Analyzing time series data is crucial for many applications. In particular, subsequence search refers to finding subsequences within an input time series T that are similar to a query sequence Q. Existing subsequence search approaches typically employ Euclidean distance or Dynamic Time Warping as similarity measures and address range queries. In this paper, we focus on Chebyshev distance, which is the largest difference between each individual pair of points across the entire length of two compared subsequences. We call such similar pairstwins. We first show how existing time series indices can be extended to perform twin subsequence search. Then, we introduce TS-Index, a novel index tailored to the computation of twin subsequence search queries. Moreover, given that specifying a distance threshold is often not straightforward, we show how TS-Index can also be used to evaluate kNN queries. Our extensive experimental evaluation compares these approaches using real time series datasets. The results demonstrate that TS-Index can retrieve twin subsequences faster than all other methods under various conditions.

We present spaTScope, a web application for visual exploration of geolocated time series. Analyzing such data is becoming increasingly important in many domains, such as energy demand management, geomarketing and geosocial networks. spaTScope allows users to visually explore large collections of geolocated time series and obtain insights about trends and patterns in their area of interest. The provided functionalities leverage a hybrid index that allows to navigate and group the available time series based not only on their similarity but also on spatial proximity. The results are visualized using linked plots combining maps and timelines.

Geolocated time series, i.e., time series associated with certain locations, abound in many modern applications. In this paper, we consider hybrid queries for retrieving geolocated time series based on filters that combine spatial distance and time series similarity. For the latter, unlike existing work, we allow filtering based on local similarity, which is computed based on subsequences rather than the entire length of each series, thus allowing the discovery of more fine-grained trends and patterns. To efficiently support such queries, we first leverage the state-of-the-art BTSR-tree index, which utilizes bounds over both the locations and the shapes of time series to prune the search space. Moreover, we propose optimizations that check at specific timestamps to identify candidate time series that may exceed the required local similarity threshold. To further increase pruning power, we introduce the SBTSR-tree index, an extension to BTSR-tree, which additionally segments the time series temporally, allowing the construction of tighter bounds. Our experimental results on several real-world datasets demonstrate that SBTSR-tree can provide answers much faster for all examined query types.

Time series exploration and mining has many applications across several industrial and scientific domains. In this paper, we consider the problem of detecting locally similar pairs and groups, called bundles, over co-evolving time series. These are pairs or groups of subsequences whose values do not differ by more than ε for at least δ consecutive timestamps, thus indicating common local patterns and trends. We first present a baseline algorithm that performs a sweep line scan across all timestamps to identify matches. Then, we propose a filter-verification technique that only examines candidate matches at judiciously chosen checkpoints across time. Specifically, we introduce two block scanning algorithms for discovering local pairs and bundles respectively, which leverage the potential of checkpoints to aggressively prune the search space. We experimentally evaluate our methods against real-world and synthetic datasets, demonstrating a speed-up in execution time by an order of magnitude over the baseline.

A geolocated time series is a sequence of values associated with a geolocation, such as measurements provided by a sensor installed at a certain location. In this paper, we address the problem of hybrid similarity joins over such geolocated time series. This operation returns all pairs of geolocated time series that exhibit similar behavior in the time series domain while also being closely located in space. First, we propose algorithms for performing such join operations using different types of indices, including spatial-only, time series-only, and hybrid indices. Such centralized indexing schemes can cope well with moderate data volumes but they face scalability issues when the dataset size increases significantly. To overcome this problem, we present a MapReduce-based processing scheme with space-driven partitioning. Our parallel and distributed algorithm leverages our hybrid index for geolocated time series to efficiently execute similarity joins locally within each partition and minimize the amount of data that needs to be shuffled between processing nodes. An extensive experimental evaluation confirms that our approach can efficiently compute all matching pairs even for datasets containing millions of geolocated time series.

Time series associated with specific locations, such as visitor check-ins or sensor readings, have increased in size and popularity in several domains. Although several works have focused on efficient time series similarity search, there has been limited attention to the inherent challenge that geolocated time series introduce for hybrid queries on both spatial proximity and time series similarity. To efficiently process such queries, we propose a hybrid index, called TSR-tree, which extends the R-tree by introducing appropriate bounds for the time series indexed at each node. This reduces node accesses during query evaluation by simultaneously pruning the search space in the spatial domain and the time series domain while traversing the index. We also present an optimized version, the BTSR-tree, which uses tighter bounds by bundling together similar time series in each node. We describe how these indices can be used to efficiently evaluate different variants of hybrid queries combining spatial and time series filtering or ranking. Finally, we experimentally evaluate our work using real-world datasets from diverse domains, demonstrating a speed-up of 1.5 to 5 times in hybrid query workloads against the baseline R-tree method.

Water management field has concentrated great interest, with the potential to affect the long term well-being, the societal economy and security. In parallel, it imposes specific research challenges which have not been already met, due to the lack of fine-grained data. Knowledge extraction and decision making for efficient management in the energy field has attracted a lot of interest in Big Data research. However, the water domain is strikingly absent, with minimal focused work on data exploitation and useful information extraction. The goal of this work is to discover persistent and meaningful knowledge from water consumption data and provide efficient and scalable big data management and analysis services. We propose a novel methodology which exploits machine learning techniques and introduces a robust probabilistic classifier which is able to operate on data of arbitrary dimensionality and of huge volume. It also provides added value services and new operation models for the water management domain, inducing sustainable behavioural changes for consumers, which can further raise social awareness. It does so through a new k-Nearest Neighbour based algorithm, developed in a parallel and distributed environment, which operates over Big Data and discovers useful knowledge about consumption classes and other water related attitudinal properties. A detailed experimental evaluation assesses the effectiveness and efficiency of the algorithm on prediction precision along with the provision of analytics. The results show that this method is prosperous and provides accurate and interesting results that allow us to identify useful characteristics, not only for the households, but also for the water utilities.