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How Functional Isolation Forest Detects Anomalies by@computational

How Functional Isolation Forest Detects Anomalies

by Computational Technology for All
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Computational Technology for All

@computational

Computational: We take random inputs, follow complex steps, and hope...

November 20th, 2024
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Functional Isolation Forest (FIF) uses random splits in functional Hilbert space and projections onto a dictionary to isolate anomalies. Its performance heavily relies on dictionary selection, influencing its scoring and adaptability.
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Computational Technology for All

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Computational: We take random inputs, follow complex steps, and hope the output makes sense. And then blog about it.

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STORY’S CREDIBILITY

Academic Research Paper

Academic Research Paper

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Authors:

(1) Guillaume Staerman, INRIA, CEA, Univ. Paris-Saclay, France;

(2) Marta Campi, CERIAH, Institut de l’Audition, Institut Pasteur, France;

(3) Gareth W. Peters, Department of Statistics & Applied Probability, University of California Santa Barbara, USA.

Abstract and 1. Introduction

2. Background & Preliminaries

2.1. Functional Isolation Forest

2.2. The Signature Method

3. Signature Isolation Forest Method

4. Numerical Experiments

4.1. Parameters Sensitivity Analysis

4.2. Advantages of (K-)SIF over FIF

4.3. Real-data Anomaly Detection Benchmark

5. Discussion & Conclusion, Impact Statements, and References


Appendix

A. Additional Information About the Signature

B. K-SIF and SIF Algorithms

C. Additional Numerical Experiments

2. Background & Preliminaries


image


2.1. Functional Isolation Forest

Consider H the functional Hilbert space equipped with a inner product ⟨., .⟩H such that any x ∈ H is a real function defined on [0, 1]. A Functional Isolation Forest is created through an assembly of functional isolation trees (F-itrees). Each F-itree is constructed via a series of random splits from a subsample (of size m) of Xn. The abnormality score for an observation x is then determined as a monotonically decreasing transformation of x’s average depth across the trees. The core concept lies in the randomness of the splits, where an observation markedly different from others is more likely to be isolated from Xn, appearing at shallower levels in the F-itrees. The F-itrees are built based on a predetermined dictionary D ⊂ H, encompassing both deterministic and/or stochastic functions capturing pertinent data properties, which may also be a subset of Xn. Before each random univariate split, all node observations are projected onto a line defined by a randomly selected element from the dictionary D. The selection of a suitable dictionary plays a pivotal role in shaping the FIF score construction. The projection criterion at each node of each F-itree is defined as:


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This paper is available on arxiv under CC BY 4.0 DEED license.


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Computational: We take random inputs, follow complex steps, and hope the output makes sense. And then blog about it.

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