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2017 | OriginalPaper | Chapter

6. Distance and Density Based Approaches

Authors : Kishan G. Mehrotra, Chilukuri K. Mohan, HuaMing Huang

Published in: Anomaly Detection Principles and Algorithms

Publisher: Springer International Publishing

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Abstract

In Chap. 3, we discussed distance based approaches for anomaly detection; however there the focus was to illustrate how distances can be measured and minor perturbation in proposed distance can change the outcome; illustrated by simple examples. In this chapter we consider anomaly detection techniques that depend on the distances and densities. The densities can be global or local to the point of concern.

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previous chapter Model-Based Anomaly Detection Approaches
next chapter Rank Based Approaches
Footnotes
1
The change in variance is also closely related to the change in the information content, e.g., the number of bits needed to describe \({\mathcal {D}} \setminus \{p\}\) vs. \(\mathcal {D}\).
 
2
Fan et al. [41] consider the closeness of a point based on each dimension separately. Thus, in their implementation, an observation p is close to another observation q if the difference between p and q is less than r in any dimension. The algorithm is easier to implement using this definition of closeness since it avoids inter-observation distance computations.
 
3
In the Syracuse region, a daily commuting distance characterized by a driving time of 25 min would be considered excessive; that same travel time would be considered to be low in the Los Angeles region. The definition of what constitutes “excessive driving time” must hence be a function of the distribution of driving times within the region of interest, rather than a constant over all regions.
 
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Metadata
Title
Distance and Density Based Approaches
Authors
Kishan G. Mehrotra
Chilukuri K. Mohan
HuaMing Huang
Copyright Year
2017
Book
Anomaly Detection Principles and Algorithms

Print ISBN: 978-3-319-67524-4

Electronic ISBN: 978-3-319-67526-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-67526-8_6

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