by Anton Auoja, Albert Backenhof & Mikael Dalkvist

Detection of OutliersTNM033 - Data Mining

Holy Outliers, Batman!!

“An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs.” - Frank E. Grubbs

Holy Causes, Batman!!

Apparatus malfunction.

Fraudulent behavior.

Human error.

Natural deviations.

Contamination.

Holy Applications, Batman!!

Fraud Detection

Medicine

Public Health

Sports statistics

Detecting measurement errors

Holy WEKA, Batman!!

Interquartile Range

One Class Classifier

DBScan

Holy Common Methods, Batman!!

Statistical

Distance

Kernel

High Dimensional

Holy Statistical Methods, Batman!!

An outlier is an object with low probability with respect to the probability distribution model of the data.

Model Based.

Assume Gaussian distribution. Calculate the mean and standard deviation of the data. The probability of each object under the distribution can then be calculated.

Holy Examples, Batman!!

Box Plots

Trimmed Means

Grubbs’ Test

Holy Box and Whisker Plots, Batman!!

Interquartile RangeQ3 - Q1

Lower Inner Fence: Q1 - 1.5*IQR

Upper Inner Fence: Q3 + 1.5*IQR

Lower Outer Fence: Q1 - 3*IQR

Upper Outer Fence: Q3 + 3*IQR

Holy Trimmed Means, Batman!!

Delete percentage of extreme values.

Calculate mean.

Use new mean for comparison.

Holy Test, Grubbs!!

Calculate the normal logarithm.

Sort data.

Calculate Z.

Compare Z to the critical Z value.

Holy Issues, Batman!!

Identifying distribution of data set.

The number of attributes

Mixtures of distribution

Holy Distance Based Methods, Batman!!

DP(p,D)

k-Nearest Neighbor

Local Distance Based

Holy DB(p,D), Knorr & Ng, Batman!!

An object o is an outlier if at least the p:th fraction of all objects of the database are at a distance greater than D from the given object o.

Holy Distance to k-Nearest Neighbors, Batman!!

Outlier score.

Score each object [0,∞[ depending on the distance to its k-nearest neighbors.

Highly dependent on the choice of k.

Can be modified to use the mean of distances of a point to all its 1NN, 2NN, ..., kNN as an outlier score.

Holy Local distance-based algorithms, Batman!!

Determine the difference of an object from its nearest neighbors.

A threshold value is set.

All objects whose outlier factors exceed this value are considered to be outliers.

Local Outlier Factor (LOF).

Holy Advantages, Batman!!

More general and easier to apply then statistical approaches

No probabilistic model needed

Can find local outliers

Unholy Disadvantages, Batman!!

Methods are typically O(n2)

Sensitive to choice of parameters

Dependent on pre-defined parameters

Can’t handle datasets with regions that have widely differing density

Holy Kernel Based Methods, Batman!!

Originalspace

Hilbert(Feature)

space

X H

Holy Implicitly, Batman!!

No additional memory or computation cost.

Holy High Dimensional, Batman!!

Curse of Dimensionality

One way is to create subspaces of original space.

Another is Angle Based Outlier Degree.

Holy References, Batman!!

Outlier Detection Techniques. Hans-Peter Kriegel, Peer Kröger and Arthur Zimek. Ludwig-Maximilians-Universität München Munich, Germany.

A Review of Statistical Outlier Methods. Steven Walfish. Pharmaceutical Technology.

Outlier Detection Algorithms in Data Mining Systems. M. I. Petrovskiy. Department of Computational Mathematics and Cybernetics, Moscow State University, Vorob’evy gory, Moscow.

Detection and Accommodation of Outliers in Normally Distributed Data Sets. Agata Fallon and Christine Spada.

Outlier Detection with Kernel Density Functions. L. J. Latecki, A. Lazarevic, D. Pokrajac. 2008.

Classification by Support Vector Machines. F. Markowetz. Max-Planck-Institute for Molecular Genetics. 2002.

Introduction to Data Mining. Pang-Ning Tan, Michael Steinbach, Vipin Kumar. 2005.