Unsupervised Semantic Segmentation (USS) involves segmenting images without
relying on predefined labels, aiming to alleviate the burden of extensive human
labeling. Existing methods utilize features generated by self-supervised models
and specific priors for clustering. However, their clustering objectives are
not involved in the optimization of the features during training. Additionally,
due to the lack of clear class definitions in USS, the resulting segments may
not align well with the clustering objective. In this paper, we introduce a
novel approach called Optimally Matched Hierarchy (OMH) to simultaneously
address the above issues. The core of our method lies in imposing structured
sparsity on the feature space, which allows the features to encode information
with different levels of granularity. The structure of this sparsity stems from
our hierarchy (OMH). To achieve this, we learn a soft but sparse hierarchy
among parallel clusters through Optimal Transport. Our OMH yields better
unsupervised segmentation performance compared to existing USS methods. Our
extensive experiments demonstrate the benefits of OMH when utilizing our
differentiable paradigm. We will make our code publicly available.

无监督语义分割涉及在没有预定义标签的情况下对图像进行分割，以减轻广泛的人工标注负担。本文介绍了一种称为 “优化匹配层次” 的新方法，以同时解决上述问题。我们的方法的核心在于对特征空间进行结构化稀疏性约束，使得特征能够以不同的粒度编码信息。通过最优输运，我们的 “优化匹配层次” 在无监督分割性能上优于现有方法。我们的大量实验证明了利用我们的可微范式以及 “优化匹配层次” 的好处。我们将使我们的代码公开可用。

OMH：通过最佳匹配层次结构实现无监督语义分割的结构稀疏化

OMH: Structured Sparsity via Optimally Matched Hierarchy for  Unsupervised Semantic Segmentation

We propose a general variational framework of fair clustering, which
integrates an original Kullback-Leibler (KL) fairness term with a large class
of clustering objectives, including prototype or graph based. Fundamentally
different from the existing combinatorial and spectral solutions, our
variational multi-term approach enables to control the trade-off levels between
the fairness and clustering objectives. We derive a general tight upper bound
based on a concave-convex decomposition of our fairness term, its
Lipschitz-gradient property and the Pinsker's inequality. Our tight upper bound
can be jointly optimized with various clustering objectives, while yielding a
scalable solution, with convergence guarantee. Interestingly, at each
iteration, it performs an independent update for each assignment variable.
Therefore, it can be easily distributed for large-scale datasets. This
scalability is important as it enables to explore different trade-off levels
between the fairness and clustering objectives. Unlike spectral relaxation, our
formulation does not require computing its eigenvalue decomposition. We report
comprehensive evaluations and comparisons with state-of-the-art methods over
various fair-clustering benchmarks, which show that our variational formulation
can yield highly competitive solutions in terms of fairness and clustering
objectives.

本文提出了一种公平聚类的一般变分框架，该框架将原始的 Kullback-Leibler（KL）公平术语与包括原型或基于图的大类聚类目标相整合。我们的变分多项式方法与现有的组合和谱解决方案基本不同，能够控制公平和聚类目标之间的折衷水平。我们的紧密上界可以与各种聚类目标一起进行联合优化，同时产生可扩展的解决方案，并具有收敛保证。