Wavelet-Based Feature Extraction and Unsupervised Clustering for Parity Detection: A Feature Engineering Perspective

TL;DR

This paper demonstrates that wavelet-based feature extraction combined with unsupervised clustering can classify parity with about 70% accuracy, revealing structural differences in a novel, signal-processing-inspired approach.

Contribution

It introduces a wavelet-based feature engineering method for parity detection, showcasing how classical signal processing can be applied to symbolic data in an unsupervised manner.

Findings

Achieved approximately 69.67% accuracy in parity classification

Revealed structural differences between odd and even numbers in wavelet domain

Illustrated potential of feature engineering for symbolic reasoning tasks

Abstract

This paper explores a deliberately over-engineered approach to the classical problem of parity detection -- determining whether a number is odd or even -- by combining wavelet-based feature extraction with unsupervised clustering. Instead of relying on modular arithmetic, integers are transformed into wavelet-domain representations, from which multi-scale statistical features are extracted and clustered using the k-means algorithm. The resulting feature space reveals meaningful structural differences between odd and even numbers, achieving a classification accuracy of approximately 69.67% without any label supervision. These results suggest that classical signal-processing techniques, originally designed for continuous data, can uncover latent structure even in purely discrete symbolic domains. Beyond parity detection, the study provides an illustrative perspective on how feature engineering and clustering may be repurposed for unconventional machine learning problems, potentially bridging symbolic reasoning and feature-based learning.