Dimensionet

Dimensionet is a term used in some mathematical and computational discussions to describe a dimensionality profile of an object or dataset. Rather than a single number, a dimensionet encodes multiple aspects of dimensionality, allowing a richer representation of structure than the conventional notion of dimension.

Formally, a dimensionet can be represented as a vector d = (d1, d2, ..., dk), where each di denotes the extent or weight of a particular dimension category, such as spatial, temporal, intrinsic, or scale-related components. In normalized variants, the components sum to one; in others they are unconstrained nonnegative values. The exact interpretation depends on the chosen taxonomy of dimensions.

Interpretation examples are context dependent. A simple geometric object might emphasize spatial components, while a time-evolving process may have a higher temporal entry. In data analysis, a dimensionet can describe how different modalities contribute to a representation, such as geometry, texture, or color in image data.

Usage and status: Dimensionet is not a standard mathematical notion, and there is no universally accepted formal theory. It appears primarily in niche discussions as a conceptual tool to compare complex objects or datasets that lack a single, conventional dimension value.

See also: Dimension, Intrinsic dimension, Fractal dimension, Manifold learning.