Comparison of Performance of Different Kernels in Kernel PCA

Abstract

Data analysis is simply the decision making based on the past data, which involves some preprocessing of the data. This preprocessing involves feature extraction and dimensionality reduction. For this purpose, Principal Component Analysis (PCA) may be useful in most of the applications. Since PCA is the linear technique for analysis of data, its use is limited till the data involved can be explained linearly. Kernel Principal Component Analysis is useful for feature extraction, especially when the underlying data is non-linear. Two algorithms are presented for computation of kernel matrix, which is used to obtain the principal components. The first algorithm uses the static training set for all the elements of the test set, while the second algorithm is recursive. The recursive algorithm uses an updated training set to compute elements of principal components for every new data from the test set. Linear PCA is compared with gaussian and polynomial kernel PCA, and shown that the kernel PCA performs better than the linear PCA. The mean square errors are also presented for the two kernels. An example of financial data set is presented as an application.