Aceleração de uma variação do problema k-nearest neighbors

• Autor(a) principal: Morais Neto, Jorge Peixoto de
• Data de Publicação: 2014
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/3687
• topic: Aceleração; Análise de dados multidimensionais; K-nearest neighbors; K vizinhos mais próximos; Matriz circulante; Processamento de imagem; Programação paralela; Transformada rápida de Fourier; Acceleration; K-nearest neighbors; Circulant matrix; Image processing; Fast Fourier transform; Multidimensional data analysis; Parallel programming; CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

Let M be a metric space and let P be a subset of M. The well known k-nearest neighbors problem (KNN) consists in finding, given q 2 M, the k elements of P with are closest to q according to the metric of M. We discuss a variation of KNN for a particular class of pseudo-metric spaces, described as follows. Let m 2 N be a natural number and let d be the Euclidean distance in Rm. Given p 2 Rm: p := (p1; : : : ; pm) let C (p) be the set of the m rotations of p’s coordinates: C (p) := f(p1; : : : ; pm); (p2; : : : ; pm; p1); : : : ; (pm; p1; : : : ; pm1)g we define the special distance de as: de(p;q) := min p02C (p) d(p0;q): de is a pseudo-metric, and (Rm;de) is a pseudo-metric space. The class of pseudo-metric spaces under discussion is f(Rm;de) j m 2 N:g The brute force approach is too costly for instances of practical size. We present a more efficient solution employing parallelism, the FFT (fast Fourier transform) and the fast elimination of unfavorable training vectors.We describe a program—named CyclicKNN —which implements this solution.We report the speedup of this program over serial brute force search, processing reference datasets.