Title :
Asymptotically Optimal Approximation of Multidimensional pdf´s by Lower Dimensional pdf´s
Author_Institution :
Dept. of Electr. & Comput. Eng., Rhode Island Univ., Kingston, RI
Abstract :
Probability density functions (pdf´s) of high dimensionality are impractical to estimate from real data. For accurate estimation, the dimensionality of the pdf can be at most 5-10. In order to reduce the dimensionality a sufficient statistic is usually employed. When none is available, there is no universal agreement on how to proceed. We show how to construct a high-dimension pdf based on the pdf of a low-dimensional statistic that is closest to the true one in the sense of divergence. The latter criterion asymptotically minimizes the probability of error in a decision rule. An application to feature selection for classification is described
Keywords :
error statistics; signal classification; asymptotically optimal approximation; dimensionality reduction; error probability; feature selection; low-dimensional statistic; lower dimensional probability density functions; multidimensional probability density functions; Data mining; Density functional theory; Face detection; Multidimensional systems; Pattern classification; Pattern recognition; Probability density function; Signal detection; Statistics; Training data; Feature extraction; pattern classification; signal detection;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2006.887112
