  In clustering we normally output one cluster variable for each datapoint.
However it is not necessarily the case that there is only one way to partition
a given dataset into cluster components. For example, one could cluster objects
by their colour, or by their type. Different attributes form a hierarchy, and
we could wish to cluster in any of them. By disentangling the learnt latent
representations of some dataset into different layers for different attributes
we can then cluster in those latent spaces. We call this "disentangled
clustering". Extending Variational Ladder Autoencoders (Zhao et al., 2017), we
propose a clustering algorithm, VLAC, that outperforms a Gaussian Mixture DGM
in cluster accuracy over digit identity on the test set of SVHN. We also
demonstrate learning clusters jointly over numerous layers of the hierarchy of
latent variables for the data, and show component-wise generation from this
hierarchical model.
