کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4605413 | 1337570 | 2009 | 14 صفحه PDF | دانلود رایگان |
Classification is a fundamental image processing task. Recent empirical evidence suggests that classification algorithms which make use of redundant linear transforms will regularly outperform their nonredundant counterparts. We provide a rigorous explanation of this phenomenon in the single-class case. We begin by developing a measure-theoretic analysis of the set of points at which a given decision rule will have an intolerable chance of making a classification error. We then apply this general theory to the special case where the class is compact and convex, showing that such a class may be arbitrarily well approximated by frame sets, namely, preimages of hyperrectangles under frame analysis operators. This leads to a frame-based classification scheme in which frame coefficients are regarded as features. We show that, indeed, the accuracy of such a classification scheme approaches perfect accuracy as the redundancy of the frame grows large.
Journal: Applied and Computational Harmonic Analysis - Volume 27, Issue 1, July 2009, Pages 73-86