The performance of sparse matrix computation highly depends on the matching
of the matrix format with the underlying structure of the data being computed
on. Different sparse matrix formats are suitable for different structures of
data. Therefore, the first challenge is identifying the matrix structure before
the computation to match it with an appropriate data format. The second
challenge is to avoid reading the entire dataset before classifying it. This
can be done by identifying the matrix structure through samples and their
features. Yet, it is possible that global features cannot be determined from a
sampling set and must instead be inferred from local features. To address these
challenges, we develop a framework that generates sparse matrix structure
classifiers using graph convolutional networks. The framework can also be
extended to other matrix structures using user-provided generators. The
approach achieves 97% classification accuracy on a set of representative sparse
matrix shapes.

本文介绍了一种使用图卷积网络生成稀疏矩阵结构分类器的框架，能够有效地匹配数据中的矩阵结构与适当的数据格式，同时通过样本和特征来识别矩阵结构，实现了对一系列代表性稀疏矩阵形状的 97% 分类精度。

局部观察，全局分类：使用 GNNs 识别稀疏矩阵结构

Observe Locally, Classify Globally: Using GNNs to Identify Sparse Matrix  Structure

Computing the Wasserstein barycenter of a set of probability measures under
the optimal transport metric can quickly become prohibitive for traditional
second-order algorithms, such as interior-point methods, as the support size of
the measures increases. In this paper, we overcome the difficulty by developing
a new adapted interior-point method that fully exploits the problem's special
matrix structure to reduce the iteration complexity and speed up the Newton
procedure. Different from regularization approaches, our method achieves a
well-balanced tradeoff between accuracy and speed. A numerical comparison on
various distributions with existing algorithms exhibits the computational
advantages of our approach. Moreover, we demonstrate the practicality of our
algorithm on image benchmark problems including MNIST and Fashion-MNIST.

本文介绍了一种新的内点法，该方法充分利用了问题的特殊矩阵结构，以降低迭代复杂度和加速牛顿过程，并在各种分布条件下进行了数值比较，展示了该方法的计算优势。此外，我们还在包括 MNIST 和 Fashion-MNIST 在内的图像基准测试问题上演示了我们算法的实用性。

内点方法反击：解决 Wasserstein 重心问题

Interior-Point Methods Strike Back: Solving the Wasserstein Barycenter  Problem

For reconstruction of low-rank matrices from undersampled measurements, we
develop an iterative algorithm based on least-squares estimation. While the
algorithm can be used for any low-rank matrix, it is also capable of exploiting
a-priori knowledge of matrix structure. In particular, we consider linearly
structured matrices, such as Hankel and Toeplitz, as well as positive
semidefinite matrices. The performance of the algorithm, referred to as
alternating least-squares (ALS), is evaluated by simulations and compared to
the Cram\'er-Rao bounds.

基于最小二乘估计的迭代算法可以用于重建低秩矩阵，并且针对线性结构的矩阵和正半定矩阵等具有先验知识的矩阵，有更好的性能，称为交替最小二乘 (ALS) 算法，并通过模拟实验和 Cramér-Rao 下界进行了比较。