intelligence, 30, (2016): .

Chenping Hou|| Feiping Nie|| Dacheng Tao. Discriminative Vanishing Component Analysis. AAAI[Internet]. 2016[cited 2023]; .


ISSN: 2374-3468


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