  The field of deep clustering combines deep learning and clustering to learn
representations that improve both the learned representation and the
performance of the considered clustering method. Most existing deep clustering
methods are designed for a single clustering method, e.g., k-means, spectral
clustering, or Gaussian mixture models, but it is well known that no clustering
algorithm works best in all circumstances. Consensus clustering tries to
alleviate the individual weaknesses of clustering algorithms by building a
consensus between members of a clustering ensemble. Currently, there is no deep
clustering method that can include multiple heterogeneous clustering algorithms
in an ensemble to update representations and clusterings together. To close
this gap, we introduce the idea of a consensus representation that maximizes
the agreement between ensemble members. Further, we propose DECCS (Deep
Embedded Clustering with Consensus representationS), a deep consensus
clustering method that learns a consensus representation by enhancing the
embedded space to such a degree that all ensemble members agree on a common
clustering result. Our contributions are the following: (1) We introduce the
idea of learning consensus representations for heterogeneous clusterings, a
novel notion to approach consensus clustering. (2) We propose DECCS, the first
deep clustering method that jointly improves the representation and clustering
results of multiple heterogeneous clustering algorithms. (3) We show in
experiments that learning a consensus representation with DECCS is
outperforming several relevant baselines from deep clustering and consensus
clustering. Our code can be found at https://gitlab.cs.univie.ac.at/lukas/deccs
