Direction-Preserving Anchor Learning for Multi-View Clustering

Anchor-based multi-view clustering commonly represents samples using orthogonal anchors and simplex-constrained assignment weights, and performs reconstruction with squared Euclidean distance. We identify an overlooked problem in this common formulation: under orthogonal anchors, the norm of the assignment vector directly determines the norm of the reconstructed sample. Since squared Euclidean loss depends on both direction and magnitude, the norm of the assignment weights also participates in minimizing the reconstruction error. As a result, the assignment weights, which are intended to describe clustering structure, are additionally influenced by reconstruction magnitude, interfering with the learning of the clustering representation. This additional influence may also hinder the clustering representation from adapting well to different numbers of anchors, making the model more sensitive to the anchor number. To address these problems, we propose Direction-Preserving Anchor Learning (DPAL), which normalizes each anchor combination before computing the reconstruction error. This preserves the representation direction determined by the assignment weights while making the reconstruction error independent of their norm. DPAL requires no additional regularization trade-off parameter and admits efficient closed-form alternating updates. Experiments on ten multi-view benchmark datasets show that DPAL substantially improves over conventional Euclidean reconstruction models, remains competitive with recent anchor-based methods, and is more stable with respect to the number of anchors.