# Linear Time Visualization and Search in Big Data using Pixellated Factor Space Mapping

## TL;DR

This paper introduces a linear time, storage-efficient visualization and search method for large datasets using pixellated factor space mapping, enabling hierarchical clustering and enhanced interpretability.

## Contribution

It proposes a novel pixellated grid approach based on m-adic and p-adic encoding for efficient large data analysis and visualization.

## Key findings

- Linear computational time achieved for large data analysis
- Hierarchical clustering naturally emerges from m-adic and p-adic representations
- Enhanced interpretability and basic processing support in large data visualization

## Abstract

It is demonstrated how linear computational time and storage efficient approaches can be adopted when analyzing very large data sets. More importantly, interpretation is aided and furthermore, basic processing is easily supported. Such basic processing can be the use of supplementary, i.e. contextual, elements, or particular associations. Furthermore pixellated grid cell contents can be utilized as a basic form of imposed clustering. For a given resolution level, here related to an associated m-adic ($m$ here is a non-prime integer) or p-adic ($p$ is prime) number system encoding, such pixellated mapping results in partitioning. The association of a range of m-adic and p-adic representations leads naturally to an imposed hierarchical clustering, with partition levels corresponding to the m-adic-based and p-adic-based representations and displays. In these clustering embedding and imposed cluster structures, some analytical visualization and search applications are described