9/17/2009. Wenyan Li (Emily Li) Sep. 15, Introduction to Clustering Analysis
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1 Introduction ti to K-means Algorithm Wenan Li (Emil Li) Sep. 5, 9 Outline Introduction to Clustering Analsis K-means Algorithm Description Eample of K-means Algorithm Other Issues of K-means Algorithm K-means Algorithm in STATISTICA
2 Introduction to Clustering Analsis What is Cluster Analsis? Cluster analsis groups data objects based onl on information found in data that describes the objects and their relationships. Goal of Cluster Analsis The objects within a group be similar to one another and different from the objects in other groups. Tpes of Clustering Hierarchical Clustering A set of nested clusters organized as a hierarchical tree Partitioning Clustering A division data objects into non-overlapping subsets (clusters) such that each data object is in eactl one subset Introduction to Clustering Analsis Partitioning Clustering Hierarchical Clustering
3 Outline Introduction to Clustering Analsis K-means Algorithm Description Eample of K-means Algorithm Other Issues of K-means Algorithm K-means Algorithm in STATISTICA K-means Algorithm Description What is K-means Algorithm? Partitioning clustering approach ; Each cluster is associated with a centroid (center point) ; Each point is assigned to the cluster with the closest centroid; Number of clusters, K, must be specified
4 K-means Algorithm Description Basic Algorithm of K-means K-means Algorithm Description Details of K-means Algorithm Initial centroids are often chosen randoml. Clusters produced var from one run to another The centroid is (tpicall) the mean of the points in the cluster. Closeness is measured b Euclidean distance, cosine similarit, correlation, etc. K-means will converge for common similarit measures mentioned above. Most of fthe convergence happens in the first tfew iterations. ti Often the stopping condition is changed to Until relativel few points change clusters 4
5 K-means Algorithm Description Euclidean Distance A simple eample: Find the distance between two points, the original point O and the point A (,4) K-means Algorithm Description Update Centroid We use the following equation to calculate the n dimensional centroid point amid k n-dimensional points Eample: Find the centroid of D points, (,4), (5,) and (8,9) 5
6 Outline Introduction to Clustering Analsis K-means Algorithm Description Eample of K-means Algorithm Other Issues of K-means Algorithm K-means Algorithm in STATISTICA Eample of K-means Algorithm Select three initial centroids Iteration
7 Eample of K-means Algorithm Assigning the points to nearest K clusters and re-compute the centroids Iteration Eample of K-means Algorithm K-means terminates since the centroids converge to certain points and do not change. Iteration
8 Eample of K-means Algorithm Iteration Iteration Iteration Iteration 4 Iteration 5 Iteration Eample of K-means Algorithm Demo of K-means 8
9 Evaluating K-means Clusters Most common measure is Sum of Squared Error (SSE) For each point, the error is the distance to the nearest cluster To get SSE, we square these errors and sum them. is a data point in cluster Ci and mi is the representative point for cluster Ci SSE K i C i dist ( m, ) can show that mi corresponds to the center (mean) of the cluster Given two clusters, we can choose the one with the smallest error One eas wa to reduce SSE is to increase K, the number of clusters A good clustering with smaller K can have a lower SSE than a poor clustering with higher K i Problem about K Centers How to choose K? Use another clustering method, like EM. Run algorithm on data with several different values of K. Use the prior knowledge about the characteristics of the problem. How to initialize centers? Random points in feature space Random points from data set Look for dense regions of space Space them uniforml around the feature space 9
10 Cluster Qualit Cluster Qualit
11 Limitation of K-means Algorithm K-means has problems when clusters are of differing Sizes Densities Non-globular shapes K-means has problems when the data contains outliers. Limitation of K-means Algorithm Original Points K-means ( Clusters)
12 AR Real le Eample Using STATISTICA Software Prepare the Data Statistica can read from Ecel,.tt and man other tpes of files
13 Open an Ecel File Click the Import selected sheet to Spreadsheet Select the desired Ecel sheet where our data is stored Get variable names from the first row Use the wind energ data set Clustering
14 Clustering Select k-means and choose the variables Clustering Choose the distance metrics and initial cluster centers 4
15 5 clusters and see the results Clustering Centroids (cluster means) Clustering 5
16 Clustering Members and their distance to the centroids Software Demonstration 6
17 Thank You 7
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