By Santosh S. Vempala
Random projection is a straightforward geometric method for lowering the dimensionality of a collection of issues in Euclidean area whereas conserving pairwise distances nearly. The procedure performs a key function in numerous leap forward advancements within the box of algorithms. In different situations, it presents dependent substitute proofs. The e-book starts with an effortless description of the approach and its easy houses. Then it develops the strategy within the context of purposes, that are divided into 3 teams. the 1st staff involves combinatorial optimization difficulties reminiscent of maxcut, graph coloring, minimal multicut, graph bandwidth and VLSI format. awarded during this context is the speculation of Euclidean embeddings of graphs. the subsequent crew is laptop studying difficulties, particularly, studying intersections of halfspaces and studying huge margin hypotheses. The projection strategy is extra sophisticated for the latter program. The final set includes difficulties encouraged by means of info retrieval, particularly, nearest neighbor seek, geometric clustering and effective low-rank approximation. influenced by way of the 1st functions, an extension of random projection to the hypercube is constructed the following. in the course of the publication, random projection is used that allows you to comprehend, simplify and fix development on those very important and doubtless unrelated difficulties. The booklet is appropriate for graduate scholars and learn mathematicians drawn to computational geometry.
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