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Low-rank matrix approximation is an integral component of tools such as principal component analysis (PCA), as well as is an important instrument used in applications like web search, text mining and computer vision, e.g., face recognition. Recently, randomized algorithms were proposed to effectively construct low rank approximations of large matrices. In(More)
Many machine learning and data-related applications require the knowledge of approximate ranks of large data matrices at hand. This letter presents two computationally inexpensive techniques to estimate the approximate ranks of such matrices. These techniques exploit approximate spectral densities, popular in physics, which are probability density(More)
Despite a large volume of research in group testing, explicit small-size group testing schemes are still difficult to construct, and the parameters of known combinatorial schemes are limited by the constraints of the problem. Relaxing the worst-case identification requirements to probabilistic localization of defectives enables one to expand the range of(More)
—Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized algorithms were proposed to effectively construct low rank approximations and obtain approximate singular value decompositions of large matrices. Similar ideas were used to solve least squares regression problems. In this(More)
Understanding the singular value spectrum of a matrix A ∈ R n×n is a fundamental task in countless numerical computation and data analysis applications. In matrix multiplication time, it is possible to perform a full SVD of A and directly compute the singular values σ 1 ,. .. , σ n in n ω time. However, little is known about algorithms that break this(More)
1. Additional Details In this supplementary material, we give additional details on the two polynomial filters discussed in the main paper. First, we give an example to illustrate how the choice of the degree in the extend McWeeny filter method affects the inflexion point and the rank estimated. Next, we discuss some details on the practical implementation(More)
This letter considers the problem of dictionary learning for sparse signal representation whose atoms have low mutual coherence. To learn such dictionaries, at each step, we first update the dictionary using the method of optimal directions (MOD) and then apply a dictionary rank shrinkage step to decrease its mutual coherence. In the rank shrinkage step, we(More)
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