Fusion of Local Manifold Learning Methods

Different local manifold learning methods are developed based on different geometric intuitions and each method only learns partial information of the true geometric structure of the underlying manifold. In this letter, we introduce a novel method to fuse the geometric information learned from local manifold learning algorithms to discover the underlying manifold structure more faithfully. We first use local tangent coordinates to compute the local objects from different local algorithms, then utilize the selection matrix to connect the local objects with a global functional and finally develop an alternating optimization-based algorithm to discover the low-dimensional embedding. Experiments on synthetic as well as real datasets demonstrate the effectiveness of our proposed method.