Parallel Multidimensional Scaling Performance on Multicore Systems

Abstract

Multidimensional scaling constructs a configuration points into the target low-dimensional space, while the interpoint distances are approximated to the corresponding known dissimilarity values as much as possible. SMACOF algorithm is an elegant gradient descent approach to solve Multidimensional scaling problem. We design parallel SMACOF program using parallel matrix multiplication to run on a multicore machine. Also, we propose a block decomposition algorithm based on the number of threads for the purpose of keeping good load balance. The proposed block decomposition algorithm works very well if the number of block columns is at least a half of the number of threads. In this paper, we investigate performance results of the implemented parallel SMACOF in terms of the block size, data size, and the number of threads. The speedup factor is almost 7.7 with 2048 points data over 8 running threads. In addition, performance comparison between jagged array and two-dimensional array in C# language is carried out. The jagged array data structure performs at least 40% better than the two-dimensional array structure.