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On the orthogonal distance to class subspaces for high-dimensional data classification

Zhu, R. ORCID: 0000-0002-9944-0369 and Xue, J-H. (2017). On the orthogonal distance to class subspaces for high-dimensional data classification. Information Sciences, 417, pp. 262-273. doi: 10.1016/j.ins.2017.07.019

Abstract

The orthogonal distance from an instance to the subspace of a class is a key metric for pattern classification by the class subspace-based methods. There is a close relationship between the orthogonal distance and the residual standard deviation of a test instance from the class subspace. In this paper, we shall show that an established and widely-used relationship, between the residual standard deviation and the sum of squares of the residual PC scores, is not precise, and thus can lead to incorrect results, for the inference of high-dimensional data which nowadays are common in practice.

Publication Type: Article
Additional Information: © 2017 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Publisher Keywords: Classification, High-dimensional data, Orthogonal distance, Principal component analysis (PCA), Soft independent modelling of class analogy (SIMCA)
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Z Bibliography. Library Science. Information Resources > Z665 Library Science. Information Science
Departments: Cass Business School > Actuarial Science & Insurance
URI: http://openaccess.city.ac.uk/id/eprint/20734
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