Parallel Space-Time Kernel Density Estimation

The exponential growth of available data has increased the need for interactive exploratory analysis. Dataset can no longer be understood through manual crawling and simple statistics. In Geographical Information Systems (GIS), the dataset is often composed of events localized in space and time; and visualizing such a dataset involves building a map of where the events occurred.We focus in this paper on events that are localized among three dimensions (latitude, longitude, and time), and on computing the first step of the visualization pipeline, space-time kernel density estimation (STKDE), which is most computationally expensive. Starting from a gold standard implementation, we show how algorithm design and engineering, parallel decomposition, and scheduling can be applied to bring near real-time computing to space-time kernel density estimation. We validate our techniques on real world datasets extracted from infectious disease, social media, and ornithology.

[1]  Irene Casas,et al.  Protection of Geoprivacy and Accuracy of Spatial Information: How Effective Are Geographical Masks? , 2004, Cartogr. Int. J. Geogr. Inf. Geovisualization.

[2]  Shahid H. Bokhari,et al.  A Partitioning Strategy for Nonuniform Problems on Multiprocessors , 1987, IEEE Transactions on Computers.

[3]  David M. Nicol,et al.  Rectilinear Partitioning of Irregular Data Parallel Computations , 1994, J. Parallel Distributed Comput..

[4]  Mehmet Deveci,et al.  Multi-Jagged: A Scalable Parallel Spatial Partitioning Algorithm , 2016, IEEE Transactions on Parallel and Distributed Systems.

[5]  H. Karimabadi,et al.  Global Hybrid Simulations of the Earth's Magnetosphere , 2006 .

[6]  RENAUD LEPÈRE,et al.  Approximation Algorithms for Scheduling Malleable Tasks Under Precedence Constraints , 2001, Int. J. Found. Comput. Sci..

[7]  Eric M. Delmelle,et al.  Visualizing the impact of space-time uncertainties on dengue fever patterns , 2014, Int. J. Geogr. Inf. Sci..

[8]  Sverre J. Aarseth,et al.  Gravitational N-Body Simulations , 2003 .

[9]  William Ribarsky,et al.  Space-Time Kernel Density Estimation for Real-Time Interactive Visual Analytics , 2017, HICSS.

[10]  Cevdet Aykanat,et al.  Sparse matrix decomposition with optimal load balancing , 1997, Proceedings Fourth International Conference on High-Performance Computing.

[11]  William B. March,et al.  ASKIT: An Efficient, Parallel Library for High-Dimensional Kernel Summations , 2016, SIAM J. Sci. Comput..

[12]  Alan T. Murray,et al.  Spatial Clustering Overview and Comparison: Accuracy, Sensitivity, and Computational Expense , 2014 .

[13]  Tor Sørevik,et al.  Partitioning an Array onto a Mesh of Processors , 1996, PARA.

[14]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[15]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[16]  R. Eisen,et al.  Using Geographic Information Systems and Decision Support Systems for the Prediction , Prevention , and Control of Vector-Borne Diseases , 2010 .

[17]  Sascha Hunold.  Scheduling Moldable Tasks with Precedence Constraints and Arbitrary Speedup Functions on Multiprocessors , 2013, PPAM.

[18]  Alex Pothen,et al.  What Color Is Your Jacobian? Graph Coloring for Computing Derivatives , 2005, SIAM Rev..

[19]  Mehmet Deveci,et al.  Parallel Graph Coloring for Manycore Architectures , 2016, 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS).

[20]  Larry S. Davis,et al.  Improved fast gauss transform and efficient kernel density estimation , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[21]  Sverre J. Aarseth.  Gravitational N-Body Simulations: Tools and Algorithms , 2003 .

[22]  Joel H. Saltz,et al.  Experimental evaluation of efficient sparse matrix distributions , 1996, ICS '96.

[23]  Bernard W. Silverman,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[24]  Unai López Novoa.  Contributions to the efficient use of general purpose coprocessors: kernel density estimation as case study , 2015 .

[25]  Eric M. Delmelle,et al.  Spatio-Temporal Patterns of Dengue Fever in Cali, Colombia , 2013, Int. J. Appl. Geospat. Res..

[26]  Ümit V. Çatalyürek,et al.  A Scalable Parallel Graph Coloring Algorithm for Distributed Memory Computers , 2005, Euro-Par.

[27]  Wenwu Tang,et al.  Accelerating the discovery of space-time patterns of infectious diseases using parallel computing. , 2016, Spatial and spatio-temporal epidemiology.

[28]  Tomoki Nakaya,et al.  Visualising Crime Clusters in a Space‐time Cube: An Exploratory Data‐analysis Approach Using Space‐time Kernel Density Estimation and Scan Statistics , 2010, Trans. GIS.

[29]  Elisabeth Larsson,et al.  Stable Computations with Gaussian Radial Basis Functions , 2011, SIAM J. Sci. Comput..