Master Variable Clustering: Measuring Similarity and Grouping Techniques

1 Variable Clustering Method

In practice, variable clustering is crucial during system analysis or evaluation to avoid overlooking important factors. Initially, many related indicators are considered, leading to an excess of variables with high intercorrelation, which complicates analysis and modeling. Therefore, researchers study variable similarity, grouping variables into clusters based on similarity to identify the main influencing factors.

2 Similarity Measures

When performing variable clustering, the first step is to define a similarity measure. Two common measures are:

1) Correlation Coefficient

Given variables X and Y, the sample correlation coefficient between them can serve as a similarity metric; using the correlation matrix is the most common approach.

2) Cosine of the Angle

The cosine of the angle between the vectors of two variables can also define their similarity.

All similarity definitions should satisfy two properties: the closer the value is to 1, the more correlated or similar the variables; the closer to 0, the weaker the similarity.

Similar to common sample clustering methods (e.g., single‑linkage, complete‑linkage), variable clustering follows the same principles. In variable clustering, common distance definitions include the maximum coefficient method and the minimum coefficient method.

Maximum Coefficient Method

The distance between two clusters is defined as the similarity measure of the most similar pair of variables from the two clusters.

Minimum Coefficient Method

The distance between two clusters is defined as the similarity measure of the least similar pair of variables from the two clusters.

Reference

ThomsonRen github https://github.com/ThomsonRen/mathmodels