Self-Organizing Algorithms for Generalized Eigen-Decomposition  

Oleh:

Chatterjee, C. ; Ramos, J. ; Roychowdhury, V. P. ; Zoltowski, M.D.

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: IEEE Transactions on Neural Networks vol. 8 no. 6 (1997), page 1518-1530.
Topik: eigendom; self - organizing; algorithms; eigen - decomposition

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: II36.2 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

Lihat Detail Induk

Isi artikel

We discuss a new approach to self - organization that leads to novel adaptive algorithms for generalized eigen - decomposition and its variance for a single - layer linear feedforward neural network. First, we derive two novel iterative algorithms for linear discriminant analysis (LDA) and generalized eigen - decomposition by utilizing a constrained least - mean - squared classification error cost function, and the framework of a two - layer linear heteroassociative network performing a one - of - m classification. By using the concept of deflation, we are able to find sequential versions of these algorithms which extract the LDA components and generalized eigenvectors in a decreasing order of significance. Next, two new adaptive algorithms are described to compute the principal generalized eigenvectors of two matrices (as well as LDA) from two sequences of random matrices. We give a rigorous convergence analysis of our adaptive algorithms by using stochastic approximation theory, and prove that our algorithms converge with probability one.

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