Pattern Classification In Symbolic Streams via Semantic Annihilation of Information

TL;DR

This paper introduces a novel pattern classification method for symbolic streams that uses semantic annihilation to erase patterns, transforming sequences into white noise for accurate detection, with theoretical guarantees and simulation validation.

Contribution

It presents a new algebraic framework for pattern classification in symbolic data using semantic annihilators based on PFSA models, offering theoretical advantages over existing methods.

Findings

Semantic annihilators effectively identify patterns in symbolic streams.

The method guarantees perfect pattern detection under certain conditions.

Simulation results validate the theoretical advantages of the approach.

Abstract

We propose a technique for pattern classification in symbolic streams via selective erasure of observed symbols, in cases where the patterns of interest are represented as Probabilistic Finite State Automata (PFSA). We define an additive abelian group for a slightly restricted subset of probabilistic finite state automata (PFSA), and the group sum is used to formulate pattern-specific semantic annihilators. The annihilators attempt to identify pre-specified patterns via removal of essentially all inter-symbol correlations from observed sequences, thereby turning them into symbolic white noise. Thus a perfect annihilation corresponds to a perfect pattern match. This approach of classification via information annihilation is shown to be strictly advantageous, with theoretical guarantees, for a large class of PFSA models. The results are supported by simulation experiments.