Graphics Hardware Implementation of the Parameter-Less Self-Organising Map

This paper presents a highly parallel implementation of a new type of Self-Organising Map (SOM) using graphics hardware. The Parameter-Less SOM smoothly adapts to new data while preserving the mapping formed by previous data. It is therefore in principle highly suited for interactive use, however for large data sets the computational requirements are prohibitive. This paper will present an implementation on commodity graphics hardware which uses two forms of parallelism to signi¯cantly reduce this barrier. The performance is analysed experi- mentally and algorithmically. An advantage to using graphics hardware is that visualisation is essentially free", thus increasing its suitability for interactive exploration of large data sets

Uncertainty-Aware Principal Component Analysis

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to non-linear methods, linear dimensionality reduction techniques have the advantage that the characteristics of such probability distributions remain intact after projection. We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data. For this, we propose factor traces as a novel visualization that enables to better understand the influence of uncertainty on the chosen principal components. We provide multiple examples of our technique using real-world datasets. As a special case, we show how to propagate multivariate normal distributions through PCA in closed form. Furthermore, we discuss extensions and limitations of our approach

Enhanced molecular dynamics performance with a programmable graphics processor

Design considerations for molecular dynamics algorithms capable of taking advantage of the computational power of a graphics processing unit (GPU) are described. Accommodating the constraints of scalable streaming-multiprocessor hardware necessitates a reformulation of the underlying algorithm. Performance measurements demonstrate the considerable benefit and cost-effectiveness of such an approach, which produces a factor of 2.5 speed improvement over previous work for the case of the soft-sphere potential.Comment: 20 pages (v2: minor additions and changes; v3: corrected typos

Fast kk-NNG construction with GPU-based quick multi-select

In this paper we describe a new brute force algorithm for building the $k$-Nearest Neighbor Graph ($k$-NNG). The $k$-NNG algorithm has many applications in areas such as machine learning, bio-informatics, and clustering analysis. While there are very efficient algorithms for data of low dimensions, for high dimensional data the brute force search is the best algorithm. There are two main parts to the algorithm: the first part is finding the distances between the input vectors which may be formulated as a matrix multiplication problem. The second is the selection of the $k$-NNs for each of the query vectors. For the second part, we describe a novel graphics processing unit (GPU) -based multi-select algorithm based on quick sort. Our optimization makes clever use of warp voting functions available on the latest GPUs along with use-controlled cache. Benchmarks show significant improvement over state-of-the-art implementations of the $k$-NN search on GPUs