Feature selection using the supervised PDF estimation based on non-uniform filter banks

As a statistical feature of observed data, the probability density function (PDF) of the data not only provides useful statistical information but can be used as a characteristic to distinguish among different observed data. To provide an improved selection of statistical features such as the PDF by taking advantage of prior knowledge of the distributions, we propose a PDF estimator and present a supervised feature selection scheme based on the PDF estimator. The proposed PDF estimator exploits a structure of non-uniform filter bank and is optimized by the least square approximation. To facilitate implementation of the proposed estimator, the non-uniform filter bank structure is converted into an equivalent uniform filter bank structure. In addition, the proposed PDF selection scheme reliably chooses the true PDF even with a small sample size. Numerical experiments demonstrate the good performance of the proposed PDF estimator and PDF selection scheme.