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This paper formulates the problem of object categorization in the discriminant analysis framework focusing on transforming visual feature data so as to make it conform to the compactness hypothesis in order to improve categorization accuracy. The sought transformation, in turn, is found as a solution to an optimization problem formulated in terms of inter-observation distances only, using the technique of iterative majorization. The proposed approach is suitable for both binary and multiple-class categorization problems, and can be applied as a dimensionality reduction technique. In the latter case, the number of discriminative features is determined automatically since the process of feature extraction is fully embedded in the optimization procedure. Performance tests validate our method on a number of benchmark data sets from the UCI repository, while the experiments in the application of visual object and content-based image categorization demonstrate very competitive results, asserting the method's capability of producing semantically relevant matches that share the same or synonymous vocabulary with the query category and allowing multiple pertinent category assignment.