PCA Driven Similarity for Segmented Univariate Time Series

Abstract

Selection of the proper similarity measure is the cornerstone of all time series data mining task. In the recent years, many similarity measures have been introduced to fulfill the needs of chemical process engineering. These measures have been guided by data reduction methods due to the large amount of data. This data reduction can be done explicitly (by segmentation) as well as implicitly (by utilizing the latent variable space). Usually, the original multivariate data is projected into a single dimension with Principal Component Analysis (PCA) and segmentation is executed. However, the similarity measures which have been used to compare univariate, segmented representations of the original processes do not consider that the main information carried by the univariate representations is the correlation of the original variables. This paper introduces a PCA inspired similarity measure for these univariate segments. Finally, it is shown that the presented method can be considered as the logical extension of the Correlation Based Dynamic Time Warping (CBDTW) to univariate time series.