ICS for multivariate outlier detection with application to quality control

Abstract

In high reliability standards fields such as automotive, avionics or aerospace, the detection of anomalies is crucial. An efficient methodology for automatically detecting multivariate outliers is introduced. It takes advantage of the remarkable properties of the Invariant Coordinate Selection (ICS) method. Based on the simultaneous spectral decomposition of two scatter matrices, ICS leads to an affine invariant coordinate system in which the Euclidian distance corresponds to a Mahalanobis Distance (MD) in the original coordinates. The limitations of MD are highlighted using theoretical arguments in a context where the dimension of the data is large. Unlike MD, ICS makes it possible to select relevant components which removes the limitations. Owing to the resulting dimension reduction, the method is expected to improve the power of outlier detection rules such as MD-based criteria. It also greatly simplifies outliers interpretation. The paper includes practical guidelines for using ICS in the context of a small proportion of outliers which is relevant in high reliability standards fields. The choice of scatter matrices together with the selection of relevant invariant components through parallel analysis and normality tests are addressed. The use of the regular covariance matrix and the so called matrix of fourth moments as the scatter pair is recommended. This choice combines the simplicity of implementation together with the possibility to derive theoretical results. A simulation study confirms the good properties of the proposal and compares it with other scatter pairs. This study also provides a comparison with Principal Component Analysis and MD. The performance of our proposal is also 1 arXiv:1612.06118v3 [stat.ME] 2 Feb 2018 evaluated on several real data sets using a user-friendly R package accompanying the paper.

ICSOutlier: Unsupervised Outlier Detection for Low-Dimensional Contamination Structure

“…For example if V 1 is the usual empirical variance-covariance matrix and V 2 is the scatter matrix based on the fourth moments (the default in the ics.outlier function), the eigenvalues are ordered according to their classical Pearson kurtosis values in decreasing order. In this case and for a small proportion of outliers, it is advisable to analyze the projections that maximize the kurtosis and are associated with the largest eigenvalues (Archimbaud et al, 2018).…”

“…Depending on the combination of the scatters V 1 (X n ) and V 2 (X n ) chosen, the ICSOutlier package incorporates automated ways to select these k invariant coordinates. The two approaches proposed in Archimbaud et al (2018) are implemented here: a test based on a quasi-inferential procedure and some normality tests. Considering V 1 (X n ) be more robust than V 2 (X n ) and a small percentage of outliers (less than 10% is recommended), the structure of the outlierness should be contained in the first k non-normal components.…”

“…Note that the structure may be also contained in the last components (associated with the smallest eigenvalues) if the proportion of outliers is large. What is meant by "large" depends on the scatter pair but also on the distribution of the data as detailed in Archimbaud et al (2018). Since the invariant coordinates are already ordered decreasingly according to a kurtosis measure, it is enough to test whether each component is Gaussian beginning by the one associated with the largest eigenvalue and stop the test procedure as soon as we find a Gaussian component.…”

“…This method is well-designed in particular for quality control. Its current version is able to handle a small proportion of outliers that lie on a subspace, using the affine equivariant Invariant Coordinate Selection (ICS) method, as presented by Archimbaud et al (2018). The method relies on a generalized diagonalization and on the selection of the invariant components associated with the largest eigenvalues.…”

Network Intrusion Detection with Threat Agent Profiling

“…(1) Density-Based Spatial Clustering of Applications with Noise (DBSCAN) [53] (2) The Invariant Coordinate Selection (ICS) [54] (3) Local Outlier Factor (LOF) [18] In Table 3, we report the concordance rate for outliers identified by other above-mentioned methods with respect to the percentile method. The rate can be interpreted as the fraction of outliers identical to those classified by the percentile method.…”