How to optimize K-means?

TL;DR

ADHCR addresses anomaly detection by transforming data into a two-cluster ADHCR space that combines local density and double-density features. It then employs a two-stage component clustering approach, first in the double-density dimension via delta clustering and then in the density dimension, to isolate anomalies as a cohesive cluster distinct from normal data. The method demonstrates robustness across complex distributions, varying levels of overlap, differing anomaly counts, and unbalanced densities, achieving strong accuracy on ten real-world datasets with low parameter sensitivity. The work contributes the ADHCR feature space, the component clustering strategy, and comprehensive empirical validation, offering a practical and scalable anomaly detection framework for diverse applications.

Abstract

Center-based clustering algorithms (e.g., K-means) are popular for clustering tasks, but they usually struggle to achieve high accuracy on complex datasets. We believe the main reason is that traditional center-based clustering algorithms identify only one clustering center in each cluster. Once the distribution of the dataset is complex, a single clustering center cannot strongly represent distant objects within the cluster. How to optimize the existing center-based clustering algorithms will be valuable research. In this paper, we propose a general optimization method called ECAC, and it can optimize different center-based clustering algorithms. ECAC is independent of the clustering principle and is embedded as a component between the center process and the category assignment process of center-based clustering algorithms. Specifically, ECAC identifies several extended-centers for each clustering center. The extended-centers will act as relays to expand the representative capability of the clustering center in the complex cluster, thus improving the accuracy of center-based clustering algorithms. We conducted numerous experiments to verify the robustness and effectiveness of ECAC. ECAC is robust to diverse datasets and diverse clustering centers. After ECAC optimization, the accuracy (NMI as well as RI) of center-based clustering algorithms improves by an average of 33.4% and 64.1%, respectively, and even K-means accurately identifies complex-shaped clusters.

Figures (9)

• Figure 1: An example of ADHCR. The dataset is transformed into a new feature space, where normal objects and anomalies are divided into two clusters. The two clusters can be easily identified by a clustering algorithm. Finally, identified results are mapped back to the original distribution, and anomalies are successfully detected.
• Figure 2: Constructing ADHCR space.
• Figure 3: clustering.
• Figure 4: Robustness on distribution. Original distribution ($A,B$) and detected anomalies ($C,D$) of t4.8k ($A,C$), t7.10k ($B,D$). ADHCR successfully detects ‘sin’ anomalies and ‘vertical lines’ anomalies interspersed between normal objects. Its performances are reliable in the anomalies with complex distributions.
• Figure 5: Robustness on overlap. Original distribution ($A,B,C$) and detected anomalies ($D,E,F$) of overlap-none ($A,D$), overlap-half ($B,E$), overlap-whole ($C,F$). From dataset overlap-none to overlap-whole, the degree of overlap between the anomalies area and the normal objects area is increasing. ADHCR is not affected by the degree of overlap, all detected results are accurate.