featuresdistances

Features distances refer to measures that quantify how similar or dissimilar two features (columns) are in a dataset, focusing on the relationships between features rather than between individual observations. They are used to assess redundancy, inform feature selection, and guide model design by revealing which features carry overlapping information.

When features are numeric, each feature is treated as a vector across samples, and the distance between two feature vectors can be computed with standard metrics such as Euclidean or Manhattan distance. A common approach for assessing similarity is a correlation-based distance, defined as 1 minus the absolute value of the Pearson correlation; this captures linear relationships while ignoring scale. For nonlinear associations, distance measures such as distance correlation or mutual information can be more informative. For categorical features, distances include Hamming distance, Gower distance, or chi-squared-based measures. Many workflows standardize or normalize features before computing distances to prevent scale from dominating the results.

Applications of feature distances include redundancy reduction through feature clustering, guiding feature selection, and informing the design of feature ensembles or metric learning approaches. A feature distance matrix can be analyzed with hierarchical clustering or multidimensional scaling to reveal structure among features and to suggest grouping or ordering of features in models.

Cautions when using features distances include sensitivity to scaling, missing values, and the high-dimensional setting where many features may appear similarly distant due to noise. Interpretation of distances depends on the data type, measurement scales, and domain context. Related concepts include feature similarity, feature selection, feature clustering, mutual information, and metric learning.