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PIF: Anomaly detection via preference embedding

Filippo Leveni, Luca Magri, Giacomo Boracchi, Cesare Alippi

TL;DR

PIF addresses anomaly detection for data that deviate from structured patterns by embedding observations into a high-dimensional preference space and applying PI-Forest, a tree-based isolation method built on nested Voronoi tessellations with the $Tanimoto$ distance. Preference embedding computes a vector of model-based preferences for each data point using a pool of parametric models sampled from the data, then PI-Forest operates in the resulting space to produce anomaly scores $\alpha_\psi(p) = 2^{-\frac{E[h(p)]}{c(\psi)}}$. The approach outperforms state-of-the-art detectors such as LOF, iFor, and EiFor on synthetic patterns and real data (AdelaideRMF), demonstrating improved separability for pattern-based anomalies and robustness across varying anomaly rates. The work demonstrates the value of combining structure-informed embeddings with distance-preserving isolation and suggests broad applicability to other metric spaces and non-parametric preference embeddings.

Abstract

We address the problem of detecting anomalies with respect to structured patterns. To this end, we conceive a novel anomaly detection method called PIF, that combines the advantages of adaptive isolation methods with the flexibility of preference embedding. Specifically, we propose to embed the data in a high dimensional space where an efficient tree-based method, PI-Forest, is employed to compute an anomaly score. Experiments on synthetic and real datasets demonstrate that PIF favorably compares with state-of-the-art anomaly detection techniques, and confirm that PI-Forest is better at measuring arbitrary distances and isolate points in the preference space.

PIF: Anomaly detection via preference embedding

TL;DR

PIF addresses anomaly detection for data that deviate from structured patterns by embedding observations into a high-dimensional preference space and applying PI-Forest, a tree-based isolation method built on nested Voronoi tessellations with the distance. Preference embedding computes a vector of model-based preferences for each data point using a pool of parametric models sampled from the data, then PI-Forest operates in the resulting space to produce anomaly scores . The approach outperforms state-of-the-art detectors such as LOF, iFor, and EiFor on synthetic patterns and real data (AdelaideRMF), demonstrating improved separability for pattern-based anomalies and robustness across varying anomaly rates. The work demonstrates the value of combining structure-informed embeddings with distance-preserving isolation and suggests broad applicability to other metric spaces and non-parametric preference embeddings.

Abstract

We address the problem of detecting anomalies with respect to structured patterns. To this end, we conceive a novel anomaly detection method called PIF, that combines the advantages of adaptive isolation methods with the flexibility of preference embedding. Specifically, we propose to embed the data in a high dimensional space where an efficient tree-based method, PI-Forest, is employed to compute an anomaly score. Experiments on synthetic and real datasets demonstrate that PIF favorably compares with state-of-the-art anomaly detection techniques, and confirm that PI-Forest is better at measuring arbitrary distances and isolate points in the preference space.
Paper Structure (12 sections, 6 equations, 5 figures, 3 tables, 4 algorithms)

This paper contains 12 sections, 6 equations, 5 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Related Work
  4. Preference Isolation Forest
  5. Preference embedding
  6. PI-Forest
  7. Anomaly score
  8. Experimental Validation
  9. Datasets
  10. Methodology
  11. Discussion
  12. Conclusion and Future Directions

Figures (5)

  • Figure 1: Left: an anomaly (marked as $\times$) is recognized as a point in a low density area. Right: anomalies are defined with respect to their deviation from patterns described by line equations.
  • Figure 2: A PI-Tree with branching factor $b=3$ and height limit $l=3$ constructed from a set of points in $\mathbb{R}^2$. Every region is recursively split in $b$ sub-regions. The most isolated samples fall in leaves at lowest heights, such as 'a' and 'd' cells.
  • Figure 3: Color-coded anomaly scores produced by different algorithms: high scores in red, low scores in blue.
  • Figure 4: Synthetic datasets. Orange dots represent normal data, while blue dots represent anomalies.
  • Figure 5: AUCs achieved at various percentages of anomalies.