Journal of Machine Learning Research 1 (2021) 1-37 Submitted 4/21; Published 00/00 Cross-Modal and Multimodal Data Analysis Based on Functional Mapping of Spectral Descriptors and Manifold Regularization Maysam Behmanesh
[email protected] Artificial Intelligence Department, Faculty of Computer Engineering, University of Isfahan, Iran Peyman Adibi
[email protected] Artificial Intelligence Department, Faculty of Computer Engineering, University of Isfahan, Iran Jocelyn Chanussot
[email protected] Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, 38000 Grenoble, France Sayyed Mohammad Saeed Ehsani
[email protected] Artificial Intelligence Department, Faculty of Computer Engineering, University of Isfahan, Iran Editor: Abstract 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 sam- ples 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 regulariza- tion framework based on the functional mapping between SGWS descriptors (FMBSD) for finding the pointwise correspondences. The second method is a manifold regularized mul- timodal classification based on pointwise correspondences (M2CPC) used for the problem of multiclass classification of multimodal heterogeneous, which the correspondences be- tween modalities are determined based on the FMBSD method.