Restricted kernel canonical correlation analysis

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 is often represented with non-negative numbers, we propose to incorporate the non-negativity restriction directly into the KCCA method. Similar restrictions have been studied in relation to the classical CCA and called restricted canonical correlation analysis (RCCA), so that we call the proposed method restricted kernel canonical correlation analysis (RKCCA). We also provide some possible approaches for solving the optimization problem to which our method translates. The motivation for introducing RKCCA is given in Section 2.