The document discusses parallel k-means clustering algorithms implemented using MapReduce and Spark. It first describes the standard k-means algorithm, which assigns data points to clusters based on distance to centroids. It then presents a MapReduce-based parallel k-means approach where the distance calculations between data points and centroids are distributed across nodes. The map tasks calculate distances and assign points to clusters, combine tasks aggregate results, and reduce tasks calculate new centroids. Experimental results show sub-linear speedup and good scaling to larger datasets. Finally, it briefly mentions k-means implementations on Spark.

1. Parallel K-Means
ncku Tien-Yang Wu

2. outline
Introduction
K-Means Algorithm
Parallel K-Means Based on MapReduce
Experimental Results
K-Means on spark

3. Introduction
They assume that all objects can reside in main
memory at the same time.
Their parallel systems have provided restricted
programming models.

4. Introduction
They assume that all objects can reside in main
memory at the same time.
Their parallel systems have provided restricted
programming models.
dataset oriented parallel clustering algorithms should be
developed.

5. K-Means Algorithm

6. K-Means Algorithm
Firstly, it randomly selects k objects from the whole objects
which represent initial cluster centers.

7. K-Means Algorithm
Each remaining object is assigned to the cluster to which it
is the most similar, based on the distance between the
object and the cluster center.

8. K-Means Algorithm
The new mean for each cluster is then calculated. This
process iterates until the criterion function converges.

9. Parallel K-Means Based
on MapReduce
most intensive calculation to occur is the calculation of
distances.
each iteration require nk distance

10. Parallel K-Means Based
on MapReduce
the distance computations between one object with the
centers is irrelevant to the distance computations
between other objects with the corresponding centers.
distance computations between different objects with
centers can be parallel executed.

11. Parallel K-Means Based
on MapReduce
1,1
2,2
3,3
11,11
12,12
13,13
data target
1,1
2,2
3,3
11,11
12,12
13,13
1 class
2 class

12. Parallel K-Means Based
on MapReduce
1,1
2,2
3,3
11,11
12,12
13,13
random two centroid
c1:(1,1)
c2:(11,11)

13. Parallel K-Means Based
on MapReduce
1,1
2,2
3,3
11,11
12,12
13,13
store two nodes
c1:(1,1)
c2:(11,11)

14. Parallel K-Means Based
on MapReduce
1,1
2,2
3,3
11,11
12,12
13,13
1,1
12,12
3,3
11,11
2,2
13,13
node1
node2
c1:(1,1)
c2:(11,11)

15. Parallel K-Means Based
on MapReduce
1,1
2,2
3,3
11,11
12,12
13,13
1,1
12,12
3,3
11,11
2,2
13,13
node1
node2
c1:(1,1)
c2:(11,11)
map
map
combine
combine
reduce

16. Parallel K-Means Based
on MapReduce
1,1
12,12
3,3
node1
map
3,3
c1:(1,1)
c2:(11,11)
assign to c1(1,1)
(1,1) , {(3,3),(3,3)}
key value
output<key,value>

17. Parallel K-Means Based
on MapReduce
(1,1) , {(3,3),(3,3)}
key value
centroid
temporary to calculate new centroid, the object
(1,1)
{(3,3),(3,3)}
output<key,value>

18. Parallel K-Means Based
on MapReduce
1,1
12,12
3,3
node1
map
c1:(1,1)
c2:(11,11)
(1,1) , {(1,1),(1,1)}
(11,11) , {(12,12),(12,12)}
(1,1) , {(3,3),(3,3)}
key value

19. Parallel K-Means Based
on MapReduce
1,1
12,12
3,3
11,11
2,2
13,13
node1
node2
c1:(1,1)
c2:(11,11)
map
map
(1,1) , {(1,1),(1,1)}
(11,11) , {(12,12),(12,12)}
(1,1) , {(3,3),(3,3)}
key value
(11,11) , {(11,11),(11,11)}
(1,1) , {(2,2),(2,2)}
key value
(11,11) , {(13,13),(13,13)}

20. Parallel K-Means Based
on MapReduce
1,1
12,12
3,3
node1 c1:(1,1)
c2:(11,11)
map
(1,1) , {(1,1),(1,1)}
(11,11) , {(12,12),(12,12)}
(1,1) , {(3,3),(3,3)}
key value
combine

21. Parallel K-Means Based
on MapReduce
(1,1) , {(1,1),(1,1)}
(11,11) , {(12,12),(12,12)}
(1,1) , {(3,3),(3,3)}
key value
combine
(1,1) , {(4,4),{(1,1),(3,3),2}
(11,11) , {(12,12),(12,12),1}
key value
same key combine

22. Parallel K-Means Based
on MapReduce
(1,1) , {(4,4),{(1,1),(3,3)},2}
(11,11) , {(12,12),(12,12),1}
key value
output<key,value>
centroid
temporary to calculate new centroid, the objects
,number of objects
(1,1)
{(4,4),{(1,1),(3,3)},2}

23. Parallel K-Means Based
on MapReduce
combine
(1,1) , {(1,1),(1,1)}
(11,11) , {(12,12),(12,12)}
(1,1) , {(3,3),(3,3)}
key value
(11,11) , {(11,11),(11,11)}
(1,1) , {(2,2),(2,2)}
key value
(11,11) , {(13,13),(13,13)}
combine
(1,1) , {(4,4),{(1,1),(3,3)},2}
(11,11) , {(12,12),(12,12),1}
key value
(1,1) , {(2,2),(2,2),1}
(11,11) , {(24,24),{(11,11),(13,13)},2}
key value

24. Parallel K-Means Based
on MapReduce
reduce
(1,1) , {(4,4),{(1,1),(3,3)},2}
(11,11) , {(12,12),(12,12),1}
key value
(1,1) , {(2,2),(2,2),1}
(11,11) , {(24,24),{(11,11),(13,13)},2}
key value
same key reduce

25. Parallel K-Means Based
on MapReduce
(1,1) , {(4,4),{(1,1),(3,3)},2}
(1,1) , {(2,2),(2,2),1}
reduce
same key reduce
(1,1) , {(2,2),{(1,1),(2,2),(3,3)}

26. Parallel K-Means Based
on MapReduce
(1,1) , {(4,4),{(1,1),(3,3)},2}
(1,1) , {(2,2),(2,2),1}
(1,1) , {(2,2),{(1,1),(2,2),(3,3)}
(4+2)/(2+1) ,(4+2)/(2+1) = 2,2
2,2 = new centroid
1,1
2,2
3,3
centroid is 2,2

27. Parallel K-Means Based
on MapReduce
(1,1) , {(4,4),{(1,1),(3,3)},2}
(1,1) , {(2,2),(2,2),1}
(1,1) , {(2,2),{(1,1),(2,2),(3,3)}
(1,1) , {(2,2),{(1,1),(2,2),(3,3)}
centroid
new centroid, the objects
,new cluster

28. Parallel K-Means Based
on MapReduce
reduce
(1,1) , {(2,2),{(1,1),(2,2),(3,3)}
(11,11) , {(12,12),{(11,11),(12,12),(13,13)}
update new centroid and next iteration
until converge or arrive to iteration number

29. Experimental Results
two 2.8 GHz cores and 4GB of memory

30. Experimental Results
Speedup
non linear,communication cost

31. Experimental Results
Scale up
performance
datasets 1GB 2GB 3GB 4GB

32. K-Means on spark

33. Reference
Parallel K-Means Clustering Based on MapReduce
Weizhong Zhao1,2, Huifang Ma1,2, and Qing He1
2009
K means algorithm