cosvw

Cosvw, short for cosine-weighted vector similarity, is a method used to quantify similarity between high-dimensional feature vectors by integrating the standard cosine similarity with a per-feature variance-based weighting scheme.

In this approach, each feature i is assigned a weight w_i derived from the variance var_i of that feature across a reference dataset, typically w_i = 1 / (var_i + epsilon). The similarity between two vectors x and y is computed as: cosvw(x, y) = (sum_i w_i x_i y_i) / (sqrt(sum_i w_i x_i^2) * sqrt(sum_i w_i y_i^2)). The weights dampen the influence of features with high observed variance, reducing sensitivity to noisy components.

Origins and context: The method arises from efforts to improve robustness of similarity measures in noisy domains such as image retrieval and text embedding comparisons. It is related to feature weighting and metric learning literature.

Typical applications include content-based image retrieval, document similarity, and recommender systems. Benefits include increased robustness to noisy features and scale differences; limitations include the need for reliable variance estimates and potential computational overhead. The effectiveness of cosvw depends on the quality of the variance data and the alignment between the weighting scheme and the discriminative power of features.

Implementation notes: compute variances from a representative corpus, apply a small epsilon to avoid division by zero, and optionally learn weights through a lightweight optimization or cross-validation.