Mathematical Computation on High-dimensional Data via Array Programming and Parallel Acceleration

TL;DR

This paper introduces a parallel computation framework that decomposes high-dimensional data into dimension-independent structures, enabling efficient scientific analysis and machine learning across diverse data types.

Contribution

It presents a novel parallel architecture based on space completeness, facilitating advanced mathematical analysis of high-dimensional data with distributed processing.

Findings

Supports diverse data types like medical and natural images

Enables integration of data mining and machine learning methods

Improves computational efficiency for high-dimensional data analysis

Abstract

While deep learning excels in natural image and language processing, its application to high-dimensional data faces computational challenges due to the dimensionality curse. Current large-scale data tools focus on business-oriented descriptive statistics, lacking mathematical statistics support for advanced analysis. We propose a parallel computation architecture based on space completeness, decomposing high-dimensional data into dimension-independent structures for distributed processing. This framework enables seamless integration of data mining and parallel-optimized machine learning methods, supporting scientific computations across diverse data types like medical and natural images within a unified system.