Erich Schubert

Outlier Detection in Axis-Parallel Subspaces of High Dimensional Data

We propose an original outlier detection schema that detects outliers in varying subspaces of a high dimensional feature space. In particular, for each object in the data set, we explore the axis-parallel subspace spanned by its neighbors and determine how much the object deviates from the neighbors in this subspace. In our experiments, we show that our novel subspace outlier detection is superior to existing full-dimensional approaches and scales well to high dimensional databases.

Local outlier detection reconsidered: a generalized view on locality with applications to spatial, video, and network outlier detection

Outlier detection research has been seeing many new algorithms every year that often appear to be only slightly different from existing methods along with some experiments that show them to “clearly outperform” the others. However, few approaches come along with a clear analysis of existing methods and a solid theoretical differentiation. Here, we provide a formalized method of analysis to allow for a theoretical comparison and generalization of many existing methods. Our unified view improves understanding of the shared properties and of the differences of outlier detection models. By abstracting the notion of locality from the classic distance-based notion, our framework facilitates the construction of abstract methods for many special data types that are usually handled with specialized algorithms. In particular, spatial neighborhood can be seen as a special case of locality. Here we therefore compare and generalize approaches to spatial outlier detection in a detailed manner. We also discuss temporal data like video streams, or graph data such as community networks. Since we reproduce results of specialized approaches with our general framework, and even improve upon them, our framework provides reasonable baselines to evaluate the true merits of specialized approaches. At the same time, seeing spatial outlier detection as a special case of local outlier detection, opens up new potentials for analysis and advancement of methods.

A General Framework for Increasing the Robustness of PCA-Based Correlation Clustering Algorithms

Most correlation clustering algorithms rely on principal component analysis (PCA) as a correlation analysis tool. The correlation of each cluster is learned by applying PCA to a set of sample points. Since PCA is rather sensitive to outliers, if a small fraction of these points does not correspond to the correct correlation of the cluster, the algorithms are usually misled or even fail to detect the correct results. In this paper, we evaluate the influence of outliers on PCA and propose a general framework for increasing the robustness of PCA in order to determine the correct correlation of each cluster. We further show how our framework can be applied to PCA-based correlation clustering algorithms. A thorough experimental evaluation shows the benefit of our framework on several synthetic and real-world data sets.

A framework for clustering uncertain data

The challenges associated with handling uncertain data, in particular with querying and mining, are finding increasing attention in the research community. Here we focus on clustering uncertain data and describe a general framework for this purpose that also allows to visualize and understand the impact of uncertainty---using different uncertainty models---on the data mining results. Our framework constitutes release 0.7 of ELKI (http://elki.dbs.ifi.lmu.de/) and thus comes along with a plethora of implementations of algorithms, distance measures, indexing techniques, evaluation measures and visualization components.

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

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.

Evaluation of Clusterings -- Metrics and Visual Support

When comparing clustering results, any evaluation metric breaks down the available information to a single number. However, a lot of evaluation metrics are around, that are not always concordant nor easily interpretable in judging the agreement of a pair of clusterings. Here, we provide a tool to visually support the assessment of clustering results in comparing multiple clusterings. Along the way, the suitability of a couple of clustering comparison measures can be judged in different scenarios.

Interactive data mining with 3D-parallel-coordinate-trees

Parallel coordinates are an established technique to visualize high-dimensional data, in particular for data mining purposes. A major challenge is the ordering of axes, as any axis can have at most two neighbors when placed in parallel on a 2D plane. By extending this concept to a 3D visualization space we can place several axes next to each other. However, finding a good arrangement often does not necessarily become easier, as still not all axes can be arranged pairwise adjacently to each other. Here, we provide a tool to explore complex data sets using 3D-parallel-coordinate-trees, along with a number of approaches to arrange the axes.

Outlier Detection in Arbitrarily Oriented Subspaces

In this paper, we propose a novel outlier detection model to find outliers that deviate from the generating mechanisms of normal instances by considering combinations of different subsets of attributes, as they occur when there are local correlations in the data set. Our model enables to search for outliers in arbitrarily oriented subspaces of the original feature space. We show how in addition to an outlier score, our model also derives an explanation of the outlierness that is useful in investigating the results. Our experiments suggest that our novel method can find different outliers than existing work and can be seen as a complement of those approaches.

Discriminative features for identifying and interpreting outliers

We consider the problem of outlier detection and interpretation. While most existing studies focus on the first problem, we simultaneously address the equally important challenge of outlier interpretation. We propose an algorithm that uncovers outliers in subspaces of reduced dimensionality in which they are well discriminated from regular objects while at the same time retaining the natural local structure of the original data to ensure the quality of outlier explanation. Our algorithm takes a mathematically appealing approach from the spectral graph embedding theory and we show that it achieves the globally optimal solution for the objective of subspace learning. By using a number of real-world datasets, we demonstrate its appealing performance not only w.r.t. the outlier detection rate but also w.r.t. the discriminative human-interpretable features. This is the first approach to exploit discriminative features for both outlier detection and interpretation, leading to better understanding of how and why the hidden outliers are exceptional.

DBSCAN Revisited, Revisited: Why and How You Should (Still) Use DBSCAN

At SIGMOD 2015, an article was presented with the title “DBSCAN Revisited: Mis-Claim, Un-Fixability, and Approximation” that won the conference’s best paper award. In this technical correspondence, we want to point out some inaccuracies in the way DBSCAN was represented, and why the criticism should have been directed at the assumption about the performance of spatial index structures such as R-trees and not at an algorithm that can use such indexes. We will also discuss the relationship of DBSCAN performance and the indexability of the dataset, and discuss some heuristics for choosing appropriate DBSCAN parameters. Some indicators of bad parameters will be proposed to help guide future users of this algorithm in choosing parameters such as to obtain both meaningful results and good performance. In new experiments, we show that the new SIGMOD 2015 methods do not appear to offer practical benefits if the DBSCAN parameters are well chosen and thus they are primarily of theoretical interest. In conclusion, the original DBSCAN algorithm with effective indexes and reasonably chosen parameter values performs competitively compared to the method proposed by Gan and Tao.