Geographically Weighted Regression (GWR) is a local version of spatial regression that captures spatial dependency in regression analysis. GWR has many application in practice as a visualization and prediction tool for spatial exploration- (e.g in climate, economy, medical). However, this locally regression model is slow in process upon the volume of calculations and the spatial getting bigger. Improving performance of GWR is an critical issue, but their distributed implementations have not been studied. Recently, with the advent of Spark as well MapReduce framework, the development of machine learning applications and parallel programming becomes easier. In this article, we propose several large-scale implementations of distributed GWR, leveraging Spark framework. We implemented and evaluated these approaches with large datasets. To our best knowledge, this is the first work addressing GWR at large-scale.

1. Hung Tien Tran, Hiep Tuan Nguyen, Viet-Trung Tran
Hanoi University of Science and Technology

2. Introduction
 What is Geographically Weighted Regression?
 What is our work?
Source: http://desktop.arcgis.com
GWR + =
- Large-scale spatial data
- Improve performance
- Distributed

3. Outline
 Background
 Problem
 Scalable GWR on Spark
 Experiments
 Discussion
 Conclusion

4. Background
 First Law of Geography - Waldo Tobler:
“Everything is related with everything else, but closer
things are more related”.
 Model GWR
 The OLS estimator takes the form
yi (u) = β0i (u) + β1i (u)x1i +β2i (u)x2i + ... + βmi (u)xmi
βˆ(u) = (X TW (u)X )−1 X TW (u)Y

5. Background
 Kernel function
 Gaussian function
 Bandwidth
5
fixed bandwidth adaptive bandwidth

6. Problem
 Estimating a local model
 Bandwidth selection
 Evaluation model
Choose kernel function
βˆ(u) = (X TW (u)X )−1 X TW (u)Y
Source: http://rose.bris.ac.uk
O(n3)
Which bandwidth is good

7. Problem
 How to apply the model for large-scale data?
 Data points
 Features
 Regression points

8. Large-Scale GWR on Spark
 Why is Spark?
 In-memory cluster-computing platform
 Support parallel programming
 Develop applications by high-level APIs
 Provides resilient distributed datasets and parallel
operations
 Integration with other components on Spark

9. Large-Scale GWR on Spark
 We propose three approach to scaling GWR
 Scaling Weighted Linear Regression
 Parallel Multiple WLR models
 Parallel Geographically Weighted Regression (combine
the first two approach)

10. Scalable GWR on Spark
 Naïve approach – Scaling Weighted Linear Regression
Foreach regPoint
Compute weight
Fit Weighted
Linear
Regression
Summary model
Compute weight
parallel
Compute WLR
model parallel

11. Scalable GWR on Spark
 Naïve approach

12. Scalable GWR on Spark
 Parallel Multiple WLR models
Regression dataset
Training dataset
WL
R
Compute weight
WL
R
Compute parallel
multiple WLR
models
Summary

13. Scalable GWR on Spark
 Parallel Multiple WLR models

14. Scalable GWR on Spark
 Parallel Geographically Weighted Regression
R
R
R
T
T
T
R
T
R
T
R
T
Regressio
n dataset
Training
dataset
Combin
e dataset
Distributed GWR Computation

15. Scalable GWR on Spark
 Parallel Geographically Weighted Regression

16. Scalable GWR on Spark
 Parallel Geographically Weighted Regression

17. Experiments
 Environment
 Cluster: 8 nodes on Amazon Web Service
 4 cores Inte Xeon E5-2670 v2 2.5 GHz
 16 GB RAM, 2x40 GB SSD
 Hadoop 2.7.2 and Spark 1.6.1
 Dataset
| − −x : double(nullable = false)
| − −y : double(nullable = false)
| − −label : double(nullable = false)
| − −f eatures : vector(nullable = false)

18. Experiments
 Testing large training dataset
0
200
400
600
800
1000
1200
10000 100000 1000000 2000000 5000000
Algorithm 1
Algorithm 2
Algorithm 3
Algorithm 4
time (sec).
Number of training points

19. Experiments
 Testing large regression dataset
0
200
400
600
800
1000
1200
1000 5000 10000 20000 50000
Algorithm 1
Algorithm 2
Algorithm 3
Algorithm 4
time
(sec).
Number of regression
points

20. Experiments
 Testing large dataset with increasing number of
features
0
200
400
600
800
1000
1200
1400
1600
1800
10 20 50 100 200
Algorithm 1
Algorithm 2
Algorithm 3
Algorithm 4
time
(sec).
Number of regression
points

21. Experiments
 Cluster
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2-node 4-node 8-node
Algorithm 1
Algorithm 2
Algorithm 3
Algorithm 4
time (sec).
Number of nodes

22. Discussion
 Related work
 Many library GWR on local
 Spgwr (multiR on GRID)
 Using GPU
 Our work
 First study distributed GWR on Spark
 Easy deployment and the advantages of Spark
 Scalable and work well on cluster

23. Conclusion
 We have
 Propose three approach
 Implement four algorithms base on Spark
 Evaluate our implementation
 Future work
 Improve performance by using Pipeline and Partitions
 Release as open-source library