Efficient Retrieval of Similar Time Sequences Using DFT

We propose an improvement of the known DFT-based indexing technique for fast retrieval of similar time sequences. We use the last few Fourier coefficients in the distance computation without storing them in the index since every coefficient at the end is the complex conjugate of a coefficient at the beginning and as strong as its counterpart. We show analytically that this observation can accelerate the search time of the index by more than a factor of two. This result was confirmed by our experiments, which were carried out on real stock prices and synthetic data

Compressive Mining: Fast and Optimal Data Mining in the Compressed Domain

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance estimation when the data are represented using different sets of coefficients is still a largely unexplored area. This work studies the optimization problems related to obtaining the \emph{tightest} lower/upper bound on Euclidean distances when each data object is potentially compressed using a different set of orthonormal coefficients. Our technique leads to tighter distance estimates, which translates into more accurate search, learning and mining operations \textit{directly} in the compressed domain. We formulate the problem of estimating lower/upper distance bounds as an optimization problem. We establish the properties of optimal solutions, and leverage the theoretical analysis to develop a fast algorithm to obtain an \emph{exact} solution to the problem. The suggested solution provides the tightest estimation of the $L_2$-norm or the correlation. We show that typical data-analysis operations, such as k-NN search or k-Means clustering, can operate more accurately using the proposed compression and distance reconstruction technique. We compare it with many other prevalent compression and reconstruction techniques, including random projections and PCA-based techniques. We highlight a surprising result, namely that when the data are highly sparse in some basis, our technique may even outperform PCA-based compression. The contributions of this work are generic as our methodology is applicable to any sequential or high-dimensional data as well as to any orthogonal data transformation used for the underlying data compression scheme.Comment: 25 pages, 20 figures, accepted in VLD

Clustering Time Series from Mixture Polynomial Models with Discretised Data

Clustering time series is an active research area with applications in many fields. One common feature of time series is the likely presence of outliers. These uncharacteristic data can significantly effect the quality of clusters formed. This paper evaluates a method of over-coming the detrimental effects of outliers. We describe some of the alternative approaches to clustering time series, then specify a particular class of model for experimentation with k-means clustering and a correlation based distance metric. For data derived from this class of model we demonstrate that discretising the data into a binary series of above and below the median improves the clustering when the data has outliers. More specifically, we show that firstly discretisation does not significantly effect the accuracy of the clusters when there are no outliers and secondly it significantly increases the accuracy in the presence of outliers, even when the probability of outlier is very low

A Linked Data representation of the Nomenclature of Territorial Units for Statistics

The recent publication of public sector information (PSI) data sets has brought to the attention of the scientific community the redundant presence of location based context. At the same time it stresses the inadequacy of current Linked Data services for exploiting the semantics of such contextual dimensions for easing entity retrieval and browsing. In this paper describes our approach for supporting the publication of geographical subdivisions in Linked Data format for supporting the e-government and public sector in publishing their data sets. The topological knowledge published can be reused in order to enrich the geographical context of other data sets, in particular we propose an exploitation scenario using statistical data sets described with the SCOVO ontology. The topological knowledge is then exploited within a service that supports the navigation and retrieval of statistical geographical entities for the EU territory. Geographical entities, in the extent of this paper, are linked data resources that describe objects that have a geographical extension. The data and services presented in this paper allows the discovery of resources that contain or are contained by a given entity URI and their representation within map widgets. We present an approach for a geography based service that helps in querying qualitative spatial relations for the EU statistical geography (proper containment so far). We also provide a rationale for publishing geographical information in Linked Data format based on our experience, within the EnAKTing project, in publishing UK PSI data

DRSP : Dimension Reduction For Similarity Matching And Pruning Of Time Series Data Streams

Similarity matching and join of time series data streams has gained a lot of relevance in today's world that has large streaming data. This process finds wide scale application in the areas of location tracking, sensor networks, object positioning and monitoring to name a few. However, as the size of the data stream increases, the cost involved to retain all the data in order to aid the process of similarity matching also increases. We develop a novel framework to addresses the following objectives. Firstly, Dimension reduction is performed in the preprocessing stage, where large stream data is segmented and reduced into a compact representation such that it retains all the crucial information by a technique called Multi-level Segment Means (MSM). This reduces the space complexity associated with the storage of large time-series data streams. Secondly, it incorporates effective Similarity Matching technique to analyze if the new data objects are symmetric to the existing data stream. And finally, the Pruning Technique that filters out the pseudo data object pairs and join only the relevant pairs. The computational cost for MSM is O(l*ni) and the cost for pruning is O(DRF*wsize*d), where DRF is the Dimension Reduction Factor. We have performed exhaustive experimental trials to show that the proposed framework is both efficient and competent in comparison with earlier works.Comment: 20 pages,8 figures, 6 Table