Multi-manifold LLE learning in pattern recognition

• We introduce Multiple Manifold Locally Linear Embedding (MM-LLE) learning.
• This method learns multiple manifolds corresponding to multiple data classes.
• MM-LLE uses supervised neighborhood selection in learning multiple manifolds.
• It finds the optimum low-dimensional space by minimizing the nearness of manifolds.
• Results show that MM-LLE outperforms many well-known manifold learning algorithms.

This paper introduces Multiple Manifold Locally Linear Embedding (MM-LLE) learning. This method learns multiple manifolds corresponding to multiple classes in a data set. The proposed approach to manifold learning includes a supervised form of neighborhood selection in learning individual manifolds that correspond to each class of data. Furthermore, MM-LLE uses manifold–manifold distance (MMD) as a measure to find the optimum low-dimensional space needed to achieve high classification accuracy. When classifying new data samples, in addition to the conventional classification techniques used in the past literature to classify new data in the manifold space, we introduce a point-to-manifold distance (PMD) metric used to measure the distance between points and manifolds. Experimental results reported in this paper compare the recognition rates for a number of different manifold learning methods. The proposed MM-LLE technique has various applications in classification and object recognition.