k/K-Nearest Neighborhood Criterion for Improvement of Locally Linear Embedding

• Authors: Armin Eftekhari;Hamid Abrishami-Moghaddam;Massoud Babaie-Zadeh
• Venue: CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
• Year: 2009

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.