Discrete mathematics

Pattern recognition (psychology)

Metric (unit)

Mathematics

Algorithm

Data mining

Machine learning

Pairwise comparison

Artificial intelligence

Economics

Operations management

Computer science

Hypergraph

Object (grammar)

Projection (relational algebra)

IEEE Transactions on Image Processing

The wide 3D applications have led to increasing amount of 3D object data, and thus effective 3D object classification technique has become an urgent requirement. One important and challenging task for 3D object classification is how to formulate the 3D data correlation and exploit it. Most of the previous works focus on learning optimal pairwise distance metric for object comparison, which may lose the global correlation among 3D objects. Recently, a transductive hypergraph learning has been investigated for classification, which can jointly explore the correlation among multiple objects, including both the labeled and unlabeled data. Although these methods have shown better performance, they are still limited due to 1) a considerable amount of testing data may not be available in practice and 2) the high computational cost to test new coming data. To handle this problem, considering the multi-modal representations of 3D objects in practice, we propose an inductive multi-hypergraph learning algorithm, which targets on learning an optimal projection for the multi-modal training data. In this method, all the training data are formulated in multi-hypergraph based on the features, and the inductive learning is conducted to learn the projection matrices and the optimal multi-hypergraph combination weights simultaneously. Different from the transductive learning on hypergraph, the high cost training process is off-line, and the testing process is very efficient for the inductive learning on hypergraph. We have conducted experiments on two 3D benchmarks, i.e., the NTU and the ModelNet40 data sets, and compared the proposed algorithm with the state-of-the-art methods and traditional transductive multi-hypergraph learning methods. Experimental results have demonstrated that the proposed method can achieve effective and efficient classification performance. We also note that the proposed method is a general framework and has the potential to be applied in other applications in practice.

Inductive Multi-Hypergraph Learning and Its Application on View-Based 3D Object Classification