This is a supporting page of the paper
Ranking and Significance of Variable-length Similarity-based Time Series Motifs
by Joan Serrą, Isabel Serra, Įlvaro Corral, and Josep Lluis Arcos
J. Serrą, I. Serra, Į. Corral,
and J.L. Arcos.
"Ranking and significance of variable-length similarity-based time
series motifs". Submitted.
detection of very similar patterns in a time series, commonly called
motifs, has received continuous and increasing attention from diverse
scientific communities. In particular, recent approaches for
discovering similar motifs of different lengths have been proposed. In
this work, we show that such variable-length similarity-based motifs
cannot be directly compared, and hence ranked, by their normalized
dissimilarities. Specifically, we find that length-normalized motif
dissimilarities still have intrinsic dependencies on the motif length,
and that lowest dissimilarities are particularly affected by this
dependency. Moreover, we find that such dependencies are generally
non-linear and change with the considered data set and dissimilarity
measure. Based on these findings, we propose a solution to rank those
motifs and measure their significance. This solution relies on a
compact but accurate model of the dissimilarity space, using a beta
distribution with three parameters that depend on the motif length in a
non-linear way. We believe the incomparability of variable-length
dissimilarities could go beyond the field of time series, and that
similar modeling strategies as the one used here could be of help in a
more broad context.
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