Feature extraction and selection are important problems in statistical learning. We study the relationships between two previously proposed principles for their optimal solution: the minimization of Bayes error and the maximization of mutual information between features and class labels. It is shown that a quantity which provides insight on this relationship is the set of non-increasing probability mass functions (NIPMFs). We derive some basic properties of the members of this set, show that any classification problem defines an ensemble of NIPMFs, and that the probability distribution of this ensemble uniquely determines the associated Bayes error and mutual information. These results are then used to show that, when the classification problem is binary and some generic constraints hold, the optimal feature space is the same under the two formulations.
The design of an effective architecture for image retrieval requires careful consideration of the interplay between the three major components of a retrieval system: feature transformation, feature
representation, and similarity function. We present a review of
ongoing work on a decision theoretic formulation of the retrieval problem that enables the design of systems where all components are optimized with respect to the same end-to-end performance criteria: the minimization of the probability of retrieval error. In addition to some previously published results on the theoretical characterization of the impact of the feature transformation and representation in the probability of error, we present an efficient algorithm for optimal feature selection. Experimental results show that decision-theoretic retrieval performs well on color, texture, and generic image databases in terms of both retrieval accuracy and perceptual relevance of similarity judgments.
We have previously introduced a Bayesian framework for content-based image retrieval that relies on a generative model for feature representation based on embedded mixtures. This is a truly generic image representation that can jointly model color and texture and has been shown to perform well across a broad spectrum of image databases. In this paper, we expand the Bayesian framework along two directions.
By formulating content-based retrieval as a problem of Bayesian inference we have previously developed a retrieval framework with various interesting properties: (1) allows the incorporation of prior beliefs about image relevance in the retrieval process, (2) leads to simple and intuitive mechanisms for combining information from several modalities, such as images, audio, and text during retrieval, (3) provides support for the development of interfaces that learn from user interaction, (4) allows retrieval directly from compressed bitstreams, and (5) lends itself to the construction of indexing structures which can also be computed as a side effect of the compression process.
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