对比三种聚类算法在高维数据的表现，发现降维方法影响大，选算法要看数据特点。
Unsupervised Learning: Comparative Analysis of Clustering Techniques on High-Dimensional Data
- 用PCA、t-SNE、UMAP降维后比较K-means、DBSCAN、谱聚类性能
- UMAP预处理让所有算法聚类效果提升，谱聚类在复杂结构上最优
- 不同数据选不同算法：快选K-means，不规则簇选DBSCAN，复杂关系选谱聚类
本文对K-means、DBSCAN和谱聚类在高维数据上的表现进行了系统性对比分析。提出一种新的评估框架，结合多种降维技术（PCA、t-SNE、UMAP）与多维度量化指标进行测试。在MNIST、Fashion-MNIST和UCI HAR数据集上的实验表明，使用UMAP预处理能持续提升所有算法的聚类质量；谱聚类在复杂流形结构上表现最优。研究发现，算法选择应依据数据特征：K-means在计算效率上占优，DBSCAN擅长处理非规则簇，谱聚类更擅长捕捉复杂关系。本研究为高维数据聚类技术的评估与选择提供了系统化方法。
原文摘要 · Abstract (English)
This paper presents a comprehensive comparative analysis of prominent clustering algorithms K-means, DBSCAN, and Spectral Clustering on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering performance across multiple dimensionality reduction techniques (PCA, t-SNE, and UMAP) using diverse quantitative metrics. Experiments conducted on MNIST, Fashion-MNIST, and UCI HAR datasets reveal that preprocessing with UMAP consistently improves clustering quality across all algorithms, with Spectral Clustering demonstrating superior performance on complex manifold structures. Our findings show that algorithm selection should be guided by data characteristics, with Kmeans excelling in computational efficiency, DBSCAN in handling irregular clusters, and Spectral Clustering in capturing complex relationships. This research contributes a systematic approach for evaluating and selecting clustering techniques for high dimensional data applications.
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