Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment
SIAM Journal on Scientific Computing
Building connected neighborhood graphs for isometric data embedding
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Building k-edge-connected neighborhood graph for distance-based data projection
Pattern Recognition Letters
Building k-Connected Neighborhood Graphs for Isometric Data Embedding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Selection of the optimal parameter value for the Isomap algorithm
Pattern Recognition Letters
Building Connected Neighborhood Graphs for Locally Linear Embedding
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 04
IEEE Transactions on Pattern Analysis and Machine Intelligence
A more topologically stable locally linear embedding algorithm based on R*-tree
PAKDD'08 Proceedings of the 12th Pacific-Asia conference on Advances in knowledge discovery and data mining
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Neighborhood construction is a necessary and important step in nonlinear dimensionality reduction algorithm. In this paper, we first summarize the two principles for neighborhood construction via analyzing existing nonlinear dimensionality reduction algorithms: 1) data points in the same neighborhood should approximately lie on a low dimensional linear subspace; and 2) each neighborhood should be as large as possible. Then a dynamic neighborhood selection algorithm based on this two principles is proposed in this paper. The proposed method exploits PCA technique to measure the linearity of a finite points set. Moreover, for isometric embedding, we present an improved method of constructing neighborhood graph, which can improve the accuracy of geodesic distance estimation. Experiments on both synthetic data sets and real data sets show that our method can construct neighborhood according to local curvature of data manifold and then improve the performance of most manifold algorithms, such as ISOMAP and LLE.