Cluster Analysis: Basic Concepts and Algorithms

Transcription

1 Cluster Analsis: Basic Concepts and Algorithms What does it mean clustering? Applications Tpes of clustering K-means Intuition Algorithm Choosing initial centroids Bisecting K-means Post-processing Strengths and weaknesses What s net? Sections., 8., 8. of course book TNM: Introduction to Data Mining What is Cluster Analsis? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups Intra-cluster distances are minimized Inter-cluster distances are maimized TNM: Introduction to Data Mining

2 Applications of Cluster Analsis Understanding Group related documents for browsing, group genes and proteins that have similar functionalit, or group stocks with similar price fluctuations Summarization Reduce the size of large data sets Discovered Clusters Applied-Matl-DOWN,Ba-Network-Down,-COM-DOWN, Cabletron-Ss-DOWN,CISCO-DOWN,HP-DOWN, DSC-Comm-DOWN,INTEL-DOWN,LSI-Logic-DOWN, Micron-Tech-DOWN,Teas-Inst-Down,Tellabs-Inc-Down, Natl-Semiconduct-DOWN,Oracl-DOWN,SGI-DOWN, Sun-DOWN Apple-Comp-DOWN,Autodesk-DOWN,DEC-DOWN, ADV-Micro-Device-DOWN,Andrew-Corp-DOWN, Computer-Assoc-DOWN,Circuit-Cit-DOWN, Compaq-DOWN, EMC-Corp-DOWN, Gen-Inst-DOWN, Motorola-DOWN,Microsoft-DOWN,Scientific-Atl-DOWN Fannie-Mae-DOWN,Fed-Home-Loan-DOWN, MBNA-Corp-DOWN,Morgan-Stanle-DOWN Baker-Hughes-UP,Dresser-Inds-UP,Halliburton-HLD-UP, Louisiana-Land-UP,Phillips-Petro-UP,Unocal-UP, Schlumberger-UP Industr Group Technolog-DOWN Technolog-DOWN Financial-DOWN Oil-UP Clustering precipitation in Australia TNM: Introduction to Data Mining What is not Cluster Analsis? Supervised classification Have class label information Simple segmentation Dividing students into different registration groups alphabeticall, b last name Results of a quer Groupings are a result of an eternal specification SELECT dept, division, AVG(salar) FROM Table GROUP BY dept, division TNM: Introduction to Data Mining

3 Eample: Churn problem Problem: Predict whether a customer is like to churn Attributes: international plan, voice mail, number of voice mail messages, total da minutes, total evening minutes, Class attribute: Churn (es, no) Model : build a classifier that predicts Churn attribute in terms of the other attributes E.g. decision trees, rule based classifiers TNM: Introduction to Data Mining 5 Churn Problem with Data Segmentation Model : Segment the customers in order to get groups of customers with similar use of compan services Use clustering a new attribute Cluster is added to each record indicating its cluster In Weka, ou can get class to clusters evaluation Describe the clusters: set the class attribute to Cluster and build a classifier that predicts the cluster in terms of the other attributes (do not use Churn) Use the data enriched with the Cluster attribute to build a classifier predicting Churn Do we get a better classifier than in Model? TNM: Introduction to Data Mining 6

4 Weka: Class to clusters evaluation Attribute Full Data C = C = C = () () (9) (9) =============================================================== Inter Plan no no no no no ( 9%) 7 ( 9%) 6 ( 89%) 8 ( 9%) es ( 9%) ( 8%) 7 ( %) 9 ( 9%) Voic Plan no no no es es 9 ( 7%) ( %) ( %) 9 (%) no ( 7%) (%) 9 (%) ( %) No of Vmail Mesgs /-.68 +/- +/- +/-.8 Median Standard deviation TNM: Introduction to Data Mining 7 Notion of a Cluster can be Ambiguous How man clusters? Si Clusters Two Clusters Four Clusters TNM: Introduction to Data Mining 8

5 Tpes of Clusterings A clustering is a set of clusters Important distinction between hierarchical and partitional sets of clusters Partitional Clustering A division data objects into non-overlapping subsets (clusters) such that each data object is in eactl one subset Hierarchical clustering A set of nested clusters organized as a hierarchical tree TNM: Introduction to Data Mining 9 Partitional Clustering Original Points A Partitional Clustering TNM: Introduction to Data Mining

6 Hierarchical Clustering p p p p p p p p Hierarchical Clustering Dendrogram p p p p p p p p Hierarchical Clustering Dendrogram TNM: Introduction to Data Mining How to Define a Cluster But, what is a cluster? There are different was to answer to this question TNM: Introduction to Data Mining

7 Tpes of Clusters: Center-Based Center-based A cluster is a set of objects such that an object in a cluster is closer (more similar) to the center of its cluster, than to the center of an other cluster The center of a cluster is often a centroid, the average of all the points in the cluster, or a medoid, the most representative point of a cluster center-based clusters TNM: Introduction to Data Mining Tpes of Clusters: Densit-Based Densit-based A cluster is a dense region of points, which is separated b lowdensit regions, from other regions of high densit. Used when the clusters are irregular or intertwined, and when noise and outliers are present. 6 densit-based clusters TNM: Introduction to Data Mining

