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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)

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)

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)

We present two computationally inexpensive techniques for estimating the numerical rank of a matrix, combining powerful tools from computational linear algebra. These techniques exploit three key ingredients. The first is to approximate the projector on the non-null invariant subspace of the matrix by using a polynomial filter. Two types of filters are… (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)

—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)

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