ON THE METHODS AND THEORY OF CLUSTERING

Area of Science:

• Psychometrics
• Statistical modeling
• Data analysis

Background:

• Clustering individuals into homogeneous groups is essential for data analysis.
• Existing clustering methods, using correlation or distance measures, have technical and logical limitations.
• A significant gap in current procedures is the lack of an underlying statistical model.

Purpose of the Study:

• To evaluate existing clustering methods based on correlation and distance measures.
• To identify the technical and logical shortcomings of these procedures.
• To propose a more robust framework for clustering analysis.

Main Methods:

• Discussion of clustering procedures utilizing correlation measures for profile similarity.
• Analysis of clustering techniques employing distance measures.
• Conceptualization of clustering as a mixture problem.

Main Results:

• Both correlation and distance measures present technical and logical challenges in clustering.
• The absence of a statistical model is identified as a key defect in most clustering procedures.
• Framing the clustering problem as a mixture problem is proposed as a potential solution.

Conclusions:

• Current clustering methods are insufficient due to inherent technical and logical flaws.
• The integration of statistical models, specifically through mixture problems, is recommended for advancing clustering techniques.
• Further interdisciplinary research involving psychologists and statisticians is necessary to develop improved clustering methodologies.