1. AMCS/CS229: Machine Learning
Clustering 2
Xiangliang Zhang
King Abdullah University of Science and Technology

2. Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning
Cluster Analysis
Partitioning Methods + EM algorithm
Hierarchical Methods
Density-Based Methods
Clustering quality evaluation
How to decide the number of clusters ?
Summary
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 2

3. The quality of Clustering
For supervised classification we have a variety of measures to evaluate how good our model is
Accuracy, precision, recall
For cluster analysis, the analogous question is how to evaluate the “goodness” of the resulting clusters?
But “clusters are in the eye of the beholder”!
Then why do we want to evaluate them?
To avoid finding patterns in noise
To compare clustering algorithms
To compare two sets of clusters
To compare two clusters
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 3

4. Measures of Cluster Validity
Numerical measures that are applied to judge various aspects of cluster validity, are classified into the following two types:
External Index: Used to measure the extent to which cluster labels match externally supplied class labels.
Purity, Normalized Mutual Information
Internal Index: Used to measure the goodness of a clustering structure without respect to external information.
Sum of Squared Error (SSE)
Cophenetic correlation coefficient, silhouette 4

5. Cluster Validity: External Index
The class labels are externally supplied (q classes)
Purity:
Larger purity values indicate better clustering solutions.
Purity of each cluster Cr of size nr
Purity of the entire clustering 5

6. Cluster Validity: External Index
Purity: 6

7. Cluster Validity: External Index
The class labels are externally supplied (q classes)
NMI (Normalized Mutual Information) :
where I is mutual information
and H is entropy 7

8. Cluster Validity: External Index
NMI (Normalized Mutual Information) :
Larger NMI values indicate better clustering solutions. 8

9. Internal Measures: SSE
Internal Index: Used to measure the goodness of a clustering structure without respect to external information
SSE is good for comparing two clustering results
average SSE
SSE curves w.r.t. various K
Can also be used to estimate the number of clusters 9

10. Internal Measures: Cophenetic correlation coefficient
a measure of how faithfully a dendrogram preserves the pairwise distances between the original data points.
Compare two hierarchical clusterings of the data
0.5
D F
0.71
A B
1.00 E
1.41 C
2.50
Single link --- Min
Compute the correlation coefficient between Dist and CP 10
Matlab functions: cophenet

11. Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning
Cluster Analysis
Partitioning Methods + EM algorithm
Hierarchical Methods
Density-Based Methods
Clustering quality evaluation
How to decide the number of clusters ?
Summary
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 11

12. Internal Measures: Cohesion and Separation
Cluster cohesion measures how closely related are objects in a cluster
= SSE or the sum of the weight of all links within a cluster.
Cluster separation measures how distinct or well-separated a cluster is from other clusters
= sum of the weights between nodes in the cluster and nodes outside the cluster.
separation
cohesion 12

13. Internal Measures: Silhouette Coefficient
Silhouette Coefficient combines ideas of both cohesion and separation
For an individual point, i
Calculate a = average distance of i to the points in its cluster
Calculate b = min (average distance of i to points in another cluster)
The silhouette coefficient for a point is then given by
Typically between 0 and 1.
The closer to 1 the better.
Can calculate the Average Silhouette width for a cluster or a clustering
Matlab functions: silhouette 13

14. Determine number of clusters by Silhouette Coefficient
compare different clusterings by the average silhouette values
K=3
mean(silh) = 0.526
K=4
mean(silh) = 0.640
K=5
mean(silh) = 0.527

15. Determine the number of clusters
Select the number K of clusters as the one maximizing averaged silhouette value of all points
Optimizing an objective criterion
Gap statistics of the decreasing of SSE w.r.t. K
Model-based method:
optimizing a global criterion (e.g. the maximum likelihood of data)
Try to use clustering methods which need not to set K, e.g., DbScan,
Prior knowledge…..
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 15

16. Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning
Cluster Analysis
Partitioning Methods + EM algorithm
Hierarchical Methods
Density-Based Methods
Clustering quality evaluation
How to decide the number of clusters ?
Summary
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 16

17. Clustering VS Classification
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 17

18. Problems and Challenges
Considerable progress has been made in scalable clustering methods
Partitioning: k-means, k-medoids, CLARANS
Hierarchical: BIRCH, ROCK, CHAMELEON
Density-based: DBSCAN, OPTICS, DenClue
Grid-based: STING, WaveCluster, CLIQUE
Model-based: EM, SOM
Spectral clustering
Affinity Propagation
Frequent pattern-based: Bi-clustering, pCluster
Current clustering techniques do not address all the requirements adequately, still an active area of research
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 18

19. Open issues in clustering
Cluster Analysis
Open issues in clustering
Clustering quality evaluation
How to decide the number of clusters ? 19

20. Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning
What you should know
What is clustering?
How does k-means work?
What is the difference between k-means and k-mediods?
What is EM algorithm? How does it work?
What is the relationship between k-means and EM?
How to define inter-cluster similarity in Hierarchical clustering? What kinds of options do you have ?
How does DBSCAN work ?
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 20

21. Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning
What you should know
What are the advantages and disadvantages of DbScan?
How to evaluate the clustering results ?
Usually how to decide the number of clusters ?
What are the main differences between clustering and classification?
Xiangliang Zhang, KAUST AMCS/CS229: Machine Learning 21