dissimilativity

Dissimilativity is a concept used in statistics, data analysis, information theory, and related fields to describe the degree to which two objects differ. In formal treatments, dissimilarity is represented by a function d(X,Y) that assigns a non-negative real value to any pair of objects X and Y, where larger values indicate greater dissimilarity. The term can refer to the function itself or to the property of a measure that quantifies how unlike objects are. It is closely related to similarity, but defined in a way that emphasizes difference rather than shared features.

Common properties of dissimilarities include non-negativity and the condition that d(X,X) = 0 for identical objects. Symmetry (d(X,Y) = d(Y,X)) is often assumed but not universal, and the triangle inequality is not required in all definitions. When a dissimilarity satisfies symmetry and triangle inequality, it is typically called a distance or metric. In practice, dissimilarities are used to compare complex objects such as sets, strings, vectors, graphs, or probability distributions, and are assembled into dissimilarity matrices for further analysis. They underpin techniques like clustering, nonmetric multidimensional scaling, and nearest-neighbor methods, where the goal is to group or embed objects based on how different they are.

Examples of dissimilarities include Jaccard distance for set-based data and Bray-Curtis dissimilarity for abundance data. Euclidean distance is a familiar dissimilarity that also satisfies all metric properties. The choice of dissimilarity affects results and interpretation, and researchers often select a measure aligned with the data type and analysis goals. See also: dissimilarity, distance, metric, similarity.