{"id":118551,"date":"2021-11-01T03:37:02","date_gmt":"2021-10-31T18:37:02","guid":{"rendered":"http:\/\/175.125.95.178\/ai-in-communication\/18551\/"},"modified":"2026-04-13T16:14:56","modified_gmt":"2026-04-13T07:14:56","slug":"18551","status":"publish","type":"ai-in-communication","link":"http:\/\/ee.presscat.kr\/en\/ai-in-communication\/18551\/","title":{"rendered":"Detection of Signal in the Spiked Rectangular Model"},"content":{"rendered":"<p>Author: Ji Hyung Jung, Hye Won Chung, Ji Oon Lee<br \/>\nConference and Year: ICML 2021<br \/>\nKeywords: Signal detection, Spiked Rectangular Model<br \/>\n&nbsp;<\/p>\n<p>We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the BBP transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.<\/p>\n<p><div class=\"\"><img decoding=\"async\" class=\"\" src=\"\/wp-content\/uploads\/drupal\/\uc815\ud61c\uc6d0\uad50\uc218\ub2d83.png\" alt=\"\" title=\"\"><\/div>\n<\/p>\n<p style=\"text-align:justify;margin-bottom:11px\"><span style=\"font-size:10pt\"><span style=\"line-height:107%\"><span>Figure1: We compare the reconstruction performance of the proposed PCA (top lines) and the standard PCA (bottom lines) for two FashionMNIST images, with the number of measurements N = [3136, 1568, 784, 588, 392] where the data dimension is M = 784. The left most column displays the original images for comparison. <\/span><\/span><\/span><\/p>\n<p style=\"text-align:justify;margin-bottom:11px\">\n<div class=\"\"><img decoding=\"async\" class=\"\" src=\"\/wp-content\/uploads\/drupal\/\uc815\ud61c\uc6d0\uad50\uc218\ub2d84.png\" alt=\"\" title=\"\"><\/div>\n<\/p>\n<p style=\"text-align:justify;margin-bottom:11px\"><span style=\"font-size:10pt\"><span style=\"line-height:107%\"><span>Figure2: The histograms of the test statistic under null hypothesis H0 and alternative hypothesis H1, respectively, for the Gaussian noise with SNR \u03c9 = 0.35 and \u03c9 = 0.45. It can be shown that the difference of the means of the test statistic under H0 and H1 is larger for \u03c9 = 0.45. <\/span><\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>887<\/p>\n","protected":false},"featured_media":0,"template":"","class_list":["post-118551","ai-in-communication","type-ai-in-communication","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"http:\/\/ee.presscat.kr\/en\/wp-json\/wp\/v2\/ai-in-communication\/118551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/ee.presscat.kr\/en\/wp-json\/wp\/v2\/ai-in-communication"}],"about":[{"href":"http:\/\/ee.presscat.kr\/en\/wp-json\/wp\/v2\/types\/ai-in-communication"}],"wp:attachment":[{"href":"http:\/\/ee.presscat.kr\/en\/wp-json\/wp\/v2\/media?parent=118551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}