Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Akira Tamamori

TL;DR

This work tackles outlier detection in data with non-linear and multi-modal structure, where traditional projection-based methods falter due to fixed metrics and a single global view. It introduces Two-Stage Localized Kernel PLO (Two-Stage LKPLO), which combines a generalized Projection-based Loss Outlyingness (PLO) with a global Kernel PCA mapping followed by a local clustering-based scoring scheme, and it evaluates two loss variants (Robust Z-score and an SVM-like loss). Empirical results across synthetic and real benchmarks show state-of-the-art performance, notably on Optdigits and Arrhythmia, with ablation studies confirming that both kernelization and localization are essential for best performance. The approach offers a flexible, hybrid framework for challenging outlier detection problems, highlighting the value of integrating kernelization, localization, and adaptive loss formulations for robust multi-modal anomaly discovery.

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.

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

TL;DR

This work tackles outlier detection in data with non-linear and multi-modal structure, where traditional projection-based methods falter due to fixed metrics and a single global view. It introduces Two-Stage Localized Kernel PLO (Two-Stage LKPLO), which combines a generalized Projection-based Loss Outlyingness (PLO) with a global Kernel PCA mapping followed by a local clustering-based scoring scheme, and it evaluates two loss variants (Robust Z-score and an SVM-like loss). Empirical results across synthetic and real benchmarks show state-of-the-art performance, notably on Optdigits and Arrhythmia, with ablation studies confirming that both kernelization and localization are essential for best performance. The approach offers a flexible, hybrid framework for challenging outlier detection problems, highlighting the value of integrating kernelization, localization, and adaptive loss formulations for robust multi-modal anomaly discovery.

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.

Paper Structure

This paper contains 27 sections, 2 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Projection-based Outlyingness
  4. Kernel-based Methods
  5. Clustering-based and Local Methods
  6. Our Contribution in Context
  7. Proposed Method: Two-Stage Localized Kernel PLO
  8. Stage 1: Global Non-linear Feature Learning via Kernel PCA
  9. Stage 2: Localization and Scoring
  10. Clustering in the Feature Space
  11. Local Projection-based Loss Outlyingness
  12. Computational Complexity
  13. Experiments
  14. Experimental Setup
  15. Datasets
  16. ...and 12 more sections

Figures (4)

  • Figure 1: Comparison of optimized decision boundaries on three synthetic datasets. Each row corresponds to a different outlier detection algorithm, and each column to a different dataset. The background color map represents the outlier score, with lighter colors indicating higher scores. The orange dashed line shows the decision boundary separating inliers from outliers.
  • Figure 2: PaCMAP visualization of the Optdigits dataset; It exhibits a clear multi-cluster structure.
  • Figure 3: PaCMAP visualization of the Vowels dataset; It is characterized by locally dense, globally separated clusters.
  • Figure 4: PaCMAP visualization of the Arrhythmia dataset; It shows a complex, unstructured distribution.