# RecurSIA-RRT: Recursive translatable point-set pattern discovery with removal of redundant translators

## TL;DR

This paper presents RECURSIA and RRT algorithms that enhance pattern discovery and compression in point-set data by recursively applying TEC cover algorithms and removing redundant translators, improving compression and recall.

## Contribution

The paper introduces recursive TEC cover algorithms and a translator removal technique to improve pattern compression in point-set pattern discovery.

## Key findings

- Increased compression factor and recall with RECURSIA.
- RRT reduces translators, increasing compression but lowering precision.
- RECURSIA with RRT outperforms existing algorithms in compression.

## Abstract

We introduce two algorithms, RECURSIA and RRT, designed to increase the compression factor achievable using point-set cover algorithms based on the SIA and SIATEC pattern discovery algorithms. SIA computes the maximal translatable patterns (MTPs) in a point set, while SIATEC computes the translational equivalence class (TEC) of every MTP in a point set, where the TEC of an MTP is the set of translationally invariant occurrences of that MTP in the point set. In its output, SIATEC encodes each MTP TEC as a pair, <P,V>, where P is the first occurrence of the MTP and V is the set of non-zero vectors that map P onto its other occurrences. RECURSIA recursively applies a TEC cover algorithm to the pattern P, in each TEC, <P,V>, that it discovers. RRT attempts to remove translators from V in each TEC without reducing the total set of points covered by the TEC. When evaluated with COSIATEC, SIATECCompress and Forth's algorithm on the JKU Patterns Development Database, using RECURSIA with or without RRT increased compression factor and recall but reduced precision. Using RRT alone increased compression factor and reduced recall and precision, but had a smaller effect than RECURSIA.