Outlier Analysis


Many machine learning algorithms are sensitive to the range and distribution of attribute values in the input data. Outliers in input data can skew and mislead the training process of machine learning algorithms resulting in longer training times, less accurate models and ultimately poorer results.

Even before predictive models are prepared on training data, outliers can result in misleading representations and in turn misleading interpretations of collected data. Outliers can skew the summary distribution of attribute values in descriptive statistics like mean and standard deviation and in plots such as histograms and scatterplots, compressing the body of the data.

Finally, outliers can represent examples of data instances that are relevant to the problem such as anomalies in the case of fraud detection and computer security.

Outlier Modeling

Outliers are extreme values that fall a long way outside of the other observations. For example, in a normal distribution, outliers may be values on the tails of the distribution.

The process of identifying outliers has many names in data mining and machine learning such as outlier mining, outlier modeling and novelty detection and anomaly detection.

In his book Outlier Analysis, Aggarwal provides a useful taxonomy of outlier detection methods, as follows:

Extreme Value Analysis: Determine the statistical tails of the underlying distribution of the data. For example, statistical methods like the z-scores on univariate data.

Probabilistic and Statistical Models:  Determine unlikely instances from a probabilistic model of the data. For example, gaussian mixture models optimized using expectation-maximization.

Linear Models: Projection methods that model the data into lower dimensions using linear correlations. For example, principle component analysis and data with large residual errors may be outliers.

Proximity-based Models: Data instances that are isolated from the mass of the data as determined by cluster, density or nearest neighbor analysis.
Information Theoretic Models: Outliers are detected as data instances that increase the complexity (minimum code length) of the dataset.

High-Dimensional Outlier Detection: Methods that search subspaces for outliers give the breakdown of distance based measures in higher dimensions (curse of dimensionality).

Aggarwal comments that the interpretability of an outlier model is critically important. Context or rationale is required around decisions why a specific data instance is or is not an outlier.

In his contributing chapter to Data Mining and Knowledge Discovery Handbook, Irad Ben-Gal proposes a taxonomy of outlier models as univariate or multivariate and parametric and nonparametric. This is a useful way to structure methods based on what is known about the data. For example:

Are you considered with outliers in one or more than one attributes (univariate or multivariate methods)?
Can you assume a statistical distribution from which the observations were sampled or not (parametric or nonparametric)?

Get Started

There are many methods and much research put into outlier detection. Start by making some assumptions and design experiments where you can clearly observe the effects of the those assumptions against some performance or accuracy measure.

I recommend working through a stepped process from extreme value analysis, proximity methods and projection methods.

Extreme Value Analysis

You do not need to know advanced statistical methods to look for, analyze and filter out outliers from your data. Start out simple with extreme value analysis.

Focus on univariate methods
Visualize the data using scatterplots, histograms and box and whisker plots and look for extreme values
Assume a distribution (Gaussian) and look for values more than 2 or 3 standard deviations from the mean or 1.5 times from the first or third quartile
Filter out outliers candidate from training dataset and assess your models performance

Proximity Methods

Once you have explore simpler extreme value methods, consider moving onto proximity-based methods.

Use clustering methods to identify the natural clusters in the data (such as the k-means algorithm)
Identify and mark the cluster centroids
Identify data instances that are a fixed distance or percentage distance from cluster centroids
Filter out outliers candidate from training dataset and assess your models performance

Projection Methods

Projection methods are relatively simple to apply and quickly highlight extraneous values.

Use projection methods to summarize your data to two dimensions (such as PCA, SOM or Sammon’s mapping)
Visualize the mapping and identify outliers by hand
Use proximity measures from projected values or codebook vectors to identify outliers
Filter out outliers candidate from training dataset and assess your models performance

Methods Robust to Outliers

An alternative strategy is to move to models that are robust to outliers. There are robust forms of regression that minimize the median least square errors rather than mean (so-called robust regression), but are more computationally intensive. There are also methods like decision trees that are robust to outliers.

You could spot check some methods that are robust to outliers. If there are significant model accuracy benefits then there may be an opportunity to model and filter out outliers from your training data.


There are a lot of webpages that discuss outlier detection, but I recommend reading through a good book on the subject, something more authoritative. Even looking through introductory books on machine learning and data mining won’t be that useful to you. For a classical treatment of outliers by statisticians, check out:

Robust Regression and Outlier Detection by Rousseeuw and Leroy published in 2003
Outliers in Statistical Data by Barnett and Lewis, published in 1994
Identification of Outliers a monograph by Hawkins published in 1980

For a modern treatment of outliers by data mining community, see:

Outlier Analysis by Aggarwal, published in 2013

Chapter 7 by Irad Ben-Gal in Data Mining and Knowledge Discovery Handbook edited by Maimon and Rokach, published in 2010

Additional Content:


ISODEPTH Algorithm
FDC (Fast Computation of 2-Dimension Depth Contours