Weighted Multiple Kernel Canonical Correlation

Abstract

In the preceding chapters we have presented several supervised and unsupervised algorithms using kernel fusion to combine multi-source and multi-representation of data. In this chapter we will investigate a different unsupervised learning problem Canonical Correlation Analysis (CCA), and its extension in kernel fusion techniques. The goal of CCA (taking two data sets for example) is to identify the canonical variables that minimize or maximize the linear correlations between the transformed variables [8]. The conventional CCA is employed on two data sets in the observation space (original space). The extension of CCA on multiple data sets is also proposed by Kettenring and it leads to different criteria of selecting the canonical variables, which are summarized as 5 different models: sum of correlation model, sum of squared correlation model, maximum variance model, minimal variance model and generalized variance model [9].