We introduce a differentiable clustering method based on minimum-weight
spanning forests, a variant of spanning trees with several connected
components. Our method relies on stochastic perturbations of solutions of
linear programs, for smoothing and efficient gradient computations. This allows
us to include clustering in end-to-end trainable pipelines. We show that our
method performs well even in difficult settings, such as datasets with high
noise and challenging geometries. We also formulate an ad hoc loss to
efficiently learn from partial clustering data using this operation. We
demonstrate its performance on several real world datasets for supervised and
semi-supervised tasks.

提出了一种基于最小权重生成树的可微聚类方法，通过线性规划的随机扰动实现平滑和高效的梯度计算，从而在端对端可训练流水线中进行聚类，并演示其在高噪声和具有挑战性的数据集上的性能和用于半监督任务的。

扰动生成树的可微聚类

Differentiable Clustering with Perturbed Spanning Forests

Graph Neural Networks (GNNs) are a promising deep learning approach for
circumventing many real-world problems on graph-structured data. However, these
models usually have at least one of four fundamental limitations:
over-smoothing, over-fitting, difficult to train, and strong homophily
assumption. For example, Simple Graph Convolution (SGC) is known to suffer from
the first and fourth limitations. To tackle these limitations, we identify a
set of key designs including (D1) dilated convolution, (D2) multi-channel
learning, (D3) self-attention score, and (D4) sign factor to boost learning
from different types (i.e. homophily and heterophily) and scales (i.e. small,
medium, and large) of networks, and combine them into a graph neural network,
GPNet, a simple and efficient one-layer model. We theoretically analyze the
model and show that it can approximate various graph filters by adjusting the
self-attention score and sign factor. Experiments show that GPNet consistently
outperforms baselines in terms of average rank, average accuracy, complexity,
and parameters on semi-supervised and full-supervised tasks, and achieves
competitive performance compared to state-of-the-art model with inductive
learning task.

通过多种设计，将 GPNet 与 dilated convolution, multi-channel learning, self-attention score 和 sign factor 进行结合，以减轻 Graph Neural Networks 模型中存在的多种限制以及提高 semi-supervised 和 inductive learning task 的性能。