Franco Woolfe

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We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular value decompositions of numerically low-rank matrices. Being probabilistic, the schemes described here have a finite probability of failure; in most cases, this(More)
We introduce a randomized procedure that, given an m×n matrix A and a positive integer k, approximates A with a matrix Z of rank k. The algorithm relies on applying a structured l×m random matrix R to each column of A, where l is an integer near to, but greater than, k. The structure of R allows us to apply it to an arbitrary m× 1 vector at a cost(More)
We introduce a fast algorithm for the numerical application to arbitrary vectors of several special function transforms. The algorithm requires O(n log(n)) operations to apply to an arbitrary vector any n×n matrix such that the rank of any p×q contiguous submatrix is bounded by a constant times pq/n. These rank bounds are proven here for the case of the(More)
The spectral study of cancer dates back 50 years, but it is still not known whether spectral measurements suffice to distinguish cancerous from normal tissue. An objective approach to that question is designing automatic classifiers for discrimination between these two classes and then estimating generalization error rates. Previous studies have not(More)
Given an m × n matrix A and a positive integer k, we introduce a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying an l×m random matrix with special structure to each column of A, where l is an integer near to, but greater than k. The spectral norm ‖A−Z‖ of the discrepancy between A and Z is of the(More)
Following spinal cord injury (SCI), descending axons that carry motor commands from the brain to the spinal cord are injured or transected, producing chronic motor dysfunction and paralysis. Reconnection of these axons is a major prerequisite for restoration of function after SCI. Thus far, only modest gains in motor function have been achieved(More)
This paper describes a new, physically interpretable, fully automatic algorithm for removal of tissue autofluorescence (AF) from fluorescence microscopy images, by non-negative matrix factorization. Measurement of signal intensities from the concentration of certain fluorescent reporter molecules at each location within a sample of biological tissue is(More)
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