DelTriC: A Novel Clustering Method with Accurate Outlier

2025-11-21

AI Summary

Traditional clustering methods (e.g., k-means, DBSCAN, HDBSCAN) suffer from degraded performance and weak outlier detection in high-dimensional data due to the curse of dimensionality. To address this, we propose DelTriC—a novel framework that decouples neighborhood construction from clustering decision. Its core innovation lies in first reducing dimensionality via PCA or UMAP, then constructing a Delaunay triangulation-based neighborhood graph in the low-dimensional space; subsequently, a reverse-projection mechanism maps this graph back to the original high-dimensional space to enable robust edge pruning, connected-component merging, and outlier identification. This design effectively mitigates dimensional distortion of neighborhood relationships, significantly improving both clustering accuracy and outlier detection robustness. Extensive experiments on multiple high-dimensional benchmark datasets demonstrate that DelTriC consistently outperforms state-of-the-art baselines, while maintaining scalability and practical applicability.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Clustering
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The paper introduces DelTriC (Delaunay Triangulation Clustering), a clustering algorithm which integrates PCA/UMAP-based projection, Delaunay triangulation, and a novel back-projection mechanism to form clusters in the original high-dimensional space. DelTriC decouples neighborhood construction from decision-making by first triangulating in a low-dimensional proxy to index local adjacency, and then back-projecting to the original space to perform robust edge pruning, merging, and anomaly detection. DelTriC can outperform traditional methods such as k-means, DBSCAN, and HDBSCAN in many scenarios; it is both scalable and accurate, and it also significantly improves outlier detection.

Problem

• Develops DelTriC clustering with projection and back-projection mechanisms
• Decouples neighborhood construction from decision-making for robust clustering
• Outperforms k-means, DBSCAN, HDBSCAN in scalability, accuracy, outlier detection

Innovation

• Integrates PCA/UMAP projection with Delaunay triangulation
• Back-projects to original space for robust clustering
• Decouples neighborhood construction from decision-making process