  Multimodal manifold modeling methods extend the spectral geometry-aware data
analysis to learning from several related and complementary modalities. Most of
these methods work based on two major assumptions: 1) there are the same number
of homogeneous data samples in each modality, and 2) at least partial
correspondences between modalities are given in advance as prior knowledge.
This work proposes two new multimodal modeling methods. The first method
establishes a general analyzing framework to deal with the multimodal
information problem for heterogeneous data without any specific prior
knowledge. For this purpose, first, we identify the localities of each manifold
by extracting local descriptors via spectral graph wavelet signatures (SGWS).
Then, we propose a manifold regularization framework based on the functional
mapping between SGWS descriptors (FMBSD) for finding the pointwise
correspondences. The second method is a manifold regularized multimodal
classification based on pointwise correspondences (M$^2$CPC) used for the
problem of multiclass classification of multimodal heterogeneous, which the
correspondences between modalities are determined based on the FMBSD method.
The experimental results of evaluating the FMBSD method on three common
cross-modal retrieval datasets and evaluating the (M$^2$CPC) method on three
benchmark multimodal multiclass classification datasets indicate their
effectiveness and superiority over state-of-the-art methods.
