288 pp. per issue
6 x 9, illustrated
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Neural Computation

November 1, 2001, Vol. 13, No. 11, Pages 2533-2548
(doi: 10.1162/089976601753196012)
© 2001 Massachusetts Institute of Technology
Random Embedding Machines for Pattern Recognition
Article PDF (205.79 KB)

Real classification problems involve structured data that can be essentially grouped into a relatively small number of clusters. It is shown that, under a local clustering condition, a set of points of a given class, embedded in binary space by a set of randomly parameterized surfaces, is linearly separable from other classes, with arbitrarily high probability. We call such a data set a local relative cluster. The size of the embedding set is shown to be inversely proportional to the squared local clustering degree. A simple parameterization by embedding hyperplanes, implementing a voting system, results in a random reduction of the nearest-neighbor method and leads to the separation of multicluster data by a network with two internal layers. This represents a considerable reduction of the learning problem with respect to known techniques, resolving a long-standing question on the complexity of random embedding. Numerical tests show that the proposed method performs as well as state-of the-art methods and in a small fraction of the time.