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Prof. Dr. Emmanuel Müller


Transformation of multivariate time series into feature spaces are common for data mining tasks like  classification. Ordinality is one important property in time series that provides a qualitative representation of the underlying dynamic regime. In a multivariate time series, ordinalities from multiple dimensions combine together to be discriminative for the classification problem. However, ordinal transformations are yet unexplored for multivariate time series. For multivariate ordinal patterns, there is a computational challenge with an explosion of pattern combinations, while not all patterns are relevant and provide novel information for the classification.
In this work, we propose a technique for the extraction and selection of relevant and non-redundant multivariate ordinal patterns from the highdimensional combinatorial search space. Our proposed approach ordex, simultaneously extracts and scores the relevance and redundancy of ordinal patterns without training a classifier. As a filter-based approach, ordex aims to select a set of relevant patterns with complementary information.
Hence, using our scoring function based on the principles of Chebyshev’s inequality, we maximize the relevance of the patterns and minimize the correlation between them. Our experiments on real-world datasets show that ordinality in time series contains valuable information for classification in several applications.

Supplementary attachment

The following attachment contains, 

1. Comparison of other information theoretic relevance measures comparison to the one introduced in the work of ordex.

2. Derivation of the upper-bound of misclassification from the principles of Chebychev inequality.

3. Parameter settings for the real wold experiments in the paper.