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Using Locality-Sensitive Hashing for SVM Classification of Large Data Sets

We propose a novel method using Locality-Sensitive Hashing (LSH) for solving the optimization problem that arises in the training stage of support vector machines for large data sets, possibly in high dimensions. LSH was introduced as an efficient way to look for neighbors in high dimensional spaces. Random projections-based LSH functions create bins so that when great probability points belonging to the same bin are close, the points that are far will not be in the same bin. Based on these bins, it is not necessary to consider the whole original set but representatives in each one of them, thus reducing the effective size of the data set. A key of our proposal is that we work with the feature space and use only the projections to search for closeness in this space. Moreover, instead of choosing the projection directions at random, we sample a small subset and solve the associated SVM problem. Projections in this direction allows for a more precise sample in many cases and an approximation of the solution of the large problem is found in a fraction of the running time with small degradation of the classification error. We present two algorithms, theoretical support, and numerical experiments showing their performances on real life problems taken from the LIBSVM data base.