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On the evaluation of unsupervised outlier detection: measures, datasets, and an empirical study

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Abstract

The evaluation of unsupervised outlier detection algorithms is a constant challenge in data mining research. Little is known regarding the strengths and weaknesses of different standard outlier detection models, and the impact of parameter choices for these algorithms. The scarcity of appropriate benchmark datasets with ground truth annotation is a significant impediment to the evaluation of outlier methods. Even when labeled datasets are available, their suitability for the outlier detection task is typically unknown. Furthermore, the biases of commonly-used evaluation measures are not fully understood. It is thus difficult to ascertain the extent to which newly-proposed outlier detection methods improve over established methods. In this paper, we perform an extensive experimental study on the performance of a representative set of standard k nearest neighborhood-based methods for unsupervised outlier detection, across a wide variety of datasets prepared for this purpose. Based on the overall performance of the outlier detection methods, we provide a characterization of the datasets themselves, and discuss their suitability as outlier detection benchmark sets. We also examine the most commonly-used measures for comparing the performance of different methods, and suggest adaptations that are more suitable for the evaluation of outlier detection results.

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Notes

  1. While only recently defined formally, SimplifiedLOF has been implicitly used (and adapted), often presumably unintentionally [i.e., not being aware of the special definition of the reachability distance (Eq. 2)], in many earlier variants of LOF. Here, for the first time, it is evaluated explicitly.

  2. In fact, the number of true outliers expected to be ranked by chance among the top n positions is a fraction n / N of |O|, which yields \(P@n = \frac{n \cdot |O|}{N}\big / n = \frac{|O|}{N}\).

  3. http://www.dbs.ifi.lmu.de/research/outlier-evaluation/.

  4. Available at: http://www.ipd.kit.edu/~muellere/HiCS/realworld.zip. Note that we have supplemented our collection with some of these datasets, without further preprocessing.

  5. For unsupervised learning, both training and test sets can be used together, and we assume this is the case unless otherwise specified.

  6. FastABOD requires at least a set of 3 neighbors, as it computes variances of angles to neighbors. LDOF, KDEOS, and ODIN require at least 2 neighbors.

  7. http://www.dbs.ifi.lmu.de/research/outlier-evaluation/.

  8. We see the same overall tendency (although much weaker due to overall low values) if we use \(P@n\) and \({{\mathrm{AP}}}\) (both adjusted and unadjusted) instead of ROC AUC. This is expected since (Adjusted) \(P@n\) and (Adjusted) \({{\mathrm{AP}}}\) can yield additional insights when comparing results that are very good in terms of ROC AUC. In this aggregated evaluation, however, many results with weak scores are included. The corresponding plots are available online.

  9. Therefore, as a side effect, such heat maps can also serve to visualize the profile of performance in terms of \(P@(x \cdot n)\) for \(x=1,\ldots ,9\).

  10. This is not surprising given the relatively large amount of outliers (\(\approx \)75 %) in the base dataset.

  11. Prima facie, this conclusion is valid, based on our experiments, for the dependency of related methods on a parameter choice regarding cardinality of a local neighborhood. Common sense suggests that we can have a similar expectation, mutatis mutandis, for other types of parameters for other kinds of methods.

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Acknowledgments

This project was partially funded by FAPESP (Brazil—Grant #2013/18698-4), CNPq (Brazil—Grants #304137/2013-8 and #400772/2014-0), NSERC (Canada), and the Danish Council for Independent Research—Technology and Production Sciences (FTP) (Denmark—Grant 10-081972).

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Authors and Affiliations

  1. University of São Paulo, SCC/ICMC/USP, C.P. 668, CEP 13566-590, São Carlos, SP, Brazil

    Guilherme O. Campos & Ricardo J. G. B. Campello

  2. Ludwig-Maximilians-Universität München, Oettingenstr. 67, 80538, Munich, Germany

    Arthur Zimek & Erich Schubert

  3. Department of Computing Science, University of Alberta, Edmonton, AB, T6G 2E8, Canada

    Jörg Sander

  4. Department of Computer Science, Aarhus University, Aabogade 34, 8200, Aarhus, Denmark

    Barbora Micenková & Ira Assent

  5. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, 101-8430, Japan

    Michael E. Houle

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  1. Guilherme O. Campos
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Campos, G.O., Zimek, A., Sander, J. et al. On the evaluation of unsupervised outlier detection: measures, datasets, and an empirical study. Data Min Knowl Disc 30, 891–927 (2016). https://doi.org/10.1007/s10618-015-0444-8

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