کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1145987 | 1489693 | 2012 | 16 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Phase transition in limiting distributions of coherence of high-dimensional random matrices Phase transition in limiting distributions of coherence of high-dimensional random matrices](/preview/png/1145987.png)
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.
Journal: Journal of Multivariate Analysis - Volume 107, May 2012, Pages 24–39