The common vector approach and its relation to principal component analysis

• Published in: IEEE transactions on speech and audio processing 2001-09, Vol.9 (6), p.655-662
• Main Authors: Gulmezoglu, M.B., Dzhafarov, V., Barkana, A.
• Format: Article
• Language: English
• Subjects: Applied sciences; Covariance matrix; Eigenvalues; Eigenvalues and eigenfunctions; Eigenvectors; Equations; Exact sciences and technology; Feature recognition; Information, signal and communications theory; Loudspeakers; Mathematical analysis; Mathematics; Principal component analysis; Principal components analysis; Recognition; Signal processing; Speech; Speech processing; Speech recognition; Studies; Telecommunications and information theory; Testing; Two dimensional displays; Vectors; Vectors (mathematics)
• ISSN: 1063-6676; 2329-9290; 1558-2353; 2329-9304
• DOI: 10.1109/89.943343

The main point of the paper is to show the close relation between the nonzero principal components and the difference subspace together with the complementary close relation between the zero principal components and the common vector. A common vector representing each word-class is obtained from the eigenvectors of the covariance matrix of its own word-class; that is, the common vector is in the direction of a linear combination of the eigenvectors corresponding to the zero eigenvalues of the covariance matrix. The methods that use the nonzero principal components for recognition purposes suggest the elimination of all the features that are in the direction of the eigenvectors corresponding to the smallest eigenvalues (including the zero eigenvalues) of the covariance matrix whereas the common vector approach suggests the elimination of all the features that are in the direction of the eigenvectors corresponding to the largest, all nonzero eigenvalues of the covariance matrix.