The Balanced-Pairwise-Affinities (BPA) feature transform is designed to upgrade the features of a set of input items to facilitate downstream matching or grouping related tasks. The transformed set encodes a rich representation of high order relations between the input features. A particular min-cost-max-flow fractional matching problem, whose entropy regularized version can be approximated by an optimal transport (OT) optimization, leads to a transform which is efficient, differentiable, equivariant, parameterless and probabilistically interpretable. While the Sinkhorn OT solver has been adapted extensively in many contexts, we use it differently by minimizing the cost between a set of features to $itself$ and using the transport plan's $rows$ as the new representation. Empirically, the transform is highly effective and flexible in its use and consistently improves networks it is inserted into, in a variety of tasks and training schemes. We demonstrate state-of-the-art results in few-shot classification, unsupervised image clustering and person re-identification. Code is available at \url{github.com/DanielShalam/BPA}.

设计了平衡成对亲和力（BPA）特征转换以升级一组输入项的特征，使其适用于下游匹配或相关任务。通过最小成本最大流分数匹配问题、基于最优传输（OT）优化来近似其熵正则化版本，得到一种高效、可微分、等变、无参数且具有概率解释性的转换。它在各种任务和训练方案中都表现出极高的效果和灵活性，并且在少样本分类、无监督图像聚类和人物重新识别等方面展示出最先进的结果。

平衡对比特征变换