matrixanchors

Matrixanchors is a term used in linear algebra and data analysis to describe a selected set of rows and/or columns of a matrix that serve as reference points for stabilizing or interpreting a matrix factorization or embedding. The central idea is to anchor a decomposition to a small, well-chosen subset of the original data so that the resulting factors are more interpretable or identifiable.

In formal terms, for a matrix X in R^{m x n}, a matrixanchor system selects sets of row indices A and column indices B. These anchors are then used to construct an anchored factorization, for example X ≈ U V with U and V constrained so that the blocks corresponding to A or B reflect the anchor information. Anchors can be chosen to maximize representativeness, stability, or interpretability, and they often serve to fix scale, orientation, or sparsity in the resulting factors.

Common construction strategies include selecting anchors by leverage scores or extreme values, clustering-based prototypes, greedy maximization of a determinant or explained variance, or by adopting established anchor sets from related decompositions such as CUR or separable nonnegative matrix factorization. The chosen anchors typically aim to capture the most informative structure of the data while remaining robust to perturbations.

Matrixanchors have applications in data compression, interpretable factorization, and data mining, where an anchored representation helps relate latent factors to concrete, observable features. They are related to, but distinct from, CUR decompositions, anchor words in topic models, and other anchored or landmark-based methods, which share the goal of tying abstract factors to identifiable data points.