Significant motifs in time series

Abstract

Time series motif discovery is the task of extracting previously unknown recurrent patterns from time series data. It is an important problem within applications that range from finance to health. Many algorithms have been proposed for the task of efficiently finding motifs. Surprisingly, most of these proposals do not focus on how to evaluate the discovered motifs. They are typically evaluated by human experts. This is unfeasible even for moderately sized datasets, since the number of discovered motifs tends to be prohibitively large. Statistical significance tests are widely used in the data mining communities to evaluate extracted patterns. In this work we present an approach to calculate time series motifs statistical significance. Our proposal leverages work from the bioinformatics community by using a symbolic definition of time series motifs to derive each motif's p-value. We estimate the expected frequency of a motif by using Markov Chain models. The p-value is then assessed by comparing the actual frequency to the estimated one using statistical hypothesis tests. Our contribution gives means to the application of a powerful technique-statistical tests-to a time series setting. This provides researchers and practitioners with an important tool to evaluate automatically the degree of relevance of each extracted motif.

Efficient Mining of Lag Patterns in Evolving Time Series

“…A normalized time series has interesting properties that allow us to quickly compute length 3 time series motifs. [2], ···} is equal to one less the number of observations in the normalized time series. In other words, ∑…”

“…Given a time series T = {v [1], v [2], ···}, its normalized time series is T = { v [1], v [2], ··· } where…”

“…Research on time series data can be categorized into clustering [8,9,12], finding lagbased correlations [34,22], and motif discovery [5,17,1,2,16].…”

Directed connectivity of brain default networks in resting state using GCA and motif

“…(1) The original fMRI data is processed via time correction, spatial registration, normalization, and smoothing, etc. (12). The whole brain time series data are obtained by filtering high-frequency physiological noise and low frequency signals.…”

Flow field forecasting for univariate time series

“…The purposes of motifs and histories are very different, though. Data mining seeks, as a matter of unsupervised learning, to extract motifs [36] and, for example, evaluate their significance [37]. Flow field forecasting, by contrast, is performing supervised learning to interpolate a new change for a current history based on a set of past observed associations between history and change.…”