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Multimodal manifold modeling methods extend the spectral geometry-aware dataanalysis to learning from several related and complementary modalities. Most ofthese methods work based on two major assumptions: 1) there are the same numberof homogeneous data samples in each modality, and 2) at least partialcorrespondences between modalities are given in advance as prior knowledge.This work proposes two new multimodal modeling methods. The first methodestablishes a general analyzing framework to deal with the multimodalinformation problem for heterogeneous data without any specific priorknowledge. For this purpose, first, we identify the localities of each manifoldby extracting local descriptors via spectral graph wavelet signatures (SGWS).Then, we propose a manifold regularization framework based on the functionalmapping between SGWS descriptors (FMBSD) for finding the pointwisecorrespondences. The second method is a manifold regularized multimodalclassification based on pointwise correspondences (M$^2$CPC) used for theproblem of multiclass classification of multimodal heterogeneous, which thecorrespondences between modalities are determined based on the FMBSD method.The experimental results of evaluating the FMBSD method on three commoncross-modal retrieval datasets and evaluating the (M$^2$CPC) method on threebenchmark multimodal multiclass classification datasets indicate theireffectiveness and superiority over state-of-the-art methods.

Cross-Modal and Multimodal Data Analysis Based on Functional Mapping of Spectral Descriptors and Manifold Regularization