S Space-in-Time and Time-in-Space Self-Organizing Maps i Ti d Ti - PowerPoint PPT Presentation

S Space-in-Time and Time-in-Space Self-Organizing Maps i Ti d Ti i S S lf O i i M for Exploring Spatiotemporal Patterns Gennady Andrienko & Natalia Andrienko http://geoanalytics.net htt // l ti t Sebastian Bremm, Tobias Schreck, Tatiana von Landesberger TU Darmstadt Peter Bak, Daniel Keim Univ. Konstanz DFG Priority Research Program on Visual Analytics SPP 1335 DFG Priority Research Program on Visual Analytics, SPP 1335 10 June 2010, presentation at EuroVis Bordeaus, FR

S Spatial Time Series: Data Structure ti l Ti S i D t St t Spatial references: states of the USA Spatial references: states of the USA Temporal references: years from 1960 till 2000 (41) Attributes: population + various crime rates Attributes: population + various crime rates Gennady Andrienko 10 June 2010, presentation at EuroVis 2 http://geoanalytics.net Bordeaux, FR

S Spatial Visualizations: animated maps, diagram maps ti l Vi li ti i t d di Gennady Andrienko 10 June 2010, presentation at EuroVis 3 http://geoanalytics.net Bordeaux, FR

T Temporal visualizations l i li ti Gennady Andrienko 10 June 2010, presentation at EuroVis 4 http://geoanalytics.net Bordeaux, FR

S Scalability problem l bilit bl What if we have � - Multiple attributes - Many places - Long time series L ti i Interactive visualization is not sufficient � We need grouping in space and time => Clustering � Gennady Andrienko 10 June 2010, presentation at EuroVis 5 http://geoanalytics.net Bordeaux, FR

D t Data sets t Cars in Milan, Italy � - 175,890 trajectories of 17,241 cars over 7 days - 2,075,216 records <id,x,y,t,speed> - Aggregated over 18x22 1km 2 rectangular regions A t d 18 22 1k 2 t l i and 7x24 hourly intervals USA crime statistics � - 7 crime attributes - 52 states - 52 states - 41 years Gennady Andrienko 10 June 2010, presentation at EuroVis 6 http://geoanalytics.net Bordeaux, FR

A Approach h Gennady Andrienko 10 June 2010, presentation at EuroVis 7 http://geoanalytics.net Bordeaux, FR

A Approach h 2) Group time intervals by similarity of spatial situations: clustering “Space in Time” 1) Group places by ) G oup p aces by similarity of temporal dynamics: clustering l t i “Time in Space” Gennady Andrienko 10 June 2010, presentation at EuroVis 8 http://geoanalytics.net Bordeaux, FR

SOM SOM Self-Organizing Map (Kohonen 2001) is a neural network type vector projection and � quantization algorithm. By means of a competitive, iterative training process, a network of prototype vectors � (or neurons, or cells) is trained (adjusted) to the input vector data. ( ) ( j ) p The output of the algorithm is a network of vectors that is approximately topology � preserving w.r.t. the input data. The network can be interpreted as a set of clusters and simultaneously as a map to Th t k b i t t d t f l t d i lt l t � lay out the input data elements (e.g., in the nearest neighbor sense w.r.t. the prototypes). Typically, two-dimensional rectangular or hexagonal prototype vector networks are � assumed. The capability of SOM to arrange input data in a regular network structure provides � good opportunities for visualization. Gennady Andrienko 10 June 2010, presentation at EuroVis 9 http://geoanalytics.net Bordeaux, FR

S Space-in-Time and Time-in-Space SOMs: visualization i Ti d Ti i S SOM i li ti Bars on top of a cell show 1. number of objects inside Shading of borders between 2. cells reflects similarity of features Similarity of colors also reflects 3. similarity of the features C l Colors are projected on other j t d th 4. displays: maps (if grouping places) and and time graphs (if grouping time intervals) Gennady Andrienko 10 June 2010, presentation at EuroVis 10 http://geoanalytics.net Bordeaux, FR

Time-in-Space SOM of driving speeds Ti i S SOM f d i i d Gennady Andrienko 10 June 2010, presentation at EuroVis 11 http://geoanalytics.net Bordeaux, FR

