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Depth-Based Novelty Detection

Yixin ChenDept. of Computer and Information ScienceUniversity of Mississippihttp://www.cs.olemiss.edu/~ychen

Joint work with Henry Bart, Xin Dang, and Hanxiang Peng

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Outline

Novelty detectionMotivationsKernelized spatial depth (KSD)Bounds on the false alarm probabilityEmpirical studiesDiscussions

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Outlier Detection

Missing label problem

One-class learning

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A Simple Outlier Detector

1-d example

Sensitivity

Threshold

Structure of the data

X

mean

median

X

X

X

?

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Median

The sign function

Median is

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Spatial Median

The spatial sign function

The spatial median is

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Spatial Depth

Spatial Depth

Sample version

The expectation of the unit vector starting from x

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Spatial Depth and Outlier Detection

outlier

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Example: Half-Moon Data

FAR = 70%

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Example: Ring Data

FAR = 100%

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Kernelized Spatial Depth (KSD)

σ→∞, KSD converges to SDσ→0, KSD → 0.293

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Example: Half-Moon Data

0.2495

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Example: Ring Data

0.2651

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KSD Outlier Detector

outliers

normal observations

b is margin

How should we decide the threshold t?

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Threshold Selection

Largest threshold such that upper bound on FAP ≤ desired level

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Bounds on the False Alarm Probability

A training set bound

A test set bound

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Empirical Study 110 species under the order Cypriniforms 989 specimens from Tulane University Museum of Natural History

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Empirical Study 1

MaskingEffect

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Empirical Study 2

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Discussions

KSD outlier detection and density based approaches

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Acknowledgment

Kory P. Northrop, Tulane UniversityHuimin Chen, University of New OrleansUniversity of MississippiNational Science Foundation