用小波分析和聚类检测奇偶数，无标签也能达到70%准确率。
Wavelet-Based Feature Extraction and Unsupervised Clustering for Parity Detection: A Feature Engineering Perspective
- 将整数转为小波域，提取多尺度统计特征
- 无监督聚类实现69.67%奇偶分类准确率
- 展示信号处理技术在符号数据中的新应用
本文探索了一种过度工程化的方法来解决经典的奇偶性检测问题——判断一个数是奇数还是偶数。不同于传统的模运算，该方法将整数转换为小波域表示，并从中提取多尺度统计特征，再使用k-means算法进行无监督聚类。结果表明，所生成的特征空间能揭示奇数与偶数之间的有意义结构差异，在无任何标签监督的情况下实现了约69.67%的分类准确率。这说明原本为连续数据设计的经典信号处理技术，也可在纯离散符号域中发现潜在结构。本研究不仅为奇偶检测提供了新视角，更展示了特征工程与聚类方法在非传统机器学习任务中的可复用性，或可促进符号推理与基于特征的学习之间的融合。
原文摘要 · Abstract (English)
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.
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