Designing unsupervised mixed‐type feature selection techniques using the heterogeneous correlation matrix

Real-life data often include both numerical and categorical features. When categorical features are ordinal, the Pearson correlation matrix (CM) can be extended to a heterogeneous CM (HCM), which combines Pearson's correlations (numerical-numerical), polyserial correlations (numerical-ordinal) and polychoric correlations (ordinal-ordinal). HCM entries are comparable, enabling assessment of pairwise-linear dependencies. An added benefit is the computation of (Formula presented.) -values for pairwise uncorrelation tests, forming a heterogeneous (Formula presented.) -values matrix (HPM). While the HCM has been used for unsupervised feature extraction (UFE), that is, transforming features into informative representations (e.g., PCA), its application to unsupervised feature selection (UFS), that is, selecting relevant features, remains unexplored. This paper proposes two HCM-based UFS methods for mixed-type features. These, called UFS-rHCM and UFS-cHCM, iteratively remove redundant features using the HCM—row-wise (UFS-rHCM) or cell-wise (UFS-cHCM). The HPM determines the stopping point, enabling a statistically grounded approach to selecting the number of features. We also introduce a visualization tool for assessing feature importance and ranking. The performance of our methods is evaluated on simulated and real datasets.