Open AccessProjection spectral analysis: A unified approach to PCA and ICA with incremental learning
Author(s) -
Kang Hoon,
Su Lee Hyun
Publication year - 2018
Publication title -
etri journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.295
H-Index - 46
eISSN - 2233-7326
pISSN - 1225-6463
DOI - 10.4218/etrij.2017-0304
Subject(s) - principal component analysis , mathematics , eigenvalues and eigenvectors , projection (relational algebra) , independent component analysis , singular value decomposition , projection pursuit , singular value , covariance , orthographic projection , dimension (graph theory) , covariance matrix , canonical correlation , singular spectrum analysis , pattern recognition (psychology) , artificial intelligence , algorithm , pure mathematics , computer science , statistics , geometry , physics , quantum mechanics
Projection spectral analysis is investigated and refined in this paper, in order to unify principal component analysis and independent component analysis. Singular value decomposition and spectral theorems are applied to nonsymmetric correlation or covariance matrices with multiplicities or singularities, where projections and nilpotents are obtained. Therefore, the suggested approach not only utilizes a sum‐product of orthogonal projection operators and real distinct eigenvalues for squared singular values, but also reduces the dimension of correlation or covariance if there are multiple zero eigenvalues. Moreover, incremental learning strategies of projection spectral analysis are also suggested to improve the performance.