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

Data-Driven Process Discovery: A Discrete Time Algebra for Relational Signal Analysis

This research presents an autonomous and computationally tractable method for scientific process analysis, combining an iterative algorithmic search and a recognition technique to discover multivariate linear and non-linear relations within experimental data series. These resultant data-driven relations provide researchers with a potentially real-time insight into experimental process phenomena and behavior. This method enables the efficient search of a potentially infinite space of relations within large data series to identify relations that accurately represent process phenomena. Proposed is a time series transformation that encodes and compresses real-valued data into a well-defined, discrete-space of 13 primitive elements where comparative evaluation between variables is both plausible and heuristically efficient. Additionally, this research develops and demonstrates binary discrete-space operations which accurately parallel their numeric-space equivalents. These operations extend the method\u27s utility into trivariate relational analysis, and experimental evidence is offered supporting the existence of traceable multivariate signatures of incremental order within the discrete-space that can be exploited for higher dimensional analysis by means of an iterative best-n first search

Efficient Algorithms for Artificial Neural Networks and Explainable AI

Artificial neural networks have allowed some remarkable progress in fields such as pattern recognition and computer vision. However, the increasing complexity of artificial neural networks presents a challenge for efficient computation. In this thesis, we first introduce a novel matrix multiplication method to reduce the complexity of artificial neural networks, where we demonstrate its suitability to compress fully connected layers of artificial neural networks. Our method outperforms other state-of-the-art methods when tested on standard publicly available datasets. This thesis then focuses on Explainable AI, which can be critical in fields like finance and medicine, as it can provide explanations for some decisions taken by sub-symbolic AI models behaving like a black box such as Artificial neural networks and transformation based learning approaches. We have also developed a new framework that facilitates the use of Explainable AI with tabular datasets. Our new framework Exmed, enables nonexpert users to prepare data, train models, and apply Explainable AI techniques effectively.Additionally, we propose a new algorithm that identifies the overall influence of input features and minimises the perturbations that alter the decision taken by a given model. Overall, this thesis introduces innovative and comprehensive techniques to enhance the efficiency of fully connected layers in artificial neural networks and provide a new approach to explain their decisions. These methods have significant practical applications in various fields, including portable medical devices