New DPP algorithm balances multi-view diversity for fair data selection

This paper from Richard Yi Da Xu tackles data subset selection when diversity must be judged across multiple, sometimes conflicting, views. Traditional determinantal point processes (DPPs) model diversity with a single kernel; for multi-view data, practitioners often average kernels, which can hide a failure in one view. Xu's "fair multi-view DPP" instead maximizes the weakest per-view log determinant. The objective is nonsmooth, so he smooths it and relaxes it onto the Stiefel manifold—the set of orthogonal k-frames. Every discrete subset embeds exactly, but unlike single-view DPPs, the relaxation has no closed-form spectral solution. Xu derives stationarity as a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights.

To solve it, Xu proposes an adaptive self-consistent-field (SCF) algorithm with damping and level shifting, a technique familiar from quantum chemistry and electronic structure. The solver only needs feature-map products per view. After convergence, he rounds the subspace to a discrete subset using leverage-score screening and fair local refinement. Experiments include conflicting-view synthetic datasets and a multimodal USPTO trademark protocol: the algorithm selects examples that cover both trademark text semantics and logo visual space. The version does not claim real-data multimodal results, because aligned logo embeddings are still needed. The work opens a practical path to fair multi-view coresets and subset selection, with applications in trademark curation, multimodal dataset pruning, active learning, and model training data selection. It improves upon averaging kernels by ensuring no view is silently underrepresented.