We propose a framework for probabilistic shape clustering based on
kernel-space embeddings derived from spectral signatures. Our root motivation is
to investigate practical yet principled clustering schemes that rely on geometrical
invariants of shapes rather than explicit registration. To that end we revisit the use
of the Laplacian spectrum and introduce a parametric family of reproducing kernels
for shapes, extending WESD [12] and shape DNA [20] like metrics. Parameters
provide control over the relative importance of local and global shape features,
can be adjusted to emphasize a scale of interest or set to uninformative values.
As a result of kernelization, shapes are embedded in an infinite-dimensional
inner product space. We leverage this structure to formulate shape clustering via
a Bayesian mixture of kernel-space Principal Component Analysers. We derive
simple variational Bayes inference schemes in Hilbert space, addressing technicalities
stemming from the infinite dimensionality. The proposed approach is
validated on tasks of unsupervised clustering of sub-cortical structures, as well as
classification of cardiac left ventricles w.r.t. pathological groups.