Detecting and classifying outliers in big functional data

Abstract

We propose two new outlier detection methods, for identifying and classifying different types of outliers in (big) functional data sets. The proposed methods are based on an existing method called Massive Unsupervised Outlier Detection (MUOD). MUOD detects and classifies outliers by computing for each curve, three indices, all based on the concept of linear regression and correlation, which measure outlyingness in terms of shape, magnitude and amplitude, relative to the other curves in the data. ‘Semifast-MUOD’, the first method, uses a sample of the observations in computing the indices, while ‘Fast-MUOD’, the second method, uses the point-wise or $L_1$ median in computing the indices. The classical boxplot is used to separate the indices of the outliers from those of the typical observations. Performance evaluation of the proposed methods using simulated data show significant improvements compared to MUOD, both in outlier detection and computational time. We show that Fast-MUOD is especially well suited to handling big and dense functional datasets with very small computational time compared to other methods. Further comparisons with some recent outlier detection methods for functional data also show superior or comparable outlier detection accuracy of the proposed methods. We apply the proposed methods on weather, population growth, and video data.