Learning principal directions: Integrated-squared-error minimization
SCIE
SCOPUS
- Title
- Learning principal directions: Integrated-squared-error minimization
- Authors
- Ahn, JH; Oh, JH; Choi, S
- Date Issued
- 2007-03
- Publisher
- ELSEVIER SCIENCE BV
- Abstract
- A common derivation of principal component analysis (PCA) is based on the minimization of the squared-error between centered data and linear model, corresponding to the reconstruction error. In fact, minimizing the squared-error leads to principal subspace analysis where scaled and rotated principal axes of a set of observed data, are estimated. In this paper, we introduce and investigate an alternative error measure, integrated-squared error (ISE), the minimization of which determines the exact principal axes (without rotational ambiguity) of a set of observed data. We show that exact principal directions emerge from the minimization of ISE. We present a simple EM algorithm, 'EM-ePCA', which is similar to EM-PCA [S.T. Roweis, EM algorithms for PCA and SPCA, in: Advances in Neural Information Processing Systems, vol. 10, MIT Press, Cambridge, 1998, pp. 626-632.], but finds exact principal directions without rotational ambiguity. In addition, we revisit the generalized Hebbian algorithm (GHA) and show that it emerges from the ISE minimization in a single-layer linear feedforward neural network. (c) 2006 Elsevier B.V. All rights reserved.
- Keywords
- EM algorithm; generalized Hebbian algorithm; generative models; probabilistic coupled models; separable LS; PCA; COMPONENT ANALYSIS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/23464
- DOI
- 10.1016/j.neucom.2006.06.004
- ISSN
- 0925-2312
- Article Type
- Article
- Citation
- NEUROCOMPUTING, vol. 70, no. 40003, page. 1372 - 1381, 2007-03
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