标题： 基于小波的特征提取与无监督聚类用于奇偶性检测：一种特征工程视角 显示英文标题

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

摘要： 本文探讨了一种故意过度设计的方法，用于解决经典的奇偶性检测问题——确定一个数是奇数还是偶数——通过结合小波基特征提取与无监督聚类。 而不是依赖模运算，整数被转换为小波域表示，从中提取多尺度统计特征，并使用k均值算法进行聚类。 结果特征空间揭示了奇数和偶数之间的有意义结构差异，在没有任何标签监督的情况下实现了约69.67%的分类准确率。 这些结果表明，最初为连续数据设计的经典信号处理技术，甚至可以在纯粹的离散符号领域中发现潜在结构。 除了奇偶性检测外，该研究提供了一个说明性的视角，展示了特征工程和聚类如何被重新用于非常规机器学习问题，可能在符号推理和基于特征的学习之间架起桥梁。 显示英文摘要

摘要： 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.