Localized Kernel Projection Outlyingness: A Two-Stage Approach for Multi-Modal Outlier Detection

TL;DR

This paper introduces a two-stage outlier detection framework called Two-Stage LKPLO that combines adaptive loss functions, kernel PCA, and local clustering to effectively identify outliers in complex, multi-modal datasets, outperforming existing methods.

Contribution

The paper proposes a novel multi-stage outlier detection method that integrates adaptive loss-based outlyingness, kernel PCA, and local clustering, addressing limitations of fixed metrics and single-structure assumptions.

Findings

Achieves state-of-the-art performance on 10 benchmark datasets.

Significantly outperforms baseline methods on multi-cluster and high-dimensional data.

Ablation study confirms the importance of kernelization and localization stages.

Abstract

This paper presents Two-Stage LKPLO, a novel multi-stage outlier detection framework that overcomes the coexisting limitations of conventional projection-based methods: their reliance on a fixed statistical metric and their assumption of a single data structure. Our framework uniquely synthesizes three key concepts: (1) a generalized loss-based outlyingness measure (PLO) that replaces the fixed metric with flexible, adaptive loss functions like our proposed SVM-like loss; (2) a global kernel PCA stage to linearize non-linear data structures; and (3) a subsequent local clustering stage to handle multi-modal distributions. Comprehensive 5-fold cross-validation experiments on 10 benchmark datasets, with automated hyperparameter optimization, demonstrate that Two-Stage LKPLO achieves state-of-the-art performance. It significantly outperforms strong baselines on datasets with challenging structures where existing methods fail, most notably on multi-cluster data (Optdigits) and complex, high-dimensional data (Arrhythmia). Furthermore, an ablation study empirically confirms that the synergistic combination of both the kernelization and localization stages is indispensable for its superior performance. This work contributes a powerful new tool for a significant class of outlier detection problems and underscores the importance of hybrid, multi-stage architectures.