Unsupervised Flow Explore The Manifold Learning Algorithm

Dimensionality reduction is an important way to processing data efficiently and robustly. Over the last decade, a large number of techniques about di-mensionality reduction have been proposed. The proposed techniques include isometric mapping(ISOMAP), locally linear embedding(LLE), Hessian locally linear embedding (HLLE), Laplacian eigenmaps(LE) and local tangent space alignment (LTSA). Most of these techniques are based on the intuition that data lies on or near a complex low-dimensional manifold that is embedded in the high-dimensional space, aiming at identifying and extracting the manifold from the high-dimensional space.In this paper, we introduce the background and related research of dimen-sionality reduction, describe the problem mathematically. Some manifold learn-ing methods, including PCA, LLE, LE and LTSA, are analyzed in detail. We offer proposals for neighbor searching and manifold learning. Weighted neigh-bor is a framework designed to overcome difficulties in neighbor searching study. Based weighted neighbor, weighted local tangent space alignment (WLTSA) is reported as an unsupervised manifold method. We discuss not only the moti-vation of WLTSA, but also its implement. Experiment results about applying WLTSA to plentiful data sets are showed at last.