We develop a novel data-driven nonlinear mixup mechanism for graph data
augmentation and present different mixup functions for sample pairs and their
labels. Mixup is a data augmentation method to create new training data by
linearly interpolating between pairs of data samples and their labels. Mixup of
graph data is challenging since the interpolation between graphs of potentially
different sizes is an ill-posed operation. Hence, a promising approach for
graph mixup is to first project the graphs onto a common latent feature space
and then explore linear and nonlinear mixup strategies in this latent space. In
this context, we propose to (i) project graphs onto the latent space of
continuous random graph models known as graphons, (ii) leverage convex
clustering in this latent space to generate nonlinear data-driven mixup
functions, and (iii) investigate the use of different mixup functions for
labels and data samples. We evaluate our graph data augmentation performance on
benchmark datasets and demonstrate that nonlinear data-driven mixup functions
can significantly improve graph classification.

本文提出了一种新的基于数据的非线性 mixup 机制，为样本对及其标签提供不同的 mixup 功能，通过在公共潜在特征空间上投射图形数据并探索非线性数据驱动的 mixup 策略，结合凸聚类生成一个最佳的数据增强方法来提高图分类的性能。

GraphMAD：使用数据驱动凸聚类的图形混合数据增强

GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering

Many real-world large-scale regression problems can be formulated as
Multi-task Learning (MTL) problems with a massive number of tasks, as in retail
and transportation domains. However, existing MTL methods still fail to offer
both the generalization performance and the scalability for such problems.
Scaling up MTL methods to problems with a tremendous number of tasks is a big
challenge. Here, we propose a novel algorithm, named Convex Clustering
Multi-Task regression Learning (CCMTL), which integrates with convex clustering
on the k-nearest neighbor graph of the prediction models. Further, CCMTL
efficiently solves the underlying convex problem with a newly proposed
optimization method. CCMTL is accurate, efficient to train, and empirically
scales linearly in the number of tasks. On both synthetic and real-world
datasets, the proposed CCMTL outperforms seven state-of-the-art (SoA)
multi-task learning methods in terms of prediction accuracy as well as
computational efficiency. On a real-world retail dataset with 23,812 tasks,
CCMTL requires only around 30 seconds to train on a single thread, while the
SoA methods need up to hours or even days.

提出一种名为 Convex Clustering Multi-Task regression Learning (CCMTL) 的算法，通过在预测模型的 k 近邻图上与凸聚类相结合，并使用新提出的优化方法有效地解决底层凸问题，使得其能够在包含大量任务的问题中实现准确性、高效性和线性可扩展性，并在真实世界和合成数据集上优于 7 种现有的 state-of-the-art 多任务学习方法。

大规模任务高效可扩展的多任务回归

Efficient and Scalable Multi-task Regression on Massive Number of Tasks

Convex clustering, a convex relaxation of k-means clustering and hierarchical
clustering, has drawn recent attentions since it nicely addresses the
instability issue of traditional nonconvex clustering methods. Although its
computational and statistical properties have been recently studied, the
performance of convex clustering has not yet been investigated in the
high-dimensional clustering scenario, where the data contains a large number of
features and many of them carry no information about the clustering structure.
In this paper, we demonstrate that the performance of convex clustering could
be distorted when the uninformative features are included in the clustering. To
overcome it, we introduce a new clustering method, referred to as Sparse Convex
Clustering, to simultaneously cluster observations and conduct feature
selection. The key idea is to formulate convex clustering in a form of
regularization, with an adaptive group-lasso penalty term on cluster centers.
In order to optimally balance the tradeoff between the cluster fitting and
sparsity, a tuning criterion based on clustering stability is developed. In
theory, we provide an unbiased estimator for the degrees of freedom of the
proposed sparse convex clustering method. Finally, the effectiveness of the
sparse convex clustering is examined through a variety of numerical experiments
and a real data application.

本文介绍了一种新的聚类方法 ——Sparse Convex Clustering，该方法采用一种正则化形式的凸聚类方法来进行特征选择，并使用基于聚类稳定性的调整标准来优化聚类效果。作者通过多种数值实验和真实数据应用验证了该聚类方法的有效性。

稀疏凸聚类

Sparse Convex Clustering

In this manuscript, we study the statistical properties of convex clustering.
We establish that convex clustering is closely related to single linkage
hierarchical clustering and $k$-means clustering. In addition, we derive the
range of tuning parameter for convex clustering that yields a non-trivial
solution. We also provide an unbiased estimate of the degrees of freedom, and
provide a finite sample bound for the prediction error for convex clustering.
We compare convex clustering to some traditional clustering methods in
simulation studies.

本文研究了凸聚类的统计特性，将其与单链式聚类和 $k$- 均值聚类密切相关，建立了凸聚类的调参范围、提供了自由度的无偏估计和预测误差的有限样本界限，并在模拟研究中与某些传统聚类方法进行了比较。