  Unsupervised learning has gained prominence in the big data era, offering a
means to extract valuable insights from unlabeled datasets. Deep clustering has
emerged as an important unsupervised category, aiming to exploit the non-linear
mapping capabilities of neural networks in order to enhance clustering
performance. The majority of deep clustering literature focuses on minimizing
the inner-cluster variability in some embedded space while keeping the learned
representation consistent with the original high-dimensional dataset. In this
work, we propose soft silhoutte, a probabilistic formulation of the silhouette
coefficient. Soft silhouette rewards compact and distinctly separated
clustering solutions like the conventional silhouette coefficient. When
optimized within a deep clustering framework, soft silhouette guides the
learned representations towards forming compact and well-separated clusters. In
addition, we introduce an autoencoder-based deep learning architecture that is
suitable for optimizing the soft silhouette objective function. The proposed
deep clustering method has been tested and compared with several well-studied
deep clustering methods on various benchmark datasets, yielding very
satisfactory clustering results.
