  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.
