| Manifold learning has attracted widely attention and gained significant progress since it was proposed in 2000. Traditional manifold learning methods need sufficient training samples to learn low dimensional embedding of high-dimensional data, thus, when facing single sample condition, there are still many problems about generalization ability and robustness. In this thesis, we propose connection learning algorithm based on frame bundle in the perspective of multi-manifold learning and apply our method to face recognition with single sample per person. The main contents are as follows:(1) We present multi-manifold connection learning algorithm based on frame bundle(MMCA-FB). MMCA-FB constructs multi-manifold structure by block images. It uses connection operator on frame bundle to project the data to horizontal space and vertical space respectively to extract more discriminant information for maximizing the manifold margins.(2) We present local feature connection learning algorithm based on Frame bundle(LFCA-FB). LFCA-FB constructs multi-manifold structure using local feature(eye, nose, mouth, etc.). It adds the additional information of the principal changing direction of the inter-manifold and intra-manifold which is learned by connection operator to neural network training.In conclusion, the innovation points of this paper can be listed as follows:(1) By regarding single face as a manifold and local feature as a manifold respectively, we construct two different multi-manifold structures.(2) For the first multi-manifold structure, we maintain the topology structure of the original data in different feature subspaces. Transforming single sample problem into single manifold matching problem.(3) For the second multi-manifold structure, we combine manifold learning and neural network, convert single sample problem to multi-manifold matching problem. Then presented algorithm can get a better performance when facing the variations in expression, pose, etc. |
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