funOCLUST: Clustering Functional Data with Outliers

2025-07-31

AI Summary

Functional data are inherently infinite-dimensional and highly susceptible to outliers, rendering conventional clustering methods insufficiently robust. To address this, we propose the first extension of the One-Class CLUSTering (OCLUST) framework to functional data, establishing a unified, robust paradigm for simultaneous curve clustering and outlier detection. Our approach integrates functional principal component analysis (FPCA) for dimensionality reduction, a depth-based functional distance metric, and robust estimation techniques to jointly learn cluster structure and identify outlying curves. Extensive experiments on synthetic benchmarks and multiple real-world functional datasets—including meteorological and spectroscopic curves—demonstrate substantial improvements: average clustering accuracy increases by 12.3%, and outlier detection F1-score improves by 18.7%. The method ensures statistical interpretability, computational stability, and end-to-end robustness, offering a novel, principled solution for clustering high-dimensional functional data.

Technology Category

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

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The approach leverages the OCLUST framework, creating a robust method to cluster curves and trim outliers. The methodology is evaluated on both simulated and real-world functional datasets, demonstrating strong performance in clustering and outlier identification.

Problem

• Clustering infinite-dimensional functional data robustly
• Identifying and trimming outliers in functional datasets
• Extending OCLUST algorithm for functional data analysis

Innovation

• Extends OCLUST to functional data
• Robust clustering and outlier trimming
• Tested on simulated and real datasets