A Copula Based ICA Algorithm and Its Application to Time Series Clustering

Independent component analysis (ICA) is a method to recover the original independent variables from the linear transformations of the observations. Most of ICA algorithms are formulated as an optimization of a contrast function which minimizes the cross-dependency among the components. In this paper, we propose an innovative algorithm for performing ICA problem which uses a contrast function based on the Hoeffding’s measure of pairwise dependence. This measure takes its minimum if and only if the random variables are independent, and takes its maximum if and only if one of the variable is a function of the other. Since the Hoeffding’s index is computed based on the rank values rather than the actual values of the data, it is significantly robust to the outliers and performs well even in the presence of noise. The proposed algorithm is evaluated using simulated data. The algorithm is utilized as a pre-processing method for clustering of trends in time series data. This pre-processing technique establish new components from original observations which have adequate information trend of time series. For illustrative purposes, the proposed methodology is applied to clustering of two real data sets involving financial time series.