Outlier detection in multivariate functional data through a contaminated mixture model

TL;DR

This paper introduces a contaminated mixture model for detecting outliers in multivariate functional data, such as high-frequency sensor measurements, without needing to specify outlier proportions, and demonstrates superior performance over existing methods.

Contribution

The paper proposes a novel contaminated mixture model for outlier detection in multivariate functional data that automatically identifies outliers without prior outlier proportion specification.

Findings

Model outperforms competitors in simulated data

High accuracy in detecting abnormal sensor behaviors

Effective clustering of heterogeneous functional data

Abstract

In an industrial context, the activity of sensors is recorded at a high frequency. A challenge is to automatically detect abnormal measurement behavior. Considering the sensor measures as functional data, the problem can be formulated as the detection of outliers in a multivariate functional data set. Due to the heterogeneity of this data set, the proposed contaminated mixture model both clusters the multivariate functional data into homogeneous groups and detects outliers. The main advantage of this procedure over its competitors is that it does not require to specify the proportion of outliers. Model inference is performed through an Expectation-Conditional Maximization algorithm, and the BIC is used to select the number of clusters. Numerical experiments on simulated data demonstrate the high performance achieved by the inference algorithm. In particular, the proposed model outperforms the competitors. Its application on the real data which motivated this study allows to correctly detect abnormal behaviors.