### abstract ###
Canonical correlation analysis is a technique to extract common features from a pair of multivariate data
In complex situations, however, it does not extract useful features because of its linearity
On the other hand, kernel method used in support vector machine is an efficient approach to improve such a linear method
In this paper, we investigate the effectiveness of applying kernel method to canonical correlation analysis \\ {Keyword:} multivariate analysis, multimodal data, kernel method, regularization
### introduction ###
This paper deals with the method to extract common features from multiple information sources
For instance, let us consider a task of learning in pattern recognition, in which an object is given by using an image and its name is given by a speech
For a newly given image, the system is required to answer its name by a speech, and for a newly given speech, the system is to answer the corresponding image
The task can be considered to be a regression problem from image to speech and vice versa
However, since the dimensionalities of images and speeches are generally very large, a regression analysis many not work effectively
In order to solve the problem, it is useful to map the inputs into low dimensional feature space and then to solve the regression problem
The canonical correlation analysis (CCA) has been used for such a purpose
CCA finds a linear transformation of a pair of multi-variates such that the correlation coefficient is maximized
From an information theoretical point of view, the transformation maximizes the mutual information between extracted features
However, if there is nonlinear relation between the  variates, CCA does not always extract useful features
On the other hand, the support vector machines (SVM) are attracted a lot of attention by its state-of-art performance in pattern recognition  CITATION  The kernel trick used in SVM is applicable not only for classification but also for other linear techniques, for example, kernel regression and kernel PCA CITATION    In this paper, we apply the kernel method to CCA
Since the kernel method is likely to overfit the data, we incorporate some regularization technique to avoid the overfitting
