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

arXiv: https://arxiv.org/abs/2510.24043 · HTML: https://mlsanity.com/paper/2510.24043/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Builds on (most cited first, 4 of 4)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Kernel Outlier Detection](https://mlsanity.com/paper/2506.22994/) (2025)
- [Data Depth as a Risk](https://mlsanity.com/paper/2507.08518/) (2025)

## Abstract (arXiv)

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.