1. Tree-Based Density Clustering using Graphics Processors
A First Marriage of MRNet and GPUs
Evan Samanas and Ben Welton
Roadmap or Through the roadmap.
What our contribution was.
Explain our contribution. Move tweet slide forward.
Some more info to catch interest. Tweet slide after this.
One person standing.

2. Tree-Based Density Clustering using Graphics Processors
The Tweet Stream v v ` `
Source: Twitter, Map: About.com
Tree-Based Density Clustering using Graphics Processors

3. Tree-Based Overlay Networks (TBONs)
Scalable multicast
Scalable gather
Scalable data aggregation FE … BE
app CP
Tree-Based Density Clustering using Graphics Processors

4. MRNet – Multicast / Reduction Network
General-purpose TBON API
Network: user-defined topology
Stream: logical data channel
to a set of back-ends
multicast, gather, and custom reduction
Packet: collection of data
Filter: stream data operator
synchronization
transformation
Widely adopted by HPC tools
CEPBA toolkit
Cray ATP & CCDB
Open|SpeedShop & CBTF
STAT
TAU FE
F(x1,…,xn) CP CP CP CP CP CP
Forgot to mention reduction operation with streams. Clean up boxes … … … BE
app BE
app BE
app BE
app
Tree-Based Density Clustering using Graphics Processors

5. Tree-Based Density Clustering using Graphics Processors
TBON Computation …
Data to process:
e.g. 40 MB
Total Time: ~60 sec
Total Time: ~30 sec
Ideal Characteristics:
Filter output size constant or decreasing
Computation rate similar across levels
Adjustable for load balance FE
~10 sec
Packet Size:
≤10 MB
~10 sec CP CP
Packet Size:
≤10 MB BE
app BE
app BE
app … 4x BE
app
~10 sec
~40 sec
Simple animation for each bullet point?
Should be constant/decreasing output size. Would hit scaling limits soon.
Nuke original bullet. Keep sub-bullet.
Mention that these are general features of MRNet (ideal computation). Replace symbol on <= with actual symbol.
Data Size:
10MB per BE
~10 sec
Tree-Based Density Clustering using Graphics Processors

6. Tree-Based Density Clustering using Graphics Processors
Why GPUs?
Natural fit
Increase compute power
Trade computation for
bandwidth
Derived summaries
Compute and send ∆ data
Compression algorithms (e.g. LZO, zlib, etc.) FE
F(x1,…,xn) CP CP CP CP CP CP
Mention Jaguar at end? … … … BE
app BE
app BE
app BE
app
Tree-Based Density Clustering using Graphics Processors

7. Clustering Example (DBSCAN[1])
The two parameters that determine if a point is in a cluster is Epsilon (Eps), and MinPts
For every discovered point, this same calculation is performed until the cluster is fully expanded
Goal: Find regions that meet minimum density and spatial distance characteristics
If the number of points in Eps is > MinPts, the point is a core point.
Min Points
Eps
Min Pts: 3
Attribute to Hans on slide, try and fix the transition between 5 and 6. Don’t say that we had gpu’s and were looking for
A problem. Change 1 on slide title.
[1] M. Ester et. al., A density-based algorithm for discovering clusters in large spatial databases with noise, (1996)
Tree-Based Density Clustering using Graphics Processors

8. Tree-Based Density Clustering using Graphics Processors
Scaling DBSCAN
PDBSCAN[2]
Quality equivalent to single DBSCAN
Linear speedup up to 8 nodes
DBDC[3]
Sacrifices quality
~30x speedup on 15 nodes
CUDA-Dclust[4]
Quality equivalent to DBSCAN
~15x faster on 1 node
CUDA-Dclust looks like a third example of an algorithm. Change sub-bullet type or do something. Define quality maybe here?
Mention speed up for number nodes for each of these. Say it’s a GPU running on a single node
[2] X. Xu et. al., A fast Parallel Clustering Algorithm for Large Spatial Databases (1999)
[3] E. Januzaj et. al., DBDC: Density Based Distributed Clustering (2004)
[4] C. Bohm et al., Density-based clustering using graphics processors (2009)
Tree-Based Density Clustering using Graphics Processors

9. Tree-Based Clustering: Mr. Scan
Algorithm Steps
SpatialDecomp: FE)
DBSCAN: CPU or BE)
DrawBoundBox: CPU or GPU
MergeCluster: CPU (x #levels) FE
MergeCluster CP CP
DBSCAN BE BE BE BE
Talk about dbdc.
15sec’s to explain where it came from.
Discuss number of levels/cpu/gpu/BE/etc on this slide. No parenthesis after function names.
Wide dash is a bad idea.
Tree-Based Density Clustering using Graphics Processors

