Author : Nina Otopal
Publisher :
ISBN 13 :
Total Pages : 92 pages
Book Rating : 4.:/5 (898 download)
Book Synopsis Restricted Kernel Canonical Correlation Analysis by : Nina Otopal
Download or read book Restricted Kernel Canonical Correlation Analysis written by Nina Otopal and published by . This book was released on 2014 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel canonical correlation analysis (KCCA) is a procedure for assessing the relationship between two sets of random variables when the classical method, canonical correlation analysis (CCA), fails because of the nonlinearity of the data. The KCCA method is mostly used in machine learning, especially for information retrieval and text mining. Because the data are often represented with non-negative numbers, we propose incorporating the non-negativity restriction directly into the KCCA method. Similar restrictions have been studied in relation to the classical CCA. This method is called restricted canonical correlation analysis (RCCA), so we call the proposed method restricted kernel canonical correlation analysis (RKCCA). With the Karush-Kuhn-Tucker theorem we show that the solution of RKCCA is equivalent to an unconstrained solution of a modified CCA problem on two random vectors with a known covariance matrix where one or several variables have been excluded. Furthermore, we use the idea of sub-vectors and sub-matrices to translate the problem of searching for the kernel canonical correlation under non-negativity restriction into an optimization problem related to eigenvalues of some generalized eigenvalue problem with a real symmetric matrix and a positive definite matrix.