An algorithm given by Golub and Kahan [2] for reducing a general matrix to bidiagonal form is shown to be very important for large sparse matrices. The singular values of the matrix are those of the bidiagonal form, and these can be easily computed. The bidiagonalization algorithm is shown to be the basis of important methods for solving the linear least squares problem for large sparse matrices. Eigenvalues of certain 2-cyclic matrices can also be efficiently computed using this bidiagonalizati...
We observed that generally the embedding representation is very rich and information dense. For example, reducing the dimensionality of the inputs using SVD or PCA, even by 10%, generally results in worse downstream performance on specific tasks.
Die Grundannahme für die Verwendung der PCA zur Clusteranalyse und Dimensionsreduktion lautet: Die Richtungen mit der größten Streuung (Varianz) beinhalten die meiste Information.
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