similaritywith

Similaritywith is a term used to describe a measure or operation that assesses how similar two objects are when viewed through a particular context, feature subset, or transformation. It is not a single established operator but a descriptive label found in literature and implementations where the notion of similarity must adapt to context.

Formal definition: Given objects x and y in a domain D and a context C that specifies the relevant features, transformations, or metric, similaritywith(x, y; C) yields a score in [0,1] (or a nonnegative real) representing similarity under that context. In practice, it is often constructed as a composition of base similarity measures over the features selected by C, for example sim_with(x, y; C) = f(s1(x1, y1), s2(x2, y2), ..., sk(xk, yk)), where si are feature-wise similarities and f is an aggregation function such as a weighted sum or harmonic mean.

Contexts C may be a subset of features, a coordinate transform, a learned embedding space, or a parameterized metric. This flexibility allows the same pair of objects to be judged differently depending on the application.

Applications include information retrieval, recommender systems, clustering with context, anomaly detection, and multi-view learning. In linguistics, similaritywith might measure semantic similarity conditioned on domain constraints; in computer vision, it might compare images under varying lighting or pose.

Relation to related concepts: similaritywith is related to contextual similarity, conditional similarity measures, and metric learning. Its effectiveness depends on the choice of context and the quality of base similarities.

Limitations include sensitivity to the chosen context, potential lack of universality, and interpretability challenges.