Topological Approach for Finding Nearest Neighbor Sequence in Time Series

Avogadro, Paolo; Dominoni, Matteo

doi:10.5220/0008493302330244

Cited by 3 publications

(3 citation statements)

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“…Time series display a form of time correlation first described as Consecutive Neighborhood Preserving (CNP) Property . This property can be regarded as a form of time topology which makes possible to improve an approximate nnd profile of a time series at a low cost (Avogadro and Dominoni, 2019). This can be summarized by noticing that there is a high chance that the Euclidean nearest neighbors of two time-close sequences (i.e.…”

Section: Short Range Time Topologymentioning

confidence: 99%

“…However, this nnd profile is still rough, so it is better to smear it with a moving average. It has been shown, in fact, that the exact nnd profile (matrix profile) displays a "sort of smoothness" Avogadro and Dominoni, 2019). A rough nnd profile is likely to contain also spikes surrounded by dips.…”

Section: Initial Re-ordering Processmentioning

confidence: 99%

“…At variance, a true good discord candidate should belong to a "peak": it should be surrounded by quite a few other sequences with high nnd values. This time coherence of the nnds spans approximately the length of a sequence (Avogadro and Dominoni, 2019), for this reason the moving average takes into account s + 1 sequences:…”

Section: Initial Re-ordering Processmentioning

confidence: 99%

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A fast algorithm for complex discord searches in time series: HOT SAX Time

Avogadro¹,

Dominoni²

2021

Preprint

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Time series analysis is quickly proceeding towards long and complex tasks. In recent years, fast approximate algorithms for discord search have been proposed in order to compensate for the increasing size of the time series. It is more interesting, however, to find quick exact solutions. In this research, we improved HOT SAX by exploiting two main ideas: the warm-up process, and the similarity between sequences close in time. The resulting algorithm, called HOT SAX Time (HST), has been validated with real and synthetic time series, and successfully compared with HOT SAX, RRA, SCAMP, and DADD. The complexity of a discord search has been evaluated with a new indicator, the cost per sequence (cps), which allows one to compare searches on time series of different lengths. Numerical evidence suggests that two conditions are involved in determining the complexity of a discord search in a non-trivial way: the length of the discords, and the noise/signal ratio. In the case of complex searches, HST can be more than 100 times faster than HOT SAX, thus being at the forefront of the exact discord search.

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Section: Short Range Time Topologymentioning

confidence: 99%

Section: Initial Re-ordering Processmentioning

confidence: 99%