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 timeseries that relates to a specific object (e.g. the motion of a person). The increasing needfor analyzing efficiently the huge amount of this information leads to the application ofdata mining techniques. At the core of these techniques lies the concept of similaritysince most of them require searching for similar patterns, such as in query by content,clustering or classification. Nevertheless, when dealing with multivariate time seriesdatasets, similarity should be sought between the whole datasets and not only betweenthe individual time series, since there are usually important correlations among themthat shouldn’t be lost. In this paper, we discuss the application of Principal ComponentAnalysis (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 asmuch as possible of the variation present in the data. We provide a thorough descriptionof the pre-processing phase with respect to PCA assumptions and limitations, as wellas, to the most frequently appeared distortions in data. Furthermore, we experimentallyexplore the potential usefulness of incorporating Piecewise Aggregate Approximationinto this phase. Finally, we discuss the various aspects of the proposed PCA-basedsimilarity (dissimilarity) measures.