Scalable approximate FRNN-OWA classification

Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1

DEVELOPMENT AND INVESTIGATION OF CHEMOMETRIC BASELINE CORRECTION APPROACHES AND METABONOMIC CLASSIFICATION ALGORITHMS

Ph.DDOCTOR OF PHILOSOPH