PCA-based Similarity Search: Pre-processing & Distance Measures

Abstract

Time series appear frequently in several domains such as in multimedia, business, industry or medicine. A multivariate time series dataset is a set of co-evolving time series that relates to a specific object (e.g. the motion of a person). The increasing need for analyzing efficiently the huge amount of this information leads to the application of data mining techniques. At the core of these techniques lies the concept of similarity since most of them require searching for similar patterns, such as in query by content, clustering or classification. Nevertheless, when dealing with multivariate time series datasets, similarity should be sought between the whole datasets and not only between the individual time series, since there are usually important correlations among them that shouldn’t be lost. In this paper, we discuss the application of Principal Component Analysis (PCA) on multivariate time series datasets for the purpose of similarity search. PCA is applied in order to reduce the high dimensionality of such data while retaining as much as possible of the variation present in the data. We provide a thorough description of the pre-processing phase with respect to PCA assumptions and limitations, as well as, to the most frequently appeared distortions in data. Furthermore, we experimentally explore the potential usefulness of incorporating Piecewise Aggregate Approximation into this phase. Finally, we discuss the various aspects of the proposed PCA-based similarity (dissimilarity) measures.