Erich Schubert

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.

Abstract High‐dimensional data in Euclidean space pose special challenges to data mining algorithms. These challenges are often indiscriminately subsumed under the term ‘curse of dimensionality’, more concrete aspects being the so‐called ‘distance concentration effect’, the presence of irrelevant attributes concealing relevant information, or simply efficiency issues. In about just the last few years, the task of unsupervised outlier detection has found new specialized solutions for tackling high‐dimensional data in Euclidean space. These approaches fall under mainly two categories, namely considering or not considering subspaces (subsets of attributes) for the definition of outliers. The former are specifically addressing the presence of irrelevant attributes, the latter do consider the presence of irrelevant attributes implicitly at best but are more concerned with general issues of efficiency and effectiveness. Nevertheless, both types of specialized outlier detection algorithms tackle challenges specific to high‐dimensional data. In this survey article, we discuss some important aspects of the ‘curse of dimensionality’ in detail and survey specialized algorithms for outlier detection from both categories. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012

Many outlier detection methods do not merely provide the decision for a single data object being or not being an outlier but give also an outlier score or "outlier factor" signaling "how much" the respective data object is an outlier. A major problem for any user not very acquainted with the outlier detection method in question is how to interpret this "factor" in order to decide for the numeric score again whether or not the data object indeed is an outlier. Here, we formulate a local density based outlier detection method providing an outlier "score" in the range of [0, 1] that is directly interpretable as a probability of a data object for being an outlier.