Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a few digits (measured in the spectral norm, relative

This paper is concerned with the computation of the principal components for a general tensor, known as the tensor principal component analysis (PCA) problem. We show that the general tensor PCA problem is reducible to its special case where the tensor in question is supersymmetric with an even

) that are not satisfied, by successively choosing a random literal from such a clause and flipping the corresponding bit, try to find a satisfying assignment. If no satisfying assignment is found after O(n) steps, start over again. Our analysis shows that for any satisfiable k-CNF formula with n variables this process

Singular Value Decomposition (and Principal Component Analysis) is one of the most widely used techniques for dimensionality reduction: successful and efficiently computable, it is nevertheless plagued by a well-known, well-documented sensitivity to outliers. Recent work has considered the setting

centrality measure by dividing by the maximum possible degree in an n-actor network (i.e., n-1). While we normalize the centrality measures used in the empirical analysis, we note that all our results are robust to using non-normalized network centrality measures instead. 8 B. Closeness While degree counts

distribution of the first hitting times of the target are thoroughly computed (expectation and variance) up to terms of order l (the size of the bitstrings) in two distinct situations: without any selection, or with the deterministic (1+1)-ES selection on the OneMax problem. In both cases, the 1-bit-flip

Abstract — On-chip spike detection and principal component analysis (PCA) sorting hardware in an integrated multi-channel neural recording system is highly desired to ease the bandwidth bottleneck from high-density microelectrode array implanted in the cortex. In this paper, we propose the first

. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find

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identification, latent variable graphical modeling, and principal components analysis. We study conditions under which recovering such a decomposition is possible via a combination of ℓ1 norm and trace norm minimization. We are specifically interested in the question of how many sparse corruptions are allowed so