A new manifold learning algorithm based on distinguishing variance analysis

Combining the ideas of maximum variance unfolding(MVU) and Laplacian eigenmaps, a new manifold learning algorithm is proposed, called distinguishing variance embeddings (DVE). DVE globally unfolds the manifold by maximizing the distances between far points, and faithfully preserves the local neighborhood with the distance-sum-constraint on the neighbors. DVE can be viewed as a variance of MVU that relaxes the strict distance-preserving constraints on the neighbors. We illustrate the algorithm on the easily visualized examples of curves and surfaces, as well as on the actual images of rotating objects, 3D faces, and handwritten digits. The results show the effectiveness of DVE.