On Manifold Learning Using Locally Linear Embedding Algorithm And Its Application

Manifold learning has attracted a lot of attentions since proposed in2000. Theassumption in manifold learning is that data in a high-dimensional space is uniformlysampled from the low-dimensional manifold of the space. On the assumption, manifoldlearning is to find the low-dimensional structure hidden in their high-dimensionalobservations and seek the corresponding embedding maps in order to achievedimensionality reduction or make the data visualization. Manifold learning methodsinclude locally linear embedding, isometric feature mapping, laplacian eigenmap, etc.Here we focus on locally linear embedding (LLE) manifold learning method, andresearch on the problem of neighborhood selection and neighborhood representation. Weintroduce the orthogonal matching pursuit (OMP) method and make a second selectionfrom the selected neighbors. Thus we improve the locally linear embedding method.This thesis proposes an LLE manifold learning algorithm based on OMP, whichmakes a sample could be linearly represented by samples from the same manifold with it.Experimental results on UCI and MNIST confirm that the proposed method can improvethe separability of data after dimensionality reduction.This thesis presents an OMP-based LLE incremental learning algorithm which couldlinearly represent new samples with known samples. The OMP method is used to get thelinear representation coefficients of a new sample. Experimental results on UCI, MNISTand face datasets show that it can get a higher recognition rate on testing sets afterdimensionality reduction.This thesis presents a supervised locally linear embedding algorithm based on OMPwhich makes samples linearly represented by samples belonging to the same class.Experimental results on UCI, MINIT and face datasets show that our method can get a better classification performance for classification problem.The experimental results of the three algorithms which put forward in this papershow that the introduction of OMP algorithm is effective.