k-Shape

Paparrizos, John; Gravano, Luis

doi:10.1145/2723372.2737793

Cited by 383 publications

(50 citation statements)

References 85 publications

(134 reference statements)

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“…In order to classify all piezometers, partitional clustering [37] was selected to create partitions. The specification of the number of clusters (k) is tedious work that must be performed before starting the algorithm.…”

Section: Time Series Clustering (Tsc)mentioning

confidence: 99%

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Clustering Groundwater Level Time Series of the Exploited Almonte-Marismas Aquifer in Southwest Spain

Naranjo‐Fernández

Guardiola‐Albert

Aguilera

et al. 2020

Water

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Groundwater resources are regularly the principal water supply in semiarid and arid climate areas. However, groundwater levels (GWL) in semiarid aquifers are suffering a general decrease because of anthropic exploitation of aquifers and the repercussions of climate change. Effective groundwater management strategies require a deep characterization of GWL fluctuations, in order to identify individual behaviors and triggering factors. In September 2019, the Guadalquivir River Basin Authority (CHG) declared that there was over-exploitation in three of the five groundwater bodies of the Almonte-Marismas aquifer, Southwest Spain. For that reason, it is critical to understand GWL dynamics in this aquifer before the new Spanish Water Resources Management Plans (2021–2027) are developed. The application of GWL series clustering in hydrogeology has grown over the past few years, as it is an extraordinary tool that promptly provides a GWL classification; each group can be related to different responses of a complex aquifer under any external change. In this work, GWL time series from 160 piezometers were analyzed for the period 1975 to 2016 and, after data pre-processing, 24 piezometers were selected for clustering with k-means (static) and time series (dynamic) clustering techniques. Six and seven groups (k) were chosen to apply k-means. Six characterized types of hydrodynamic behaviors were obtained with time series clustering (TSC). Number of clusters were related to diverse affections of water exploitation depending on soil uses and hydrogeological spatial distribution parameters. TSC enabled us to distinguish local areas with high hydrodynamic disturbance and to highlight a quantitative drop of GWL during the studied period.

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Section: Time Series Clustering (Tsc)mentioning

confidence: 99%

“…Considering this singularity of GWL behavior, the most appropriate distance to measure GWL time series is Shape-Based Distance (SBD) [15]. SBD warps the time series and it is based on the cross-correlation with coefficient normalization (NCCc) and shape extraction as a prototype function (Equation 5) [37]:…”

Section: Time Series Clustering (Tsc)mentioning

confidence: 99%

Clustering Groundwater Level Time Series of the Exploited Almonte-Marismas Aquifer in Southwest Spain

Naranjo‐Fernández

Guardiola‐Albert

Aguilera

et al. 2020

Water

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“…end if 24: end for 25: end for 26: iter ← iter + 1 27: end while (*) "S hapeExtraction()" that is reffer to Algorithm 2 in paper [15].…”

Section: Workflow For Aprep-s 31 Overview Of Aprep-s Workflowmentioning

confidence: 99%

“…We use the "k-Shape [15]" method for evaluating the data similarity. This method considers the shape of the time series in clustering tasks, in contrast to traditional methods such as k-means.…”

Section: K-shapementioning

confidence: 99%

Recommendation of Imputing Value for Sensor Data based on Programming by Example

Nagashima

Kato

2020

Journal of Information Processing

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Large volumes of data are typically used during analyses. Data preprocessing, which involves detecting outliers, handling missing data, data formatting, integration, and normalization, is essential for achieving accurate results. Many tools and methods are available for reducing preprocessing time. However, most analysts face difficulties when using them. This paper proposes a method for handling outliers and missing data, called Automated PRE-Processing for Sensor Data (APREP-S). For reducing analysis resources, we combine programming by example and machine learning via Bayesian inference, inputting human knowledge to APREP-S as an example and calculating a proper proportion by machine learning via Bayesian inference. We also define k-Shape as the calculation of the rate of similarity of time-series data. In evaluation, we use sensor data of temperature and humidity and compare the sum of the square of the errors of four methods, between original data and outputs of each methods, (1) APREP-S, (2) mean of the entire data, (3) mean of the around-the-target imputation data, and (4) spline interpolation. It is verified that APREP-S is a more suitable method for humidity data than temperature data. preprocessing method. we consider the reason is that humidity data have more changing points.

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“…Various clustering algorithms have been proposed for data series [25,34], and such approaches can be used to facilitate nearest neighbor search. The general approach involves adapting distance measure between data series and using a clustering algorithm on top (e.g., K-means [40], K-shape [50], agglomerative [25], etc.). Such algorithms require multiple passes over the data to build (e.g., to measure distances between all pairs of points as in agglomerative clustering, or to iteratively refine clusters with K-means).…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

Coconut: sortable summarizations for scalable indexes over static and streaming data series

et al. 2019

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Many modern applications produce massive streams of data series that need to be analyzed, requiring efficient similarity search operations. However, the state-of-the-art data series indexes that are used for this purpose do not scale well for massive datasets in terms of performance, or storage costs. We pinpoint the problem to the fact that existing summarizations of data series used for indexing cannot be sorted while keeping similar data series close to each other in the sorted order. To address this problem, we present Coconut, the first data series index based on sortable summarizations, and the first efficient solution for indexing and querying streaming series. The first innovation in Coconut is an inverted, sortable data series summarization that organizes data series based on a z-order curve, keeping similar series close to each other in the sorted order. As a result, Coconut is able to use bulkloading and updating techniques that rely on sorting to quickly build and maintain a contiguous index using large sequential disk I/Os. We then explore prefixbased and median-based splitting policies for bottomup bulk-loading, showing that median-based splitting outperforms the state of the art, ensuring that all nodes are densely populated. Finally, we explore the impact H. Kondylakis FORTH-ICS of sortable summarizations on variable size window queries, showing that they can be supported in the presence of updates through efficient merging of temporal partitions. Overall, we show analytically and empirically that Coconut dominates the state-of-the-art data series indexes in terms of construction speed, query speed, and storage costs.

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k-Shape

Cited by 383 publications

References 85 publications

Clustering Groundwater Level Time Series of the Exploited Almonte-Marismas Aquifer in Southwest Spain

Clustering Groundwater Level Time Series of the Exploited Almonte-Marismas Aquifer in Southwest Spain

Recommendation of Imputing Value for Sensor Data based on Programming by Example

Coconut: sortable summarizations for scalable indexes over static and streaming data series

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