# TwoStep Cluster Analysis

The TwoStep Cluster Analysis procedure is an exploratory tool designed to reveal natural groupings (or clusters) within a dataset that would otherwise not be apparent. The algorithm employed by this procedure has several desirable features that differentiate it from traditional clustering techniques:

• Handling of categorical and continuous variables. By assuming variables to be independent, a joint multinomial-normal distribution can be placed on categorical and continuous variables.
• Automatic selection of number of clusters. By comparing the values of a model-choice criterion across different clustering solutions, the procedure can automatically determine the optimal number of clusters.
• Scalability. By constructing a cluster features (CF) tree that summarizes the records, the TwoStep algorithm allows you to analyze large data files.

Example. Retail and consumer product companies regularly apply clustering techniques to data that describe their customers' buying habits, gender, age, income level, etc. These companies tailor their marketing and product development strategies to each consumer group to increase sales and build brand loyalty.

Distance Measure. This selection determines how the similarity between two clusters is computed.

• Log-likelihood. The likelihood measure places a probability distribution on the variables. Continuous variables are assumed to be normally distributed, while categorical variables are assumed to be multinomial. All variables are assumed to be independent.
• Euclidean. The Euclidean measure is the "straight line" distance between two clusters. It can be used only when all of the variables are continuous.

Number of Clusters. This selection allows you to specify how the number of clusters is to be determined.

• Determine automatically. The procedure will automatically determine the "best" number of clusters, using the criterion specified in the Clustering Criterion group. Optionally, enter a positive integer specifying the maximum number of clusters that the procedure should consider.
• Specify fixed. Allows you to fix the number of clusters in the solution. Enter a positive integer.

Count of Continuous Variables. This group provides a summary of the continuous variable standardization specifications made in the Options dialog box. See the topic TwoStep Cluster Analysis Options for more information.

Clustering Criterion. This selection determines how the automatic clustering algorithm determines the number of clusters. Either the Bayesian Information Criterion (BIC) or the Akaike Information Criterion (AIC) can be specified.

TwoStep Cluster Analysis Data Considerations

Data. This procedure works with both continuous and categorical variables. Cases represent objects to be clustered, and the variables represent attributes upon which the clustering is based.

Case Order. Note that the cluster features tree and the final solution may depend on the order of cases. To minimize order effects, randomly order the cases. You may want to obtain several different solutions with cases sorted in different random orders to verify the stability of a given solution. In situations where this is difficult due to extremely large file sizes, multiple runs with a sample of cases sorted in different random orders might be substituted.

Assumptions. The likelihood distance measure assumes that variables in the cluster model are independent. Further, each continuous variable is assumed to have a normal (Gaussian) distribution, and each categorical variable is assumed to have a multinomial distribution. Empirical internal testing indicates that the procedure is fairly robust to violations of both the assumption of independence and the distributional assumptions, but you should try to be aware of how well these assumptions are met.

Use the Bivariate Correlations procedure to test the independence of two continuous variables. Use the Crosstabs procedure to test the independence of two categorical variables. Use the Means procedure to test the independence between a continuous variable and categorical variable. Use the Explore procedure to test the normality of a continuous variable. Use the Chi-Square Test procedure to test whether a categorical variable has a specified multinomial distribution.

To Obtain a TwoStep Cluster Analysis

This feature requires the Statistics Base option.