
On the Recognition of StrongRobinsonian Incomplete Matrices
A matrix is incomplete when some of its entries are missing. A Robinson ...
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Hadamard matrices in {0,1} presentation and an algorithm for generating them
Hadamard matrices are square n× n matrices whose entries are ones and mi...
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Optimal Adaptive Matrix Completion
We study the problem of exact completion for m × n sized matrix of rank ...
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The surrogate matrix methodology: A reference implementation for lowcost assembly in isogeometric analysis
A reference implementation of a new method in isogeometric analysis (IGA...
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Adaptive Estimation of Noise Variance and Matrix Estimation via USVT Algorithm
Consider the problem of denoising a large m× n matrix. This problem has ...
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A random algorithm for lowrank decomposition of largescale matrices with missing entries
A Random SubMatrix method (RSM) is proposed to calculate the lowrank de...
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Simultaneous Diagonalization of Incomplete Matrices and Applications
We consider the problem of recovering the entries of diagonal matrices {...
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Convolutional Imputation of Matrix Networks
A matrix network is a family of matrices, where the relationship between them is modeled as a weighted graph. Each node represents a matrix, and the weight on each edge represents the similarity between the two matrices. Suppose that we observe a few entries of each matrix with noise, and the fraction of entries we observe varies from matrix to matrix. Even worse, a subset of matrices in this family may be completely unobserved. How can we recover the entire matrix network from noisy and incomplete observations? One motivating example is the cold start problem, where we need to do inference on new users or items that come with no information. To recover this network of matrices, we propose a structural assumption that the matrix network can be approximated by generalized convolution of low rank matrices living on the same network. We propose an iterative imputation algorithm to complete the matrix network. This algorithm is efficient for large scale applications and is guaranteed to accurately recover all matrices, as long as there are enough observations accumulated over the network.
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