Crossrelations

Crossrelations is a broad term used across disciplines to describe the relationships or correspondences between two or more entities, sequences, or data sets. It is not a single formal theory; rather, it encompasses several related ideas used to quantify or characterize how one side relates to the other.

In statistics and signal processing, the closest formal concept is cross-correlation, which measures the similarity between two signals as a function of a displacement or time lag. Crossrelation analysis can identify lead-lag relationships, align signals, or detect repeated patterns across data streams.

In data science and machine learning, cross-relations refer to modeling interactions between different modalities or feature groups, such as combining text and image information or linking heterogeneous sources in multimodal learning. They also appear in multivariate models where the focus is on how changes in one set of variables relate to changes in another.

In social sciences and linguistics, cross-relations may describe correspondences between groups, cultures, languages, or networked actors, often studied with relational data methods or cross-cultural analyses.

In biology and ecology, cross-relations describe how one biological variable relates to another across populations, regions, or time, informing studies of interaction, co-evolution, or ecosystem response.

In mathematics, the term is used descriptively to describe relationships between elements of different structures or categories, rather than as a single formal object. Across domains, common methods include cross-correlation, cross-covariance, mutual information, and matrix or network-based approaches to capture inter-relational patterns.