8 Clustering Algorithms K-means and its variants K-means is available in Weka Parameters: Distance function (e.g. Euclidian, Manhattan) and number of clusters Hierarchical clustering Densit-based clustering (DBSCAN) Available in Weka TNM: Introduction to Data Mining 5 K-means: intuition. Select K= initial centroids (seeds). K = number of clusters K is a user-specified parameter TNM: Introduction to Data Mining 6

9 K-means: intuition. Select K= initial centroids (seeds).. Assign data points to the closest seed. Recompute the centroids of each cluster. Reassign data points to the closest centroid. If no points are shifting from one cluster to another (centroids do not change) then STOP. TNM: Introduction to Data Mining 7 Clustering and Objective Functions Clusters defined b an objective function Finds clusters that minimize (or maimize) an objective function. Most common measure is Sum of Squared Error (SSE) For each point, the error is the distance to the nearest centroid To get SSE, we square these errors and sum them. is a data point in cluster C i and m i is the centroid for cluster C i can show that m i corresponds to the center (mean) of the cluster How to compute? Enumerate all possible was of dividing the points into clusters and evaluate the `goodness' of each potential set of clusters b using the given objective function. Not feasible : problem is NP Hard!!! TNM: Introduction to Data Mining 8

10 K-means Clustering Partitional 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 The basic algorithm is ver simple TNM: Introduction to Data Mining 9 K-means Clustering Details 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 the convergence happens in the first few iterations Often the stopping condition is changed to Until relativel few points change clusters Compleit is O( n * K * d * I ) n = number of points, K = number of clusters, I = number of iterations, d = number of attributes TNM: Introduction to Data Mining

11 Getting K Right Tr different k, looking at the change in the average distance to centroid, as k increases. Average falls rapidl until right k, then changes little. Average distance to centroid k Best value of k TNM: Introduction to Data Mining Two different K-means Clusterings.5.5 Original Points Optimal Clustering Sub-optimal Clustering TNM: Introduction to Data Mining

12 Importance of Choosing Initial Centroids Iteration TNM: Introduction to Data Mining Importance of Choosing Initial Centroids Iteration Iteration Iteration Iteration Iteration 5 Iteration TNM: Introduction to Data Mining

13 Importance of Choosing Initial Centroids Iteration TNM: Introduction to Data Mining 5 Importance of Choosing Initial Centroids Iteration Iteration Iteration Iteration Iteration TNM: Introduction to Data Mining 6

14 Clusters Eample 8 Iteration Starting with two initial centroids in one cluster of each pair of clusters TNM: Introduction to Data Mining 7 Clusters Eample 8 Iteration 8 Iteration Iteration Iteration Starting with two initial centroids in one cluster of each pair of clusters TNM: Introduction to Data Mining 8

15 Clusters Eample 8 Iteration Starting with some pairs of clusters having three initial centroids, while other have onl one. TNM: Introduction to Data Mining 9 Clusters Eample 8 Iteration 8 Iteration Iteration Iteration Starting with some pairs of clusters having three initial centroids, while other have onl one. TNM: Introduction to Data Mining

16 Solutions to Initial Centroids Problem Multiple runs Select the set of clusters with least SSE Ma not help! Select a first point as the centroid of all points. Then, select (K- ) most widel separated points Problem: can select outliers Solution: Use a sample of points Post-processing Bisecting K-means Not as susceptible to initialization issues TNM: Introduction to Data Mining Pre-processing and Post-processing Pre-processing Normalize the data Attribute values fall roughl into the same range Eliminate outliers Centroids ma not be good representatives SSE will be also higher Post-processing Eliminate small clusters that ma represent outliers Split loose clusters, i.e., clusters with relativel high SSE or high standard deviation for an attribute Merge clusters that are close and that have relativel low SSE TNM: Introduction to Data Mining

17 Bisecting K-means Bisecting K-means algorithm Variant of K-means that can produce a partitional or a hierarchical clustering TNM: Introduction to Data Mining Bisecting K-means Eample TNM: Introduction to Data Mining

18 Strengths and Weaknesses of K-means Strengths Efficient for medium size data BIRCH and CURE for ver large data sets Bisecting K-means not so susceptible to initialization problems Weaknesses Not suitable for all data tpes Clusters are of differing sizes Densities Non-globular shapes Outliers are a problem Choice of seeds (initial centroids) TNM: Introduction to Data Mining 5 Limitations of K-means: Differing Sizes Original Points K-means ( Clusters) TNM: Introduction to Data Mining 6

19 Limitations of K-means: Differing Densit Original Points K-means ( Clusters) TNM: Introduction to Data Mining 7 Limitations of K-means: Non-globular Shapes Original Points K-means ( Clusters) TNM: Introduction to Data Mining 8

20 Net Similarit measures Is Euclidian distance appropriate for all tpes of problems? Hierarchical clustering DBSCAN algorithm Cluster validation TNM: Introduction to Data Mining 9