Semi-Supervised Affine Alignment of Manifolds

Rui Jia, Ting Lu


High dimensional data is usually produced by the source that only enjoys a limited number of degrees of freedom. Manifold leaning technique plays an important part in finding the correlation among the high dimensional data datasets. By making use of manifold alignment, the paired mapping relationship can be explored easily. However, the common manifold alignment algorithm can only give the mapping result of the training set, and cannot deal with a new coming point. A new manifold alignment algorithm is proposed in this paper. The benefit of our algorithm is two fold: First, the method is a semi-supervised approach, which makes better use of the local geometry information of the unpaired points and improves the learning effect when the labeled proportion is very low. Second, an extended spectral aggression trick is used in the algorithm, which can produce a linear mapping between the raw data space and the aligned space. The experiments result shows that, the correlation mapping can be precisely obtained, the hidden space can be aligned effectively, and the cost of mapping a coming point is very low.




manifold alignment; out of sample; affine transformation; spectral regression

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