211,051 research outputs found

    Principal Component Analysis and Higher Correlations for Distributed Data

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    We consider algorithmic problems in the setting in which the input data has been partitioned arbitrarily on many servers. The goal is to compute a function of all the data, and the bottleneck is the communication used by the algorithm. We present algorithms for two illustrative problems on massive data sets: (1) computing a low-rank approximation of a matrix A=A1+A2+…+AsA=A^1 + A^2 + \ldots + A^s, with matrix AtA^t stored on server tt and (2) computing a function of a vector a1+a2+…+asa_1 + a_2 + \ldots + a_s, where server tt has the vector ata_t; this includes the well-studied special case of computing frequency moments and separable functions, as well as higher-order correlations such as the number of subgraphs of a specified type occurring in a graph. For both problems we give algorithms with nearly optimal communication, and in particular the only dependence on nn, the size of the data, is in the number of bits needed to represent indices and words (O(log⁑n)O(\log n)).Comment: rewritten with focus on two main results (distributed PCA, higher-order moments and correlations) in the arbitrary partition mode

    A Tutorial on Independent Component Analysis

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    Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating an intuition for ICA from first principles. The goal of this tutorial is to provide a solid foundation on this advanced topic so that one might learn the motivation behind ICA, learn why and when to apply this technique and in the process gain an introduction to this exciting field of active research
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