1 Clustering of location- based data Mohammad Rezaei May 2013

Data mining and Clustering - Huge amount of location-based Data - Need for mechanisms to extract knowledge - Clustering as an important field in spatio- temporal data mining 2

Clustering 3

Some applications Routing Interesting places Recommendation of services Marketing management Users with same interests Visualization 4

Clustering Problems in Mopsi Clutter of markers on the map Similar services or photos in a list Categorization of services Distribution of users locations Timeline view of photos Clustering of events 5

Clutter of markers 6

Search results 7 Clustering

Photos 8

Users 9

Solutions Grid based clustering Distance based clustering 10

Google Maps version Using location in pixels for grid-base clustering - 22 zoom levels - 256*256 in zoom level 0 to * in zoom level *10 12 cells in the zoom level 21 with cell size(60,80) 11

Some issues - Photos are added or deleted dynamically - Querying for a certain time, certain user or according to photo description - Different zoom levels, moving map 12

Hierarchical Clustering on server 13

Hierarchical Clustering on server Individual clustering for different zoom levels Clustering of whole data How to extract clusters for a specific query? Are clusters for a lower zoom level can be derived from higher level? 14

Client side clustering - Query from server (Resulting N objects) - Take the zoom view Not too many cells - Taking objects in the zoom view and do clustering only for them (M objects) - It takes O(N) to find out the objects in the zoom view! 15

Grid based clustering Input location (lat, lon) of markers Width and height of markers (H m,W m ) Width and height of cells in the grid (H, W) Output Location of clusters 16 Location of the marker W H WmWm HmHm

Representation - Middle of cell -No overlap -Locations can be misleading 17

Representation- First object 18

Representation – Average Location 19

Proposed approach - Grids start from beginning of the whole map - Extend the grid in current zoom view By moving map clustersdo not change - Average location for representative By moving map clusters do not change 20 W H (x min, y min ) (x max, y max )

Algorithm 1. nRow = ceil((x max -x min )/W) 2. nColumn = ceil((y max -y min )/H) 3. nCell = nRow * nColumn 4. Clusters = all cells // empty clusters 5. For all the markers 6. row = floor((y-y min )/gridHeight) 7. column = floor((x-x min )/gridWidth) 8. cellNum = row*nColumn + column 9. Add the marker to Clusters[cellNum] 10. Update the cluster: Clusters[cellNum] 21 W H (x max, y max ) (x min, y min ) (x,y) Cell number 1820

Merging algorithm- Average location as representative 1. MergeClusters(clusters) 2. change the order of clusters descending according to the size of clusters 3. set parent of each cluster, the same cluster 4. k=1 (K is number of clusters) 5. while (k < K ) 6. if ( k is not processed ) 7. checkNeighbors(k); 8. mark the cluster k processed 9. k=k CheckNeighbors(k) 11. cluster1=clusters[k] 12. For all 8 neighbors 13. cluster2 = one of the neighbors // 14. if cluster2 is not an empty cell 15. checkNeighbor(cluster1, cluster2) 22

Merging algorithm 1. checkNeighbor(cluster1, cluster2) 2. find the distance d between the two clusters 3. if d<T // distance threshold T 4. while ( cluster2 is processed ) // means it has been merged 5. cluster2 = clusters[cluster2.parent] 6. MergeClusters(cluster1, cluster2); 1. MergeClusters(cluster1, cluster2) 2. n1 and n2: size of the clusters 3. (x1,y1) and (x2,y2): location of clusters 4. x=(n1*x1+n2*x2)/(n1+n2) 5. y=(n1*y1+n2*y2)/(n1+n2) 6. x1 x and y1 y 7. mark the second cluster processed 8. cluster2.parent = k 23

Grid based clustering Width and height of a cell H>H m and W>W m Minimum distance of the markers to avoid overlap 24 d WmWm HmHm Marker Location of marker

Distance based clustering Input location (lat, lon) of markers Width and height of markers (H m, W m ) Output location of clusters Time complexity: O(N 2 ) 25

Algorithm 1. i= 0; 2. While (i<N) // N=number of markers 3. if ( marker i is not clustered ) 4. Label marker i as clustered 5. Calculate distance (d j ) to other non-clustered markers 6. for all markers j 7. If d j <T // T: distance threshold 8. merge the markers i and j 9. Label marker j as clustered 10. i = i+1; 26

Timeline view of photos Displaying n photos in a limited space 27

Timeline view of photos Input Timestamps Number of clusters Output Partitions Algorithm K-means 28

Location clusters 29 Homes of users Shop Walking street Market place Swim hall Science park

Clustering of trajectories 30

Similarity or distance Start and end of the routes 31

Similarity or distance Speed, length, accelaration, time, etc km/h 72 km/h 50 km/h 30 km/h 60 km/h These two routes are more similar in speed than others

Similarity or distance Closeness of points and shape (Comparing whole route or segments of the routes) 33 t1 T1 t2 t3 t4 t5 t6 t7 t8 T2 t1 t2 t3 t4 t1 T1 t2 t3 t4 t5 t6 t7 t8 T2 t1 t2 t3 t4 Closest pair distance Sum of pair distance

Cluttering problem for routes 34