clustering in research cluster analysis.ppt
- 1. © 2007 Prentice Hall 20-1 Chapter Outline 1) Overview 2) Basic Concept 3) Statistics Associated with Cluster Analysis 4) Conducting Cluster Analysis i. Formulating the Problem ii. Selecting a Distance or Similarity Measure iii. Selecting a Clustering Procedure iv. Deciding on the Number of Clusters v. Interpreting and Profiling the Clusters vi. Assessing Reliability and Validity
- 2. © 2007 Prentice Hall 20-2 Statistics Associated with Cluster Analysis Agglomeration schedule. An agglomeration schedule gives information on the objects or cases being combined at each stage of a hierarchical clustering process. Cluster centroid. The cluster centroid is the mean values of the variables for all the cases or objects in a particular cluster. Cluster centers. The cluster centers are the initial starting points in nonhierarchical clustering. Clusters are built around these centers, or seeds. Cluster membership. Cluster membership indicates the cluster to which each object or case belongs.
- 3. © 2007 Prentice Hall 20-3 Statistics Associated with Cluster Analysis Dendrogram. A dendrogram, or tree graph, is a graphical device for displaying clustering results. Vertical lines represent clusters that are joined together. The position of the line on the scale indicates the distances at which clusters were joined. The dendrogram is read from left to right. Figure 20.8 is a dendrogram. Distances between cluster centers. These distances indicate how separated the individual pairs of clusters are. Clusters that are widely separated are distinct, and therefore desirable.
- 4. © 2007 Prentice Hall 20-4 Statistics Associated with Cluster Analysis Icicle diagram. An icicle diagram is a graphical display of clustering results, so called because it resembles a row of icicles hanging from the eaves of a house. The columns correspond to the objects being clustered, and the rows correspond to the number of clusters. An icicle diagram is read from bottom to top. Figure 20.7 is an icicle diagram. Similarity/distance coefficient matrix. A similarity/distance coefficient matrix is a lower- triangle matrix containing pairwise distances between objects or cases.
- 5. © 2007 Prentice Hall 20-5 Conducting Cluster Analysis Formulate the Problem Assess the Validity of Clustering Select a Distance Measure Select a Clustering Procedure Decide on the Number of Clusters Interpret and Profile Clusters Fig. 20.3
- 6. © 2007 Prentice Hall 20-6 Attitudinal Data For Clustering Case No. V1 V2 V3 V4 V5 V6 1 6 4 7 3 2 3 2 2 3 1 4 5 4 3 7 2 6 4 1 3 4 4 6 4 5 3 6 5 1 3 2 2 6 4 6 6 4 6 3 3 4 7 5 3 6 3 3 4 8 7 3 7 4 1 4 9 2 4 3 3 6 3 10 3 5 3 6 4 6 11 1 3 2 3 5 3 12 5 4 5 4 2 4 13 2 2 1 5 4 4 14 4 6 4 6 4 7 15 6 5 4 2 1 4 16 3 5 4 6 4 7 17 4 4 7 2 2 5 18 3 7 2 6 4 3 19 4 6 3 7 2 7 20 2 3 2 4 7 Table 20.1
- 7. © 2007 Prentice Hall 20-7 Conducting Cluster Analysis Formulate the Problem Perhaps the most important part of formulating the clustering problem is selecting the variables on which the clustering is based. Inclusion of even one or two irrelevant variables may distort an otherwise useful clustering solution. Basically, the set of variables selected should describe the similarity between objects in terms that are relevant to the marketing research problem. The variables should be selected based on past research, theory, or a consideration of the hypotheses being tested. In exploratory research, the researcher should exercise judgment and intuition.
- 8. © 2007 Prentice Hall 20-8 Conducting Cluster Analysis Select a Distance or Similarity Measure The most commonly used measure of similarity is the Euclidean distance or its square. The Euclidean distance is the square root of the sum of the squared differences in values for each variable. Other distance measures are also available. The city- block or Manhattan distance between two objects is the sum of the absolute differences in values for each variable. The Chebychev distance between two objects is the maximum absolute difference in values for any variable. If the variables are measured in vastly different units, the clustering solution will be influenced by the units of measurement. In these cases, before clustering respondents, we must standardize the data by rescaling each variable to have a mean of zero and a standard deviation of unity. It is also desirable to eliminate outliers (cases with atypical values). Use of different distance measures may lead to different clustering results. Hence, it is advisable to use different measures and compare the results.