A selecting landmark hierarchical manifold learning algorithm

The manifold data query needs the manifold embedded representation. Thus it often involves accessing considerable volume of data. An approach of hierarchical manifold learning algorithm based on selecting landmark points from the given samples is proposed for representing data on manifold. The landmarks set can help locate the novel points on the data manifold. Firstly, an adaptive nearest neighbor's method is employed to extract the nearest neighborhood of each data. Then the geodesic matrix is constructed. Finally, a landmark point is randomly selected in landmark point set, and its maximum cell is found till the manifold set is empty and the rough landmark point set is formed. In addition, the landpoint set is optimized. The experimental results prove that the proposed method preserves the topological features of manifold, and it helps inquire the manifold data efficiently.