Functional Bipartite Ranking: a Wavelet-Based Filtering Approach

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments

How to Evaluate the Quality of Unsupervised Anomaly Detection Algorithms?

When sufficient labeled data are available, classical criteria based on Receiver Operating Characteristic (ROC) or Precision-Recall (PR) curves can be used to compare the performance of un-supervised anomaly detection algorithms. However , in many situations, few or no data are labeled. This calls for alternative criteria one can compute on non-labeled data. In this paper, two criteria that do not require labels are empirically shown to discriminate accurately (w.r.t. ROC or PR based criteria) between algorithms. These criteria are based on existing Excess-Mass (EM) and Mass-Volume (MV) curves, which generally cannot be well estimated in large dimension. A methodology based on feature sub-sampling and aggregating is also described and tested, extending the use of these criteria to high-dimensional datasets and solving major drawbacks inherent to standard EM and MV curves

Multi-criteria Anomaly Detection using Pareto Depth Analysis

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria using a linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.Comment: Removed an unnecessary line from Algorithm