基于自适应NEPv的公平多视图行列式核心集

中文摘要 AI 辅助

从大型候选池中选择小型且多样的子集时，往往需要平衡多种不相容的多样性概念。例如在商标管理中，子集应同时涵盖描述商标的语言和商标标志的视觉空间。单一的行列式点过程（DPP）核可能会掩盖某一视图的缺陷，而平均核则通过普通的单核谱问题替代了多视图松弛。我们提出了公平多视图行列式选择方法：最大化大小为k的子集的各视图对数行列式的最小值。我们对该非光滑目标进行平滑处理，并将其松弛到施蒂费尔流形上，该松弛能精确嵌入每个离散子集，但与单视图对应方法不同，它通常没有闭式谱解。其平稳性条件是一个具有依赖于特征向量的视图自适应权重的规范不变非线性特征值问题。我们推导了带阻尼和电平偏移的自适应自洽场（SCF）求解器，并通过杠杆得分筛选再结合公平局部细化来对所得子空间进行圆整。该求解器仅需各视图的特征图乘积。我们报告了冲突视图的合成实验，并指定了多模态USPTO协议；真实数据的多模态结果需要对齐的标志嵌入，且本版本不对此进行声明。

英文摘要

Selecting a small, diverse subset from a large candidate pool often means balancing several incompatible notions of diversity. In trademark curation, for instance, a subset should cover both the language used to describe marks and the visual space of their logos. A single determinantal point process (\DPP) kernel can hide failure in one view, and averaging kernels replaces the multi-view relaxation by an ordinary single-kernel spectral problem. We formulate \emph{fair multi-view determinant selection}: maximize the weakest per-view log determinant of a size-$k$ subset. We smooth this nonsmooth objective and relax it to the Stiefel manifold. The relaxation embeds every discrete subset exactly, but unlike its single-view counterpart it has no closed-form spectral solution in general. Its stationarity condition is a gauge-invariant nonlinear eigenvalue problem with eigenvector-dependent, view-adaptive weights. We derive an adaptive self-consistent-field (\SCF) solver with damping and level shifting, and round the resulting subspace by leverage-score screening followed by fair local refinement. The solver needs only feature-map products for each view. We report conflicting-view synthetic experiments and specify a multimodal USPTO protocol; the real-data multimodal results require aligned logo embeddings and are not claimed in this version.

发表机构

• Hong Kong Baptist University（香港浸会大学）
• TadReamk Limited（TadReamk有限公司）

机构由 AI 辅助整理，请以论文原文为准。