1d-SAX: A Novel Symbolic Representation for Time Series

Malinowski, Simon; Guyet, Thomas; Quiniou, René; Tavenard, Romain

doi:10.1007/978-3-642-41398-8_24

Cited by 56 publications

(31 citation statements)

References 10 publications

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“…Data adaptive methods include: piecewise polynomials, Adaptive Piecewise Constant Approximation (APCA), Singular Value Decomposition (SVD), symbolic, and trees. Symbolic methods include commonly used SAX [11] and its derivatives iSAX [21], 1D-SAX [12].…”

Section: Related Work a Time Series Data Representationmentioning

confidence: 99%

Visualization of Generic Utility of Sequential Patterns

et al. 2020

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Most of the literature on utility pattern mining (UPM) assumes that the particular patterns' utility in known in advance. Concurrently, in frequent pattern mining (FPM) it is assumed that all patterns take the same value. In reality, the information about the utility of patterns is not or hardly available in most cases. Moreover, the utility and frequency of the particular pattern are not directly proportional. An algorithm for estimating a generic pattern utility has been recently proposed, but the numeric results might be difficult to interpret. In particular, in datasets with many independent instances or groups. In this paper, we present an approach to generating utility bitmaps that provide visual representation of the numeric data obtained using generic pattern utility algorithm. We demonstrate validity of this approach on two datasets: PAMAP2 Physical Activity Monitoring Data Set, an open dataset from the UCI Machine Learning Repository, and an ECG dataset collected using Biopac Student Lab during Ruffier's test. For PAMAP2 dataset, utility bitmaps allow for immediate separation of various physical activities. Variation between participants are present, but do not overshadow differences between the activity types. For the ECG dataset, utility bitmaps immediately indicate age and fitness differences between the participants, even thought this information was not available to the algorithm. In both cases, partial similarity in bitmaps can be traced back to partial similarity in activities or participants generating the data. Based on these tests, the approach seems to be promising for exploratory analysis of large collections of long time series and possibly other sequential patterns such as distance series common in sports data analysis and depth series common in petroleum engineering.

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Section: Related Work a Time Series Data Representationmentioning

confidence: 99%

Visualization of Generic Utility of Sequential Patterns

et al. 2020

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“…The SAX variation known as 1d-SAX [22] extends the usual alphabetic symbols to a system able to contain information about the average and the trend of the series within a segment. A natural extension of 1d-SAX takes median values on each interval, and provides similar results to linear regression.…”

Section: Multiresolution Based On Quantilesmentioning

confidence: 99%

“…There are a few works related to multiresolution time series with respect to climate or weather time series, including solar irradiance and climate reconstructions [19] and a hybrid approach to removing noise from a climate time series [20]. However, the work introduced in this paper is closer to the hierarchy-ofclusters approach proposed for use in multiresolution image analysis [21]; being a variation of 1d-SAX [22] but extending the more common SAX methodology to deal with time series quantiles. MRQ starts with the typical piecewise aggregate approximation (PAA) to divide the series into segments of equal length [23].…”

Section: Introductionmentioning

confidence: 99%

SAX-quantile based multiresolution approach for finding heatwave events in summer temperature time series

Herrera

Ferreira

Coley³

et al. 2016

AIC

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Time series pattern discovery is of great importance in a large variety of environmental and engineering applications, from supporting predictive models to helping to understand hidden underlying processes. This work develops a multiresolution time series method for extracting patterns in weather records, particular temperature data. The topic is important, as, given a warming climate, morbidity and mortality are expected to rise as heatwave frequency and intensity increase. By analysing summer temperature quantiles at different levels of coarseness, it was found that compounding models can contain a complete description of severe weather events. This new multiresolution quantile approach is developed as an extension of the symbolic aggregate approximation of the temperature time series in which quantiles are computed at every stretch of the piecewise partition. The process is iterated at different scales of the partition, and it was found to be a very useful approach for finding patterns related to both heatwave periods and intensities. The method is successfully tested using real weather records from Brazil (Recife) and the UK (London), and it was found that in both locations heatwave intensity and frequency are increasing at a substantial rate. In addition, it was found that the rate of increase in intensity of the heatwaves is far outstripping the rate of increase in mean summer temperature: by a factor of 2 in Recife and a factor of 6 in London. The approach will be of use to those looking at the impact of future climates on civil engineering, water resources, energy use, agriculture and health care, or those looking for sustained extreme events in any time series.

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“…The SAX algorithm uses piecewise aggregate approximation (PAA) [23] for dimensionality reduction, but this method cannot capture local trends, and in turn the overall general shape of the time series, due to smoothing of perceptually important points (PIP) [13]. In order to overcome this limitation recent methods suggest storing additional data with each symbol, such as slope information, maximum and minimum amplitude points, regression and PIPs [3,42,29,53,48,35,37]. In [30] Li et al stored additional information along with SAX symbols and visually represent them using Sector Visualization and VizTree.…”

Section: Dimensionality Reductionmentioning

confidence: 99%

Shape grammar extraction for efficient query-by-sketch pattern matching in long time series

Muthumanickam

Vrotsou

Cooper

et al. 2016

2016 IEEE Conference on Visual Analytics Science and Technology (VAST)

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Figure 1: A schematic representation of the work flow. A sketched pattern of interest is matched to the time-series data. Efficient approximation, classification and symbol assignment, based on gradient ratios, enables real-time pattern searching within very large time-series. The steps depicted with green boxes are executed when a new input time series is loaded or when it undergoes hierarchical approximation, yellow boxes only when a new sketch is entered. ABSTRACTLong time-series, involving thousands or even millions of time steps, are common in many application domains but remain very difficult to explore interactively. Often the analytical task in such data is to identify specific patterns, but this is a very complex and computationally difficult problem and so focusing the search in order to only identify interesting patterns is a common solution. We propose an efficient method for exploring user-sketched patterns, incorporating the domain expert's knowledge, in time series data through a shape grammar based approach. The shape grammar is extracted from the time series by considering the data as a combination of basic elementary shapes positioned across different amplitudes. We represent these basic shapes using a ratio value, perform binning on ratio values and apply a symbolic approximation. Our proposed method for pattern matching is amplitude-, scale-and translation-invariant and, since the pattern search and pattern constraint relaxation happen at the symbolic level, is very efficient permitting its use in a real-time/online system. We demonstrate the effectiveness of our method in a case study on stock market data although it is applicable to any numeric time series data.

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1d-SAX: A Novel Symbolic Representation for Time Series

Cited by 56 publications

References 10 publications

Visualization of Generic Utility of Sequential Patterns

Visualization of Generic Utility of Sequential Patterns

SAX-quantile based multiresolution approach for finding heatwave events in summer temperature time series

Shape grammar extraction for efficient query-by-sketch pattern matching in long time series

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