In the last decade, recent successes in deep clustering majorly involved the
Mutual Information (MI) as an unsupervised objective for training neural
networks with increasing regularisations. While the quality of the
regularisations have been largely discussed for improvements, little attention
has been dedicated to the relevance of MI as a clustering objective. In this
paper, we first highlight how the maximisation of MI does not lead to
satisfying clusters. We identified the Kullback-Leibler divergence as the main
reason of this behaviour. Hence, we generalise the mutual information by
changing its core distance, introducing the Generalised Mutual Information
(GEMINI): a set of metrics for unsupervised neural network training. Unlike MI,
some GEMINIs do not require regularisations when training as they are
geometry-aware thanks to distances or kernels in the data space. Finally, we
highlight that GEMINIs can automatically select a relevant number of clusters,
a property that has been little studied in deep discriminative clustering
context where the number of clusters is a priori unknown.

本文介绍了深度聚类中相互信息作为无监督训练神经网络的客观标准的最大化并不能得到令人满意的聚类结果，并将核心距离更改为常见的挑战导致的原因。因此，我们通过引入广义相互信息 (GEMINI) 来推广相互信息，它是一组用于无监督神经网络训练的指标。与相互信息不同，一些 GEMINI 在训练时不需要正则化，因为它们在数据空间中具有几何意识的距离或核函数。最后，我们强调 GEMINI 可以自动选择相关的聚类数目，这是在深度判别聚类上很少研究的一个特性，因为聚类数目是先验未知的。

广义互信息：一种用于判别聚类的框架

Generalised Mutual Information: a Framework for Discriminative  Clustering

In the last decade, recent successes in deep clustering majorly involved the
mutual information (MI) as an unsupervised objective for training neural
networks with increasing regularisations. While the quality of the
regularisations have been largely discussed for improvements, little attention
has been dedicated to the relevance of MI as a clustering objective. In this
paper, we first highlight how the maximisation of MI does not lead to
satisfying clusters. We identified the Kullback-Leibler divergence as the main
reason of this behaviour. Hence, we generalise the mutual information by
changing its core distance, introducing the generalised mutual information
(GEMINI): a set of metrics for unsupervised neural network training. Unlike MI,
some GEMINIs do not require regularisations when training. Some of these
metrics are geometry-aware thanks to distances or kernels in the data space.
Finally, we highlight that GEMINIs can automatically select a relevant number
of clusters, a property that has been little studied in deep clustering context
where the number of clusters is a priori unknown.

本文提出了一种新的无监督神经网络训练度量标准 —— 广义互信息 (GEMINI)，相比于互信息，它不需要正则化且可自动选择群聚数目，并且是数据空间的几何感知度量，从而提供更好的聚类效果。