Sparse p-Adic Data Coding for Computationally Efficient and Effective Big Data Analytics

TL;DR

This paper introduces a p-adic sparse coding method for big data that enables efficient storage, linear processing, and constant-time search and retrieval, improving data encoding and display.

Contribution

The paper develops a novel p-adic sparse coding framework that replaces traditional sparsity criteria with p-adic norms, offering computational efficiency and effective data structuring.

Findings

Linear computational time for data processing

Constant time search and retrieval for bounded p-adic norm data

Effective content-driven data encoding and display

Abstract

We develop the theory and practical implementation of p-adic sparse coding of data. Rather than the standard, sparsifying criterion that uses the $L_0$ pseudo-norm, we use the p-adic norm. We require that the hierarchy or tree be node-ranked, as is standard practice in agglomerative and other hierarchical clustering, but not necessarily with decision trees. In order to structure the data, all computational processing operations are direct reading of the data, or are bounded by a constant number of direct readings of the data, implying linear computational time. Through p-adic sparse data coding, efficient storage results, and for bounded p-adic norm stored data, search and retrieval are constant time operations. Examples show the effectiveness of this new approach to content-driven encoding and displaying of data.