k/K-Nearest Neighborhood Criterion for Improving Locally Linear Embedding

Spectral manifold learning techniques have recently found extensive applications in machine vision. The common strategy of spectral algorithms for manifold learning is exploiting the local relationships in a symmetric adjacency graph, which is typically constructed using k-nearest neighborhood (k-NN) criterion. In this paper, with our focus on locally linear embedding as a powerful and well-known spectral technique, shortcomings of k-NN for construction of the adjacency graph are first illustrated, and then a new criterion, namely k/K-nearest neighborhood (k/K-NN) is introduced to overcome these drawbacks. The proposed criterion involves finding the sparsest representation of each sample in the dataset, and is realized by modifying Robust-SL0, a recently proposed algorithm for sparse approximate representation. k/K-NN criterion gives rise to a modified spectral manifold learning technique, namely Sparse-LLE, which demonstrates remarkable improvement over conventional LLE through our experiments.