Similarity Beyond Correlation: Symmetry-Based Approach
Ildar Batyrshin, Thongchai Dumrongpokaphan, Владик Крейнович, Olga M. Kosheleva · scholarworks - UTEP (The University of Texas at El Paso) · 2016
When practitioners analyze the similarity between time series, they often use correlation to gauge this similarity. Sometimes this works, but sometimes, this leads to counter-intuitive results. In this paper, we use natural symmetries -- scaling and shift -- to explain this discrepancy between correlation and common sense, and then use the same symmetries to come up with more adequate measures of similarity.