An Unbiased Distance-based Outlier Detection Approach for

An Unbiased Distance-based
Outlier Detection Approach for
High Dimensional Data
Hoang Vu Nguyen, Vivekanand Gopalkrishnan and Ira Assent
Presented By
Salman Ahmed Shaikh (D1)
Subspace Outlier Detection Challenges
Objectives of Research
The Approach
– Subspace Outlier Score Function: FSout
– HighDOD Algorithm
• Empirical Results and Analysis
• Conclusion
• An outlier, is one that appears to deviate
markedly from other members of the sample
in which it occurs. [1]
• Popular techniques of outlier detection
– Distance based
– Density base
• Since these techniques take fulldimensional space into account, their
performance is impacted by noisy or
irrelevant features.
• Recently, researchers have switched to
subspace anomaly detection.
o1, o2 and o3 are anomalous instances w.r.t. the data
Anomalous Subsequence
Subspace Outlier Detection Challenges
• Unavoidable exploration of all subspaces to mine full result
– As the monotonicity property does not hold in the case of outliers,
one cannot apply apriori-like heuristic for mining outliers.
• Difficulty in devising an outlier notion:
– Full-dimensional outlier detection techniques suffer the issue of
dimensionality bias in subspaces.
– They assign higher outlier score in high dimensional subspaces than in
lower dimensions
• Exposure to high false alarm rate:
– Binary decision on each data point (normal or outlier) in each
subspace flag too many points as outliers.
– Solution is ranking-based algorithm.
• Build an efficient technique for mining outliers
in subspaces, which should
– Avoid expensive scan of all subspaces while still
yielding high detection accuracy
– Eases the task of parameter setting
– Facilitates the design of pruning heuristics to
speed up the detection process
– Provide a ranking of outliers across subspaces.
The Approach
• The authors have made an assertion and given some definitions
to explain their research approach.
Non-monotonicity Property: Consider a data point p in the
dataset DS. Even if p is not anomalous in subspace S of DS, it
may be an outlier in some projection(s) of S. Even if p is a normal
data point in all projections of S, it may be an outlier in S.
A is an outlier in full space but not in subspace
B is an outlier in subspace but not in fullspace
(Subspace) Outlier Score Function
• Outlier Score Function: Fout as given by Angiulli et al. for full space [2]
The dissimilarity of a point p with respect to its k nearest neighbors is
known by its cumulative neighborhood distance. This is defined as the total
distance from p to its k nearest neighbors in DS.
– In order to ensure that non-monotonicity property is not violated, the outlier
score function is redefined by the authors as below.
• Subspace Outlier Score Function: FSout
The dissimilarity of a point p with respect to its k nearest neighbors in a
subspace S of dimensionality dim(S), is known by its cumulative
neighborhood distance. This is defined as the total distance from p to its k
nearest neighbors in DS (projected onto S), normalized by dim(S).
– Where ps is the projection of a data point p∊ DS onto S.
FSout is Dimensionality Unbiased
• FSout assigns multiple outlier scores to each data point and is dimensionality
• Example: let k=1 and l=2
• In Fig.(a), A's outlier score in the 2-dimensional space is 1/(2)1/2 which is the
largest across all subspaces.
• In Fig.(b), the outlier score of B when projected on the subspace of the x-axis
is 1, which is also the largest in all subspaces.
• Hence, FSout flags A and B as outliers.
Subspace Outlier Detection Problem
• Using FSout for outliers in subspaces, mining
problem now can be re-defined as
Given two positive integers k and n, mine the
top n distinct anomalies whose outlier scores
(in any subspace) are largest.
HighDOD-Subspace Outlier Detection Algorithm
• HighDOD (High dimensional Distance based Outlier Detection)
– A Distance based approach towards detecting outliers in very highdimensional datasets.
– Unbiased w.r.t. the dimensionality of different subspaces.
– Capable of producing ranking of outliers
• HighDOD is composed of following 3 algorithms
– OutlierDetection
– CandidateExtraction
– SubspaceMining
• Algorithm OutlierDetection examine subspaces of
dimensionality up to some threshold m = O(logN) as
suggested by Aggarwal and Ailon in [3, 4]
Algorithm 1: Outlier Detection
• Carry out a bottom-up exploration of all subspaces of up to a
dimensionality of m = O(logN)
Algorithm 2: CandidateExtraction
• Estimate the data points’ local densities by using a kernel density
estimator and choose βn data points with the lowest estimates as
potential candidates .
Algorithm 3: SubspaceMining
• This procedure is used to update the set of outliers TopOut with 2n
candidate outliers extracted from a subspace S.
Empirical Results and Analysis
• Authors have compared HighDOD with DenSamp, HighOut,
• Experiments have been performed to compare detection
accuracy and scalability.
• Precision-Recall trade-off curve is used to evaluate the quality
of an unordered set of retrieved items.
• Datasets
– 4 Real data sets from UCI Repository have been used.
Comparison of Detection Accuracy
Detection accuracy of HighDOD, DenSamp, HighOut, PODM and LOF
Comparison of Scalability
• Since PODM and LOF yields unsatisfactory accuracy, they are not included
in this experiment.
• Scalability test is done with CorelHistogram (CH) dataset consisting of
68040 records in 32-dimensional space.
Scalability of HighDOD, DenSamp and HighOut
• Work proposed a new outlier detection
technique which is dimensionality unbiased.
• Extends distance-based anomaly detection to
subspace analysis.
• Facilitates the design of ranking-based
• Introduced HighDOD, a ranking-based
technique for subspace outlier mining.
[1] Wikipedia
[2] Angiulli, F., Pizzuti, C.: Outlier mining in large highdimensional data sets. IEEE Trans. Knowl. Data Eng.,
[3] Aggarwal, C.C., Yu, P.S.: An effective and efficient
algorithm for high-dimensional outlier detection.
VLDB Journal, 2005.
[4] Ailon, N., Chazelle, B.: Faster dimension reduction.
Commun. CACM, 2010.

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