Semi-supervised Manifold Learning And Its Application

As a non-linear dimensionality reduction method, manifold learning can discover the intrinsic construction of complex data for further processing. Several manifold learning algorithms have been developed and were widely used in pattern recognition and machine vision etc. area.Most of the existing manifold learning algorithms are unsupervised method without using prior-information. If we can obtain some prior-information of training samples, we can use this information to help the study step to increase the classification ability, so improving the original method to semi-supervised method.The objective of this paper is to research about the semi-supervised manifold learning. After analyzing existing methods, we propose a semi-supervised manifold learning algorithm based on Laplacian Eigenmaps, named semi-supervised Laplacian Eigenmaps (SS-LE). SS-LE uses prior information of very few samples to calculate more accurate low dimensional embedding coordinates. We also analyze its superior in accuracy and computation complexity compared with other methods. Compared with SS-LLE, the computation time of SS-LE is dramatically reduced and the drop of the accuracy is within an acceptable range. Besides, the accuracy of our method can achieve nearly best result of SS-LLE only need to set K (the number of neighbors) to a relative small value. We demonstrated the usefulness of our algorithm by synthetic and real world problems, especially its efficiency in object tracking problem.