Fast Algorithms on Random Matrices and Structured Matrices by Liang Zhao
Randomization of matrix computations has become a hot research area in the big data era. Sampling with randomly generated matrices has enabled fast algorithms to perform well for some most fundamental problems of numerical algebra with probability close to 1. The dissertation develops a set of algorithms with random and structured matrices for the following applications: 1) We prove that using random sparse and structured sampling enables rank-r approximation of the average input matrix having numerical rank r. 2) We prove that Gaussian elimination with no pivoting (GENP) is numerically safe for the average nonsingular and well-conditioned matrix preprocessed with a nonsingular and well-conditioned f-Circulant or another v structured multiplier. This can be an attractive alternative to the customary Gaussian elimination with partial pivoting (GEPP). 3) By using structured matrices of a large family we compress large-scale neural networks while retaining high accuracy. The results of our extensive are in good accordance with those of our theoretical study.
Image Credit: NASA/JPL-Caltech/Space Science Institute
N00281695.jpg was taken on 2017-05-14 19:21 (PDT) and received on Earth 2017-05-15 06:09 (PDT). The camera was pointing toward Saturn-rings, and the image was taken using the CL1 and CL2 filters.
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1 comment:
I'll read that paper later:
On this video about lasso:
https://youtu.be/Hn8NtydkeDs
I made this comment:
"You are saying that the reconstructed data lies on an L1 manifold. You can learn a manifold using say a single layer neural network autoencoder. Then to reconstruct you can invert the dimensionally reduced data, get the autoencoder to correct it, send it back through the dimensional reduction and correct only the reduced aspect. Just bounce back and forth between the two.
Or you could set the manifold to be the moving average of the data which is a very easy manifold to correct to and bounce between the two. Anyway: https://drive.google.com/open?id=0BwsgMLjV0BnhOGNxOTVITHY1U28"
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