kweighted

Kweighted is a term used in data analysis and computer science to describe a family of weighting schemes parameterized by a real nonnegative exponent k. It is used to adjust the influence of components in a dataset, such as features, nodes in a graph, or items in a ranking, by applying a power-law transformation controlled by k. The approach aims to tailor the emphasis on large versus small values to suit a specific task.

In a typical use, given a collection of nonnegative values v_i, the k-weighted weight w_i is computed as w_i = (v_i)^k / sum_j (v_j)^k, providing a normalized distribution of weights. For k>1, larger values gain more emphasis; for 0<k<1, the distribution flattens, giving smaller values relatively more weight. When applied to edge weights in a graph, or to feature scores in machine learning, this transformation can improve robustness to skew or highlight dominant components.

Applications include information retrieval, where kweighted scores influence ranking; graph algorithms, where edge or node weights are adjusted before computing centrality or shortest paths; and feature selection, where kweighted weights guide the selection of informative features. It is also used in normalization pipelines to stabilize variance across features.

Variants of kweighted include using different base transformations, such as w_i = log(1+ (v_i)^k) to dampen extreme values, or using softmax normalization after the transformation. The method is typically simple to implement and can be integrated with existing weighting schemes.

See also: Weighted average, Power mean, Kernel weighting, Normalization.