Sparse Manifold Learning based on Laplacian Matrix

Abstract

In machine learning, a group of high-dimensional data point set which represents an image set can be looked upon as the point set distributing on a nonlinear manifold. Typically, the manifold dimension is much lower than the dimension of data points. Therefore, it is important to explore the real dimension and the real geometry of high-dimensional data point set. Based on this objective, researchers put forward the concept of manifold learning. Traditional manifold learning can achieve dramatic dimensional reduction on high-dimension points, but there are still some problems of it. In the aspect of processing a large amount of data currently, traditional manifold learning algorithm reveals many weaknesses mainly in time consumption. To improve the deficiency, the paper puts forward a new algorithm, aiming at simplifying the time process of manifold learning algorithm which is also abbreviated as SLEP. In the part of the experiment, the study makes a comparative experiment between the synthetic data set and the real data set. The result shows that the proposed algorithm improves time efficiency.