PCA and ICA Package

This package contains functions that implement Principal Component Analysis (PCA) and Independent Component Analysis (ICA).
PCA and ICA are implemented as functions in this package, and multiple examples are included to demonstrate their use.
In PCA, multi-dimensional data is projected onto the singular vectors corresponding to a few of its largest singular values. Such an operation effectively decomposes the input single into orthogonal components in the directions of largest variance in the data. As a result, PCA is often used in dimensionality reduction applications, where performing PCA yields a low-dimensional representation of data that can be reversed to closely reconstruct the original data.
In ICA, multi-dimensional data is decomposed into components that are maximally independent in an appropriate sense (kurtosis and negentropy, in this package). ICA differs from PCA in that the low-dimensional signals do not necessarily correspond to the directions of maximum variance; rather, the ICA components have maximal statistical independence. In practice, ICA can often uncover disjoint underlying trends in multi-dimensional data.