By Santosh S. Vempala
Random projection is an easy geometric procedure for decreasing the dimensionality of a suite of issues in Euclidean area whereas retaining pairwise distances nearly. The process performs a key function in different leap forward advancements within the box of algorithms. In different situations, it presents based substitute proofs. The e-book starts off with an ordinary description of the strategy and its simple homes. 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 structure. awarded during this context is the speculation of Euclidean embeddings of graphs. the following team is computer studying difficulties, in particular, studying intersections of halfspaces and studying huge margin hypotheses. The projection technique is extra subtle for the latter software. The final set contains difficulties encouraged through details retrieval, specifically, nearest neighbor seek, geometric clustering and effective low-rank approximation. inspired by means of the 1st functions, an extension of random projection to the hypercube is built the following. during the publication, random projection is used in an effort to comprehend, simplify and fix growth on those vital and likely unrelated difficulties. The ebook is acceptable for graduate scholars and study mathematicians drawn to computational geometry.
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