Segmentwise

Segmentwise is an adjective and adverb used to describe actions, analyses, or definitions that are applied to individual segments of a domain or dataset. In many technical contexts, segmentwise approaches partition a whole into disjoint intervals or regions and treat each segment separately, often using different models or parameters for each piece.

In mathematics and data modeling, a segmentwise (or piecewise) function is defined on a partition of the domain into segments, with a distinct expression on each segment. Common examples include segmentwise constant and segmentwise linear functions, where the function value or slope can change from one segment to another at specified breakpoints. The segment boundaries may be fixed or determined from data, and continuity at boundaries is not guaranteed unless explicitly enforced.

In signal processing and time-series analysis, segmentwise processing involves analyzing or transforming data within windows or segments. This enables localized modeling, adaptive filtering, or feature extraction that accounts for non-stationarity. Segmentwise or piecewise regression, also known as segmented regression, fits different models to different portions of the data, usually with a breakpoint where the relationship changes.

In computing, graphics, and geographic information systems, segmentwise operations apply transformations or computations to each segment of a partitioned object or region. This approach supports localized rendering, statistics, or analysis that respects the inherent segmentation of the data.

See also: piecewise function, segmented regression, segmentation.