Time-in-Space SOM of driving speeds Ti i S SOM f d i i d Inside cells: � index images (what is grouped) Gennady Andrienko 10 June 2010, presentation at EuroVis 12 http://geoanalytics.net Bordeaux, FR

Time-in-Space SOM of driving speeds Ti i S SOM f d i i d Inside cells: � feature images (what are the features) Gennady Andrienko 10 June 2010, presentation at EuroVis 13 http://geoanalytics.net Bordeaux, FR

Time-in-Space SOM of driving speeds Ti i S SOM f d i i d Inside cells: � index images (what is grouped) � feature images (what are the features) Gennady Andrienko 10 June 2010, presentation at EuroVis 14 http://geoanalytics.net Bordeaux, FR

Ti Time-in-Space SOM: details i S SOM d t il Gennady Andrienko 10 June 2010, presentation at EuroVis 15 http://geoanalytics.net Bordeaux, FR

Ti Time-in-Space SOM: details i S SOM d t il Gennady Andrienko 10 June 2010, presentation at EuroVis 16 http://geoanalytics.net Bordeaux, FR

Space-in-time SOM (index images) S i ti SOM (i d i ) Gennady Andrienko 10 June 2010, presentation at EuroVis 17 http://geoanalytics.net Bordeaux, FR

Space-in-time SOM (index & feature images) S i ti SOM (i d & f t i ) Gennady Andrienko 10 June 2010, presentation at EuroVis 18 http://geoanalytics.net Bordeaux, FR

Space-in-time SOM (colours of time intervals) S i ti SOM ( l f ti i t l ) Gennady Andrienko 10 June 2010, presentation at EuroVis 19 http://geoanalytics.net Bordeaux, FR

Space-in-time SOM (colours of time intervals) S i ti SOM ( l f ti i t l ) Gennady Andrienko 10 June 2010, presentation at EuroVis 20 http://geoanalytics.net Bordeaux, FR

D t Detect the expected t th t d One more data set about Milan: � mobile phone calls for 9 days aggregated by hours and regions We expect high periodicity and clear regionalization of the calling activity � Gennady Andrienko 10 June 2010, presentation at EuroVis 21 http://geoanalytics.net Bordeaux, FR

Ti Time-in-Space i S SOM of mobile phone calls Gennady Andrienko 10 June 2010, presentation at EuroVis 22 http://geoanalytics.net Bordeaux, FR

S Space-in-Time i Ti SOM of mobile phone calls Gennady Andrienko 10 June 2010, presentation at EuroVis 23 http://geoanalytics.net Bordeaux, FR

Di Discover the unexpected th t d USA crime statistics � - 7 crime attributes - 52 states - 41 years 41 Problems: Problems Different ranges of attributes � Outliers Outliers � Gennady Andrienko 10 June 2010, presentation at EuroVis 24 http://geoanalytics.net Bordeaux, FR

C i Crime attributes tt ib t Gennady Andrienko 10 June 2010, presentation at EuroVis 25 http://geoanalytics.net Bordeaux, FR

C i Crime attributes: normalized tt ib t li d Gennady Andrienko 10 June 2010, presentation at EuroVis 26 http://geoanalytics.net Bordeaux, FR

Si Similarity of states by crime dynamics il it f t t b i d i Gennady Andrienko 10 June 2010, presentation at EuroVis 27 http://geoanalytics.net Bordeaux, FR

Similarity of time periods by situations Si il it f ti i d b it ti Gennady Andrienko 10 June 2010, presentation at EuroVis 28 http://geoanalytics.net Bordeaux, FR

C Conclusions l i Interactive and animated maps and graphs are not sufficient for analyzing large and � complex space-time data. Visual methods need to be augmented by computations. With space-in-time and time-in-space SOMs we consider data from two different � perspectives: p p - places grouped by similar attribute dynamics - time intervals grouped by similar spatial distributions of attribute values Colours of the groups reflect their similarity � Case studies demonstrate the value of the approach � - for detecting the expected - for detecting the expected - for discovering the unexpected Current work: non-tabular data, other clustering/projection methods � Live demo is possible Gennady Andrienko 10 June 2010, presentation at EuroVis 29 http://geoanalytics.net Bordeaux, FR