Cluster Analysis with SPSS (ENG, ITA, ESP)

Consider a matrix of n rows and p columns, composed of p quantitative variables: - Description and presentation of the dataset, and its preparation; elimination of missing data, almost collinear variables, etc. (p and n are small so we proceed with the analysis of the clusters and there isn't the reduction of the variables). - Determination of the optimal number of clusters: a hierarchical clustering method is applied (WARD), arriving at a dendrogram, which will be cut in correspondence with the "elbow" method; the number of clusters can also be increased or decreased by 1 to make performance comparisons. - Identification of clusters and their interpretation: the syntheses of the distributions of the variables on the statistical units of the whole population and their main quantiles are considered. Synthesis: min, max, average, quadratic deviation, variance, asymmetry, kurtosis. Order quantiles 0.05 0.10 0.25 0.5 (median) 0.75 0.90 0.95. These summaries and population quantiles must be compared with the correspondents of the distributions of the variables for the statistical units of each cluster, in order to have a description of the characteristics of the statistical units of which each cluster is composed with respect to variables. - Application of a non-hierarchical clustering technique (K-MEANS): 1. choose the number of clusters determined through the dendrogram obtained previously from the application of a hierarchical clustering technique. 2. Use the K-Means method and do the interpretation of clusters with summaries. 3. Comparison between clusters formed with the hierarchical method with those formed with the non-hierarchical method. 4. Final scientific conclusions. The project can be in english, italian or spanish.