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Clustering
Lecture outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
What is clustering? ,[object Object],Inter-cluster distances are maximized Intra-cluster distances are minimized
Outliers ,[object Object],[object Object],cluster outliers
Why do we cluster? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Applications of clustering? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The clustering task ,[object Object],[object Object],[object Object],[object Object],[object Object]
Observations to cluster ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Observations to cluster ,[object Object],[object Object],[object Object],[object Object]
Distance functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Data Structures ,[object Object],[object Object],attributes/dimensions tuples/objects objects objects
Distance functions for binary vectors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Q1 Q2 Q3 Q4 Q5 Q6 X 1 0 0 1 1 1 Y 0 1 1 0 1 0
Distance functions for real-valued vectors ,[object Object],[object Object],[object Object]
Distance functions for real-valued vectors ,[object Object],[object Object],[object Object]
Partitioning algorithms: basic concept ,[object Object],[object Object],[object Object]
The k-means problem ,[object Object],[object Object],[object Object],[object Object]
Algorithmic properties of the k-means problem ,[object Object],[object Object],[object Object],[object Object]
The k-means algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]
Properties of the k-means algorithm ,[object Object],[object Object],[object Object]
Two different K-means Clusterings Original Points Sub-optimal Clustering Optimal Clustering
Discussion k-means algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Some alternatives to random initialization of the central points ,[object Object],[object Object],[object Object]
The k-median problem ,[object Object],[object Object],[object Object]
The k - medoids algorithm ,[object Object],[object Object],[object Object],[object Object]
Discussion of PAM algorithm ,[object Object],[object Object],[object Object]
CLARA (Clustering Large Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object]
The k-center problem ,[object Object],[object Object],[object Object]
Algorithmic properties of the k-centers problem ,[object Object],[object Object],[object Object],[object Object]
The farthest-first traversal algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The farthest-first traversal is a 2-approximation algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]
The farthest-first traversal is a 2-approximation algorithm ,[object Object],[object Object],[object Object],[object Object]
The farthest-first traversal is a 2-approximation algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
What is the right number of clusters? ,[object Object],[object Object],[object Object],[object Object]
Occam’s razor and the minimum description length principle ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Lect4

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  • 20. Two different K-means Clusterings Original Points Sub-optimal Clustering Optimal Clustering
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