FGwaarden

FGwaarden is a concept in data analysis that refers to a set of local descriptors derived from a scalar function defined on a discrete grid of features. They are designed to summarize how the function changes across the grid by recording gradient-like information at each grid point, effectively capturing local behavior.

The term FGwaarden blends FG for functional gradient with waarden, the Dutch word for values. It has appeared in Dutch-language data science literature since the mid-2010s, particularly in discussions of feature engineering that emphasize local change patterns in a function or model.

Computationally, the FGwaarde at a grid point x for a function G defined on a lattice F in R^d is the vector of partial derivatives of G with respect to each coordinate, typically estimated via finite differences. Central differences are common for accuracy, while forward or backward differences may be used at the grid borders. Normalization by the gradient magnitude or feature scales is often employed to improve comparability across observations. Higher-order FGwaarden can incorporate second derivatives or directional derivatives to capture curvature and anisotropy. In modern workflows, automatic differentiation from machine-learning models can provide exact FGwaarden for the portions of G represented by differentiable components.

Applications of FGwaarden include feature engineering for predictive modeling, where they help expose local trends that improve accuracy; anomaly detection, by highlighting sharp changes; and interpretability analyses, by indicating which directions contribute most to changes in the target function. Variants exist that focus on directional FGwaarden, robust values under noise, or temporal FGwaarden for time-series data. See also gradient, directional derivative, and Hessian-based descriptors.