Improving hybrid MDS with pivot-based searching

Abstract

An algorithm is presented for the visualisation of multidimensional abstract data, building on a hybrid model introduced at InfoVis 2002. The most computationally complex stage of the original model involved performing a nearestneighbour search for every data item. The complexity of this phase has been reduced by treating all high-dimensional relationships as a set of discretised distances to a constant number of randomly selected pivot items. In improving this computational bottleneck, the complexity is reduced from). As well as documenting this improvement, the paper describes evaluation with a data set of 108000 14-dimensional items; a considerable increase on the size of data previously tested. Results illustrate that the reduction in complexity is reflected in significantly improved run times and that no negative impact is made upon the quality of layout produced.

Eigensolver Methods for Progressive Multidimensional Scaling of Large Data

“…It was addressed as early as in the 1960s [23], and since then, many approaches to speeding up spring-force computations have been devised [6,16,25,26]. Likewise, methods for speeding up the spectral methods have been proposed [11,31].…”

Steerable, Progressive Multidimensional Scaling

“…In 2003 Morrison [11,13] improved the performance of computing starting spots for unplaced points by applying an efficient nearest-neighbor search technique at the interpolation stage. The hierarchical binning approach we developed to provide steerability also allows us to find a good starting location for unplaced points efficiently, so we present an alternate approach.…”

“…Dimensionality reduction techniques have been published in many fields: psychology [9,18], cartography [7], machine learning [16,17], and information visualization [1,4,11,12,13]. Error minimization requires many computationally expensive highdimensional distance or matrix computations, and the challenge is reducing the cost and number of these calculations.…”

“…Methods with an O(n 2 ) cost that can handle * e-mail: mwill@cs.ubc.ca † e-mail: tmm@cs.ubc.ca thousands of points have become common [1,4,9,10]. Recently, a subquadratic algorithm was proposed by Morrison that could lay out thousands of points in minutes [11,12,13]. Despite the extensive previous work, there is a gap in the literature: no currently available algorithm or system allows interactive exploration of high-dimensional datasets with both a large number of dimensions and a large number of points.…”

“…Despite the extensive previous work, there is a gap in the literature: no currently available algorithm or system allows interactive exploration of high-dimensional datasets with both a large number of dimensions and a large number of points. Although Morrison does handle hundreds of thousands of points in minutes [11,12], that is only true when the number of dimensions is low. On our real-world dataset of 120,000 nodes and 294 dimensions, the HIVE system [15] took over 2 hours to compute the layout.…”