A note on order statistics-based parametric pattern classification. Issue 1 (January 2015) - Hu, Lixia
Abstract Recently, a novel classification paradigm is proposed, named Classification by Moments of Order Statistics (CMOS), which is shown to attain the optimal Bayesian bound for symmetric distributions and a near-optimal accuracy for asymmetric distributions [13, 9]. However, in the process of deriving the order statistics-based classification scheme, the authors use a plausible relation "<alternatives><inline-graphic xlink:href="ark:/27927/pgh206f3r8j" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />E[Φ(xk, n)]=k/(n+1)⟹E[xk, n]=Φ−1(k/(n+1))</alternatives>", where <alternatives><inline-graphic xlink:href="ark:/27927/pgh206fb5xm" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />Φ</alternatives> is the cumulative distribution function of random variable <alternatives><inline-graphic xlink:href="ark:/27927/pgh206f8hxt" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />X</alternatives>, and <alternatives><inline-graphic xlink:href="ark:/27927/pgh206f7zgw" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />xk, n</alternatives> is the k-th order statistics of a sample of size n from X. Therefore, the new approach actually should be viewed as the classification scheme based on the percentiles of distribution, instead of the so-called order statistics-based classification. In this paper, we will build the CMOS using 2-OS criteria in its true sense. Furthermore, we show that the order statistics-based classification reaches the optimal Bayesian bound for symmetric distributions, and compare the accuracy of CMOS, Bayesian classification, median-based classifier and percentiles-based classification for non-symmetric distributions. The theoretical results are verified by rigorous experiments as well.