Dimension reduction and visualization of large high-dimensional data via interpolation

Abstract

The recent explosion of publicly available biology gene sequences and chemical compounds offers an unprecedented opportunity for data mining. To make data analysis feasible for such vast volume and high-dimensional scientific data, we apply high performance dimension reduction algorithms. It facilitates the investigation of unknown structures in a three dimensional visualization. Among the known dimension reduction algorithms, we utilize the multidimensional scaling and generative topographic mapping algorithms to configure the given high-dimensional data into the target dimension. However, both algorithms require large physical memory as well as computational resources. Thus, the authors propose an interpolated approach to utilizing the mapping of only a subset of the given data. This approach effectively reduces computational complexity. With minor trade-off of approximation, interpolation method makes it possible to process millions of data points with modest amounts of computation and memory requirement. Since huge amount of data are dealt, we represent how to parallelize proposed interpolation algorithms, as well. For the evaluation of the interpolated MDS by STRESS criteria, it is necessary to compute symmetric all pairwise computation with only subset of required data per process, so we also propose a simple but efficient parallel mechanism for the symmetric all pairwise computation when only a subset of data is available to each process. Our experimental results illustrate that the quality of interpolated mapping results are comparable to the mapping Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. HPDC '10 Chicago, Illinois USA Copyright 2010 ACM X-XXXXX-XX-X/XX/XX ...$10.00. results of original algorithm only. In parallel performance aspect, those interpolation methods are well parallelized with high efficiency. With the proposed interpolation method, we construct a configuration of two-million out-of-sample data into the target dimension, and the number of out-of-sample data can be increased further.

Browsing large scale cheminformatics data with dimension reduction

“…Authors have been researching on developing high performance visualization algorithms, such as parallel MDS and GTM and their interpolation extensions [7,8], to visualize large PubChem dataset in 3D space by using our in-house 3D data point visualization tool and now we extend its functionality to access external data sources in a dynamic way.…”

Multidimensional Scaling by Deterministic Annealing with Iterative Majorization Algorithm

“…Also, DAexp95 results are very similar to or even better than DA-exp99 results although DA-exp95 takes shorter time than DA-exp99 case. In future work, we will integrate these ideas with the interpolation technology described in [29] to give a robust approach to dimension reduction of large datasets that scales like O(N) rather O(N 2 ) of general MDS methods.…”

A Robust and Scalable Solution for Interpolative Multidimensional Scaling with Weighting

“…It has applied linear discriminant analysis to the labeled objects in the representation space. In contrast to them, [7] has proposed an EM-like optimization solution, called MI-MDS to solve the problem with STRESS criteria in (26), which found embedding of approximating to the distance rather than the inner product as in CMDS. In addition to that, [6] has proposed a heuristic method, called HE-MI, to lower the time cost of MI-MDS.…”

“…MI-MDS is an iterative majorization algorithm proposed by [7] to minimize the STRESS value in (32), where all weights are assumed to be 1. It will find nearest neighbors from insample points of a given out-of-sample point � at first, denoted as = { 1 , 2 , 3 , … , } .…”

“…Then MDS uses the result from it as input. Furthermore, to deal with largescale data, DACIDR uses an interpolation algorithm called Majorizing Iterative MDS (MI-MDS) [7] to reduce the memory usage. It has been proven that DACIDR could visualize and cluster over millions of sequences with limited computing power.…”