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.

翻译：本文对K-means、DBSCAN和谱聚类三种主流聚类算法在高维数据集上进行了系统性对比分析。我们提出了一种新颖的评估框架，通过多种量化指标结合不同降维技术（PCA、t-SNE和UMAP）来综合评价聚类性能。在MNIST、Fashion-MNIST和UCI HAR数据集上的实验表明：UMAP预处理能持续提升所有算法的聚类质量，其中谱聚类在复杂流形结构上表现最优。研究发现算法选择应遵循数据特性——K-means在计算效率方面具有优势，DBSCAN擅长处理不规则簇结构，而谱聚类在捕捉复杂关系时表现突出。本研究为高维数据应用中的聚类技术评估与选择提供了系统性方法。