用两种距离度量改进k-means，提升聚类准确性和异常值处理能力。
A novel k-means clustering approach using two distance measures for Gaussian data
- 融合类内距与类间距作为距离度量，优化聚类过程。
- 在合成数据和UCI基准数据集上，聚类收敛更准确。
- 对异常值的识别与归类优于传统k-means方法。
聚类算法是无监督学习中研究最广泛的方向之一。为从原始数据中挖掘结构与规律，本文提出一种新型k-means聚类方法，同时采用类内距离（WCD）和类间距离（ICD）作为距离度量，结合Calinski-Harabasz准则确定预设聚类数k，以增强聚类结果的鲁棒性。该方法通过引入双重距离度量，使数据向所属簇的收敛更加稳定可靠。实验使用合成数据及来自UCI数据集的基准数据进行验证，结果表明，相比传统k-means，该方法在聚类准确性方面表现更优，尤其能更有效地将异常值归入其真实簇中。此外，研究还揭示了一些值得进一步探索的潜在方向。
原文摘要 · Abstract (English)
Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper explores a novel approach to k-means clustering. Here we present a k-means clustering algorithm that takes both the within cluster distance (WCD) and the inter cluster distance (ICD) as the distance metric to cluster the data into k clusters pre-determined by the Calinski-Harabasz criterion in order to provide a more robust output for the clustering analysis. The idea with this approach is that by including both the measurement metrics, the convergence of the data into their clusters becomes solidified and more robust. We run the algorithm with some synthetically produced data and also some benchmark data sets obtained from the UCI repository. The results show that the convergence of the data into their respective clusters is more accurate by using both WCD and ICD measurement metrics. The algorithm is also better at clustering the outliers into their true clusters as opposed to the traditional k means method. We also address some interesting possible research topics that reveal themselves as we answer the questions we initially set out to address.
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