10. Spatial Decomposition
Eps
1. Start with an input of Spatially Referenced points
2. Partition the region into equal sized density regions across one dimension
3. Add the shadow region area of one Epsilon to all density regions
Partition #3
Partition #1
Partition #2
Split the area so that we show points split in area. Label Eps.
Tree-Based Density Clustering using Graphics Processors

11. Tree-Based Density Clustering using Graphics Processors
DBSCAN - CPU
Run on local slice for each BE
R* tree
Start at random point
Cluster w/ respect to
Eps, MinPts
Complexity: O(n log n) A B
R* - show something about it. Say it in a way that we extended dbscan via the following.
Discuss the relationship of the levels of the tree. How does it work. C D E
R* Tree Example
Tree-Based Density Clustering using Graphics Processors

12. GPU DBSCAN Filter
Candidate Clusters are potential clusters being explored concurrently in the GPU
Number of cluster candidates is limited by GPU Characteristics
State array stores the current state of points in the search space
States
Candidate #1
Coarse grain search space
Chain Collisions causing cluster merges
Candidate #2 .
Canidate Clusters == Chains. What happens to chain number 1/2 do after states merge. What is a thread block maybe replace with limited by gpu charactoristics.
Reference the cuda-dclust algorithm.
More spacing between text. Consistentcy with justification.
Candidate #N
GPU DBSCAN operates similarly to the CPU version with two exceptions
CUDA-DCLUST [09 – Böhm] 
Tree-Based Density Clustering using Graphics Processors

13. DrawBoundBox – CPU | | GPU
Tree-Based Density Clustering using Graphics Processors

14. Tree-Based Density Clustering using Graphics Processors
MergeBoundBox - CPU
Checks for merge if box within shadow
At least one point MUST be in common
Iterate through ALL points in right cluster
Match!
Tree-Based Density Clustering using Graphics Processors

15. Tree-Based Density Clustering using Graphics Processors
The Tweet Stream ` `
Source: Twitter, Map: About.com
Tree-Based Density Clustering using Graphics Processors

16. Tree-Based Density Clustering using Graphics Processors
Evaluation
Dataset: 1-3 “Tweet Days”
Measuring:
Time to completion
Quality compared to single-threaded DBSCAN
Algorithms:
Single-Threaded DBSCAN
DBDC
MRNet w/DBSCAN filter
MRNet w/DBSCAN GPU filter
Not a results slide, this is an eval slide. Maybe use Evaluation.
Tree-Based Density Clustering using Graphics Processors

17. Tree-Based Density Clustering using Graphics Processors
Results
Tree-Based Density Clustering using Graphics Processors

18. Tree-Based Density Clustering using Graphics Processors
Results
Tree-Based Density Clustering using Graphics Processors

19. Tree-Based Density Clustering using Graphics Processors
Results
Tree-Based Density Clustering using Graphics Processors

20. Tree-Based Density Clustering using Graphics Processors
Quality
Change range to 120%, 100k or a comma or something. Change colors.
Change xxx.00%. Drop decimals
Tree-Based Density Clustering using Graphics Processors

21. Tree-Based Density Clustering using Graphics Processors
Future Work
Scaling Issues
Spatial Decomposition
Merging Algorithm
Tree-Based Density Clustering using Graphics Processors

22. 2D Spatial Decomposition
Eps
7pts
11pts
1D Spatial Decomposition has some severe limitations
Splits can have wildly differing point counts
Number of splits limited by Epsilon
2D Spatial Decomposition would allow for more Splits with more equal point counts
Tree-Based Density Clustering using Graphics Processors

23. Tree-Based Density Clustering using Graphics Processors
Merging Algorithm
Bounding Box
No quality degradation
Limits iteration, but still iterates
Possible Alternative: Concave Hull
DBSCAN on border points
Avoids iteration
Constant output size
O(n2) on BEs
Tree-Based Density Clustering using Graphics Processors

24. Tree-Based Density Clustering using Graphics Processors
Use Cases
Twitter Data
“Flu Tweets”
Mood/Topic clustering
Riot prediction
Any Spatial data
Currently limited to 2D
Tree-Based Density Clustering using Graphics Processors

25. Tree-Based Density Clustering using Graphics Processors
Conclusion
DBSCAN performance scales
Quality able to be maintained
Goal: Scale O(100,000 nodes)
Tree-Based Density Clustering using Graphics Processors