The PDF projection theorem and the class-specific method

@article{citeulike:1378493, abstract = {We present the theoretical foundation for optimal classification using class-specific features and provide examples of its use. A new probability density function (PDF) projection theorem makes it possible to project probability density functions from a low-dimensional feature space back to the raw data space. An M-ary classifier is constructed by estimating the PDFs of class-specific features, then transforming each PDF back to the raw data space where they can be fairly compared. Although statistical sufficiency is not a requirement, the classifier thus constructed becomes equivalent to the optimal Bayes classifier if the features meet sufficiency requirements individually for each class. This classifier is completely modular and avoids the dimensionality curse associated with large complex problems. By recursive application of the projection theorem, it is possible to analyze complex signal processing chains. We apply the method to feature sets, including linear functions of independent random variables, cepstrum, and Mel cepstrum. In addition, we demonstrate how it is possible to automate the feature and model selection process by direct comparison of log-likelihood values on the common raw data domain.}, author = {Baggenstoss, P. M. }, citeulike-article-id = {1378493}, journal = {Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]}, keywords = {features, statistics, sufficient}, number = {3}, pages = {672--685}, posted-at = {2007-06-11 12:26:07}, priority = {1}, title = {The PDF projection theorem and the class-specific method}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1179761}, volume = {51}, year = {2003} }

TY - JOUR ID - citeulike:1378493 L3 - citeulike-article-id:1378493 TI - The PDF projection theorem and the class-specific method JF - Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on] VL - 51 IS - 3 SP - 672 EP - 685 N2 - We present the theoretical foundation for optimal classification using class-specific features and provide examples of its use. A new probability density function (PDF) projection theorem makes it possible to project probability density functions from a low-dimensional feature space back to the raw data space. An M-ary classifier is constructed by estimating the PDFs of class-specific features, then transforming each PDF back to the raw data space where they can be fairly compared. Although statistical sufficiency is not a requirement, the classifier thus constructed becomes equivalent to the optimal Bayes classifier if the features meet sufficiency requirements individually for each class. This classifier is completely modular and avoids the dimensionality curse associated with large complex problems. By recursive application of the projection theorem, it is possible to analyze complex signal processing chains. We apply the method to feature sets, including linear functions of independent random variables, cepstrum, and Mel cepstrum. In addition, we demonstrate how it is possible to automate the feature and model selection process by direct comparison of log-likelihood values on the common raw data domain. KW - features KW - statistics KW - sufficient AU - Baggenstoss, PM PY - 2003/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1179761 ER -