Clustering-based Locally Linear Embedding

Locally linear embedding approach (LLE) is one of most efficient nonlinear dimensionality reduction approaches with good representational capacity for a broader range of manifolds and high computational efficiency. However, LLE and its variants fail to nicely deal with sparsely sampled or noise contaminated datasets,where the local neighborhood structure is critically distorted. To solve this problem, this paper utilizes the clustering approaches to partition the input data into clusters and then rescale the distance between any points based on the clustering structure so as to make data points from different clusters separated more easily. This rescaled distance matrix is then provided to improve LLE so as to achieve the better performance. Unlike the supervised approaches, this approach does not take the labelled dataset as prerequisite, so that it is unsupervised. This makes it applicable to broader range of domains. The conducted experiments by classification on benchmark datasets have validated the proposed approach.