Translational symmetry in subsequence time-series clustering
JSAI'06 Proceedings of the 20th annual conference on New frontiers in artificial intelligence
Why does subsequence time-series clustering produce sine waves?
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
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We propose a new theoretical framework for generalizing the traditional notion of covariance. First, we discuss the role of pairwise cross-cumulants by introducing a cluster expansion technique for the cumulant generating function. Next, we introduce a novel concept of symmetry decomposition of probability density functions according to the C_4v group. By utilizing the irreducible representations, generalized covariances are explicitly defined, and their utility is demonstrated using an analytically solvable model.