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Mar 30

Independent Components Analysis

Posted by abiao at 17:05 | Code » Matlab | Comments(0) | Reads(8796)
The FastICA package is a free (GPL) MATLAB program that implements the fast independent component analysis.  

Independent component analysis (ICA) or blind source separation is a modern signal processing technique to multivariate financial time series such as a portfolio of stocks to multivariate financial time series such as a portfolio of stocks. The key idea of ICA is to linearly map the observed multivariate time series into a new space of statistically independent components (ICs). This can be viewed as a factorization of the portfolio since joint probabilities become simple products in the coordinate system of the ICs.

The major difference between Independent component analysis and more familiar principal component analysis (PCA) is in the type of components obtained. The goal of PCA is to obtain principal components which are uncorrelated. Moreover, PCA gives projections of the data in the direction of the maximum variance. The principal components (PCs) are ordered in terms of their variances: the first PC defines the direction that captures the maximum variance possible, the second PC defines (in the remaining orthogonal subspace) the direction of maximum variance, and so forth. In ICA however, the aim is to obtain statistically independent components. What's more, PCA algorithms use only second order statistical information (variance dominates). On the other hand, ICA algorithms may use higher order2 statistical information for separating the signals.

To download FastICA and more about the book Independent Component Analysis check http://www.cis.hut.fi/projects/ica/fastica/, the book can be bought at Amazon through: Independent Component Analysis

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