Dimension reduction by local principal component analysis
Neural Computation
GTM: the generative topographic mapping
Neural Computation
Non-linear dimensionality reduction techniques for unsupervised feature extraction
Pattern Recognition Letters
Self-Organizing Maps
A k-segments algorithm for finding principal curves
Pattern Recognition Letters
Non-Linear Dimensionality Reduction
Advances in Neural Information Processing Systems 5, [NIPS Conference]
Non-linear dimensionality reduction techniques for classification and visualization
Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining
Outex - New Framework for Empirical Evaluation of Texture Analysis Algorithms
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Unsupervised Learning Using Locally Linear Embedding: Experiments with Face Pose Analysis
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
Robust locally linear embedding
Pattern Recognition
Weighted locally linear embedding for plant leaf visualization
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Locally linear embedding: a survey
Artificial Intelligence Review
Investigating the dynamics of facial expression
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
ISOLLE: locally linear embedding with geodesic distance
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
Geometrically local embedding in manifolds for dimension reduction
Pattern Recognition
Selection of the optimal parameter value for the ISOMAP algorithm
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
Improvement of data visualization based on ISOMAP
MICAI'05 Proceedings of the 4th Mexican international conference on Advances in Artificial Intelligence
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In this paper, we explore the capabilities of a recently proposed method for non-linear dimensionality reduction and visualization called Locally Linear Embedding (LLE). LLE is proposed as an alternative to the traditional approaches. Its ability to deal with large sizes of high dimensional data and non-iterative way to find the embeddings make it more and more attractive to several researchers. All the studies which investigated and experimented this approach have concluded that LLE is a robust and efficient algorithm when the data lie on a smooth and well-sampled single manifold. None explored the behavior of the algorithm when the data include some noise (or outliers). Here, we show theoretically and empirically that LLE is significantly sensitive to the presence of a few outliers. Then we propose a robust extension to tackle this problem. Further, we investigate the behavior of the LLE algorithm in cases of disjoint manifolds, demonstrate the lack of single global coordinate system and discuss some alternatives.