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ICDM'07 1
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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ICDM'07 2
Outline
Novelty detectionMotivationsKernelized spatial depth (KSD)Bounds on the false alarm probabilityEmpirical studiesDiscussions
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ICDM'07 3
Outlier Detection
Missing label problem
One-class learning
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ICDM'07 4
A Simple Outlier Detector
1-d example
Sensitivity
Threshold
Structure of the data
X
mean
median
X
X
X
?
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ICDM'07 5
Median
The sign function
Median is
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ICDM'07 6
Spatial Median
The spatial sign function
The spatial median is
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ICDM'07 7
Spatial Depth
Spatial Depth
Sample version
The expectation of the unit vector starting from x
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ICDM'07 8
Spatial Depth and Outlier Detection
outlier
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ICDM'07 9
Example: Half-Moon Data
FAR = 70%
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ICDM'07 10
Example: Ring Data
FAR = 100%
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ICDM'07 11
Kernelized Spatial Depth (KSD)
σ→∞, KSD converges to SDσ→0, KSD → 0.293
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ICDM'07 12
Example: Half-Moon Data
0.2495
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ICDM'07 13
Example: Ring Data
0.2651
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ICDM'07 14
KSD Outlier Detector
outliers
normal observations
b is margin
How should we decide the threshold t?
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ICDM'07 15
Threshold Selection
Largest threshold such that upper bound on FAP ≤ desired level
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ICDM'07 16
Bounds on the False Alarm Probability
A training set bound
A test set bound
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ICDM'07 17
Empirical Study 110 species under the order Cypriniforms 989 specimens from Tulane University Museum of Natural History
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ICDM'07 18
Empirical Study 1
MaskingEffect
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ICDM'07 19
Empirical Study 2
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ICDM'07 20
Discussions
KSD outlier detection and density based approaches
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ICDM'07 21
Acknowledgment
Kory P. Northrop, Tulane UniversityHuimin Chen, University of New OrleansUniversity of MississippiNational Science Foundation