Bajaj Chandrajit, Gao Tingran, He Zihang, Huang Qixing, Liang Zhenxiao
Department of Computer Science, The University of Texas at Austin.
Department of Statistics, The University of Chicago.
Proc Mach Learn Res. 2018 Jul;80:324-333.
We introduce a principled approach for (SMAC) for establishing consistent maps across heterogeneous object collections (e.g., 2D images or 3D shapes). Our approach takes as input a heterogeneous object collection and a set of maps computed between some pairs of objects, and outputs a homogeneous object clustering together with a new set of maps possessing optimal intra- and inter-cluster consistency. Our approach is based on the spectral decomposition of a data matrix storing all pairwise maps in its blocks. We additionally provide tight theoretical guarantees for the accuracy of SMAC under established noise models. We also demonstrate the usefulness of our approach on synthetic and real datasets.
我们引入了一种用于建立跨异构对象集合（例如二维图像或三维形状）的一致映射的原则性方法（SMAC）。我们的方法将异构对象集合以及在某些对象对之间计算的一组映射作为输入，并输出一个同构对象聚类以及一组具有最佳簇内和簇间一致性的新映射。我们的方法基于一个数据矩阵的谱分解，该数据矩阵在其块中存储所有成对映射。我们还在既定的噪声模型下为SMAC的准确性提供了严格的理论保证。我们还在合成数据集和真实数据集上展示了我们方法的实用性。
