Space and time are two critical components of many real world systems. For this reason, analysis of anomalies in spatiotemporal data has been a great of interest. In this work, application of tensor decomposition and eigenspace techniques on spatiotemporal hotspot detection is investigated. An algorithm called SST-Hotspot is proposed which accounts for spatiotemporal variations in data and detect hotspots using matching of eigenvector elements of two cases and population tensors. The experimental results reveal the interesting application of tensor decomposition and eigenvector-based techniques in hotspot analysis.
Related spatiotemporal techniques can be divided into two main categories: scan statistics and clustering-based techniques. Clustering-based approaches @cite_16 @cite_12 @cite_6 @cite_8 @cite_7 are based on this idea that first, thresholds are inferred from the population data and then estimated thresholds are applied on clustering of data points of cases data. Clustering-based approaches have their own limitations and strengths. Their prominent benefit is that they provide exact shape of clusters opposed to the scan statistics-based methods where clusters necessarily should be a regular shape and are not realistic. On the other hand, handling complex data is not straightforward for clustering-based techniques.
@cite_7 @cite_8 @cite_6 @cite_16 @cite_12
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When clusters with different densities and noise lie in a spatial point set, the major obstacle to classifying these data is the determination of the thresholds for classification, which may form a series of bins for allocating each point to different clusters. Much of the previous work has adopted a model-based approach, but is either incapable of estimating the thresholds in an automatic way, or limited to only two point processes, i.e. noise and clusters with the same density. In this paper, we present a new density-based cluster method (DECODE), in which a spatial data set is presumed to consist of different point processes and clusters with different densities belong to different point processes. DECODE is based upon a reversible jump Markov Chain Monte Carlo (MCMC) strategy and divided into three steps. The first step is to map each point in the data to its mth nearest distance, which is referred to as the distance between a point and its mth nearest neighbor. In the second step, classification thresholds are determined via a reversible jump MCMC strategy. In the third step, clusters are formed by spatially connecting the points whose mth nearest distances fall into a particular bin defined by the thresholds. Four experiments, including two simulated data sets and two seismic data sets, are used to evaluate the algorithm. Results on simulated data show that our approach is capable of discovering the clusters automatically. Results on seismic data suggest that the clustered earthquakes, identified by DECODE, either imply the epicenters of forthcoming strong earthquakes or indicate the areas with the most intensive seismicity, this is consistent with the tectonic states and estimated stress distribution in the associated areas. The comparison between DECODE and other state-of-the-art methods, such as DBSCAN, OPTICS and Wavelet Cluster, illustrates the contribution of our approach: although DECODE can be computationally expensive, it is capable of identifying the number of point processes and simultaneously estimating the classification thresholds with little prior knowledge. The scan statistic is commonly used to test if a one dimensional point process is purely random, or if any clusters can be detected. Here it is simultaneously extended in three directions:(i) a spatial scan statistic for the detection of clusters in a multi-dimensional point process is proposed, (ii) the area of the scanning window is allowed to vary, and (iii) the baseline process may be any inhomogeneous Poisson process or Bernoulli process with intensity pro-portional to some known function. The main interest is in detecting clusters not explained by the baseline process. These methods are illustrated on an epidemiological data set, but there are other potential areas of application as well. Clustering is one of the basic data mining tasks that can be used to extract hidden information from data in the absence of target classes. One of the most well-known density based clustering algorithms for processing spatial data is Density-Based Spatial Clustering of Application with Noise (DBSCAN) that uses learning parameters epsiv and minPts to define the density that will be sought in the data set while forming the clusters. The major drawbacks of the DBSCAN algorithm are its sensitivity to user input required to execute the algorithm, inability to recognize clusters with different densities, and computational complexity. In this study, we propose a three-level clustering method to address the second issue. The first level selects appropriate grids so that the density is homogeneous in each grid. The second stage merges cells with similar densities and identifies the most suitable values of epsiv and minPts in each grid that remain after merging. The third step of the proposed method executes the DBSCAN method with these identified parameters in the dataset. The proposed method is tested in three artificial benchmark data sets to demonstrate that the clusters are correctly identified. Visualizing large geo-demographical datasets using pixel-based techniques involves mapping the geospatial dimensions of a data point to screen coordinates and appropriately encod- ing its statistical value by color. The analysis of such data presents a great challenge. General tasks involve clustering, categorization, and searching for patterns of interest for sociological or economic research. Available visual encodings and screen space limitations lead to over-plotting and hiding of patterns and clusters in densely populated areas, while sparsely populated areas waste space and draw the attention away from the areas of interest. In this paper, two new approaches (RadialScale and AngularScale) are introduced to create density-equalized maps, while preserving recognizable features and neighborhoods in the visualization. These approaches build the core of a multi-scal- ing technique based on local features of the data described as local minima and maxima of point density. Scaling is conducted several times around these features, which leads to more homogeneous distortions. Results are illustrated using several real-world datasets. Our evaluation shows that the proposed techniques outperform traditional techniques as regard the homogeneity of the resulting data distributions and therefore build a more appropriate basis for analytic purposes.