  Deep clustering has increasingly been demonstrating superiority over
conventional shallow clustering algorithms. Deep clustering algorithms usually
combine representation learning with deep neural networks to achieve this
performance, typically optimizing a clustering and non-clustering loss. In such
cases, an autoencoder is typically connected with a clustering network, and the
final clustering is jointly learned by both the autoencoder and clustering
network. Instead, we propose to learn an autoencoded embedding and then search
this further for the underlying manifold. For simplicity, we then cluster this
with a shallow clustering algorithm, rather than a deeper network. We study a
number of local and global manifold learning methods on both the raw data and
autoencoded embedding, concluding that UMAP in our framework is best able to
find the most clusterable manifold in the embedding, suggesting local manifold
learning on an autoencoded embedding is effective for discovering higher
quality discovering clusters. We quantitatively show across a range of image
and time-series datasets that our method has competitive performance against
the latest deep clustering algorithms, including out-performing current
state-of-the-art on several. We postulate that these results show a promising
research direction for deep clustering. The code can be found at
https://github.com/rymc/n2d
