SIAM Journal on Imaging Sciences, Volume 13, Issue 3, Page 1113-1156, January 2020.
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment flow takes a pairwise data affinity matrix as input data and maximizes the correlation with a low-rank matrix that is parametrized by the variables of the assignment flow, which entails an assignment of the data to themselves through the formation of latent labels (feature prototypes). A single user parameter, the neighborhood size for the geometric regularization of assignments, drives the entire process. By smooth geodesic interpolation between different normalizations of self-assignment matrices on the positive definite matrix manifold, a one-parameter family of self-assignment flows is defined. Accordingly, our approach can be characterized from different viewpoints, e.g., as performing spatially regularized, rank-constrained discrete optimal transport, or as computing spatially regularized normalized spectral cuts. Regarding combinatorial optimization, our approach successfully determines completely positive factorizations of self-assignments in large-scale scenarios, subject to spatial regularization. Various experiments, including the unsupervised learning of patch dictionaries using a locally invariant distance function, illustrate the properties of the approach.

中文翻译：

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图上无监督数据标记的自分配流

SIAM影像科学杂志，第13卷，第3期，第1113-1156页，2020年1月。
本文将最近引入的用于监督图像标记的分配流方法扩展到没有监督的未监督场景。生成的自分配流将成对数据亲和矩阵作为输入数据，并与由分配流的变量参数化的低秩矩阵的相关性最大化，这需要通过形成潜伏来将数据分配给自己标签（功能原型）。单个用户参数（用于分配的几何正则化的邻域大小）驱动整个过程。通过在正定矩阵流形上的自赋值矩阵的不同归一化之间进行平滑测地插值，定义了一个单参数族的自赋值流。因此，我们的方法可以从不同的角度进行表征，例如，执行空间正则化，秩受限的离散最优传输，或计算空间正则化归一化光谱切割。关于组合优化，我们的方法在空间正则化的前提下成功地确定了大规模场景中自我分配的完全正因式分解。各种实验，包括使用局部不变距离函数的无监督补丁字典学习，都说明了该方法的特性。在空间正则化的前提下，我们的方法成功地确定了大规模情景中自我分配的完全正分解。各种实验，包括使用局部不变距离函数的无监督补丁字典学习，都说明了该方法的特性。在空间正则化的前提下，我们的方法成功地确定了大规模情景中自我分配的完全正因式分解。各种实验，包括使用局部不变距离函数的无监督补丁字典学习，都说明了该方法的特性。