Local Linear ICA for Mutual Information Estimation in Feature Selection

Mutual information is an important tool in many applications. Specifically, in classification systems, feature selection based on MI estimation between features and class labels helps to identify the most useful features directly related to the classification performance. MI estimation is extremely difficult and imprecise in high dimensional feature spaces with an arbitrary distribution. We propose a framework using ICA and sample-spacing based entropy estimators to estimate MI. In this framework, the higher dimensional MI estimation is reduced to independent multiple one-dimensional MI estimation problems. This approach is computationally efficient, however, its precision heavily relies on the results of ICA. In our previous work, we assumed the feature space has linear structure, hence linear ICA was adopted. Nevertheless, this is a weak assumption, which might not be true in many applications. Although non-linear ICA can solve any ICA problem in theory, its complexity and the requirement of data samples restrict its application. A better trade-off between linear and non-linear ICA could be local linear ICA, which uses piecewise linear ICA to approximate the non-linear relationships among the data. In this paper, we propose that by replacing linear ICA with local linear ICA, we can get precise MI estimation without greatly increasing the computational complexity. The experiment results also substantiate this claim.