The Estimation Algorithm of Laplacian Eigenvalues for the Tangent Bundle

In Recent years, manifold learning has become an important research direction in the field of machine learning and pattern recognition. As an effective way of representation embedded in low-dimensional space of high-dimensional data, the manifold learning algorithm, which is based on the spectral theory, has been widely used. This paper presents an estimation algorithm of Laplacian Eigenvalues and expands the LE algorithm´s advantage of maintaining the local geometry to remaining globally through the global coordinates of the tangent bundle. The estimation algorithm of Laplacian Eigenvalues for the tangent bundle is effectively applied to nonlinear manifold dimensionality reduction and maintains the geometry of manifolds. Experimental results show that the algorithm proposed is very effective.