Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Generalized Locally Linear Embedding Based on Local Reconstruction Similarity
FSKD '08 Proceedings of the 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery - Volume 05
Weighted locally linear embedding for dimension reduction
Pattern Recognition
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Automatic Choice of the Number of Nearest Neighbors in Locally Linear Embedding
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Rapid and brief communication: Incremental locally linear embedding
Pattern Recognition
Regularization parameter choice in locally linear embedding
Neurocomputing
Image synthesis based on manifold learning
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part II
Stability of dimensionality reduction methods applied on artificial hyperspectral images
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
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The crux in the locally linear embedding algorithm is the selection of the number of nearest neighbors k. Some previous techniques have been developed for finding this parameter based on embedding quality measures. Nevertheless, they do not achieve suitable results when they are tested on several kind of manifolds. In this work is presented a new method for automatically computing the number of neighbors by means of analyzing global and local properties of the embedding results. Besides, it is also proposed a second strategy for choosing the parameter k, on manifolds where the density and the intrinsic dimensionality of the neighborhoods are changeful. The first proposed technique, called preservation neighborhood error, calculates a unique value of k for the whole manifold. Moreover, the second method, named local neighborhood selection, computes a suitable number of neighbors for each sample point in the manifold. The methodologies were tested on artificial and real-world datasets which allow us to visually confirm the quality of the embedding. According to the results our methods aim to find suitable values of k and appropriated embeddings.