Efficient algorithms for the optical multi-trees (OMULT) architecture.

In this thesis, we have reported our investigations on efficiently implementing algorithms on the recently proposed Optical Multi-Trees (OMULT) multi-processors interconnection architecture that uses both electronic and optical links among processors. We have investigated algorithms for matrix multiplication of two matrices of size n2 x n2 and two matrices of arbitrary size, the prefix-sum of a series and some fundamental computational geometry problems. We show that some common algorithms for computational geometry---finding the convex hull, the smallest enclosing box, the empirical cumulative distribution function and the all-nearest neighbor problems of n data points can be computed on the OMULT network in O(log n) time, compared to O(√n) algorithms on the Optical Transpose Interconnection System (OTIS) mesh for each of these problems. Finally we have implemented our algorithm for matrix multiplication using the SimJava simulation tool and feel that this is a convenient environment for testing such parallel algorithms.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .I85. Source: Masters Abstracts International, Volume: 43-05, page: 1751. Adviser: Subir Bandyopadhyay. Thesis (M.Sc.)--University of Windsor (Canada), 2004

An Attempt to Find Neighbors

In this paper, we present our continuous research on similarity search problems. Previously we proposed PanKNN[18]which is a novel technique that explores the meaning of K nearest neighbors from a new perspective, redefines the distances between data points and a given query point Q, and efficiently and effectively selects data points which are closest to Q. It can be applied in various data mining fields. In this paper, we present our approach to solving the similarity search problem in the presence of obstacles. We apply the concept of obstacle points and process the similarity search problems in a different way. This approach can assist to improve the performance of existing data analysis approaches

Towards Solving Similarity Search Problems Using Fuzzy Concept for Multi-Dimensional Data

In this paper, we present continuous research on data analysis based on our previous work on similarity search problems. PanKNN[13] is a novel technique which explores the meaning of K nearest neighbors from a new perspective, redefines the distances between data points and a given query point Q, and efficiently and effectively select data points which are closest to Q. It can be applied in various data mining fields. In this paper, we applied the Fuzzy concept to improve the performance of PanKNN, targeting the better decision making for the calculation of the distance between a data point and Q. This approach can assist to improve the performance of existing data analysis approaches

Compact Random Feature Maps

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this challenge, we propose compact random feature maps (CRAFTMaps) to approximate polynomial kernels more concisely and accurately. We prove the error bounds of CRAFTMaps demonstrating their superior kernel reconstruction performance compared to the previous approximation schemes. We show how structured random matrices can be used to efficiently generate CRAFTMaps, and present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class classifiers. We present experiments on multiple standard data-sets with performance competitive with state-of-the-art results.Comment: 9 page