Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixture Probabilistic Principal Geodesic Analysis   Dimensionality reduction on Riemannian manifolds is challenging due to the
complex nonlinear data structures. While probabilistic principal geodesic
analysis~(PPGA) has been proposed to generalize conventional principal
component analysis (PCA) onto manifolds, its effectiveness is limited to data
with a single modality. In this paper, we present a novel Gaussian latent
variable model that provides a unique way to integrate multiple PGA models into
a maximum-likelihood framework. This leads to a well-defined mixture model of
probabilistic principal geodesic analysis (MPPGA) on sub-populations, where
parameters of the principal subspaces are automatically estimated by employing
an Expectation Maximization algorithm. We further develop a mixture Bayesian
PGA (MBPGA) model that automatically reduces data dimensionality by suppressing
irrelevant principal geodesics. We demonstrate the advantages of our model in
the contexts of clustering and statistical shape analysis, using synthetic
sphere data, real corpus callosum, and mandible data from human brain magnetic
resonance~(MR) and CT images.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: q-alg