کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1145987 1489693 2012 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Phase transition in limiting distributions of coherence of high-dimensional random matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
Phase transition in limiting distributions of coherence of high-dimensional random matrices
چکیده انگلیسی

The coherence of a random matrix, which is defined to be the largest magnitude of the Pearson correlation coefficients between the columns of the random matrix, is an important quantity for a wide range of applications including high-dimensional statistics and signal processing. Inspired by these applications, this paper studies the limiting laws of the coherence of n×pn×p random matrices for a full range of the dimension pp with a special focus on the ultra high-dimensional setting. Assuming the columns of the random matrix are independent random vectors with a common spherical distribution, we give a complete characterization of the behavior of the limiting distributions of the coherence. More specifically, the limiting distributions of the coherence are derived separately for three regimes: 1nlogp→0, 1nlogp→β∈(0,∞), and 1nlogp→∞. The results show that the limiting behavior of the coherence differs significantly in different regimes and exhibits interesting phase transition phenomena as the dimension pp grows as a function of nn. Applications to statistics and compressed sensing in the ultra high-dimensional setting are also discussed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 107, May 2012, Pages 24–39
نویسندگان
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