distancehow

Distancehow is a term used in data analysis to describe methods for measuring the similarity or dissimilarity between objects by combining multiple distance measures into a single composite score. It is not a single metric but a framework for integrating information from diverse feature spaces or modalities.

Common implementations fall into three broad approaches. The linear or weighted combination method constructs distancehow as a weighted sum of base distances: distancehow(x, y) = sum_j w_j d_j(x, y), where d_j are base distances (for example Euclidean, Manhattan, cosine, or graph-based distances) and w_j are nonnegative weights. To make this approach robust, each base distance is typically normalized to a common scale before combining. Weights can be fixed or learned from data.

Distancehow can also be developed through distance learning, where the weights or the fusion function are optimized to improve a downstream task such as clustering quality, classification accuracy, or retrieval performance. Kernel-based fusion represents another variant, where the combined similarity is mapped into a kernel space and a distance is derived from that representation.

Applications span clustering, nearest-neighbor search, recommendation systems, image or text retrieval, and geographic information systems, particularly when objects are described by heterogeneous features. Limitations include the sensitivity to the choice and scaling of base distances, potential violation of metric properties in nonlinear combinations, and the need for sufficient data to learn effective weights.

See also: distance metrics, metric learning, multi-modal similarity, feature fusion.