  Though manifold-based clustering has become a popular research topic, we
observe that one important factor has been omitted by these works, namely that
the defined clustering loss may corrupt the local and global structure of the
latent space. In this paper, we propose a novel Generalized Clustering and
Multi-manifold Learning (GCML) framework with geometric structure preservation
for generalized data, i.e., not limited to 2-D image data and has a wide range
of applications in speech, text, and biology domains. In the proposed
framework, manifold clustering is done in the latent space guided by a
clustering loss. To overcome the problem that the clustering-oriented loss may
deteriorate the geometric structure of the latent space, an isometric loss is
proposed for preserving intra-manifold structure locally and a ranking loss for
inter-manifold structure globally. Extensive experimental results have shown
that GCML exhibits superior performance to counterparts in terms of qualitative
visualizations and quantitative metrics, which demonstrates the effectiveness
of preserving geometric structure.
