AN IMPROVED LOCALLY LINEAR EMBEDDING FOR SPARSE DATA SETS

Locally linear embedding is often invalid for sparse data sets because locally linear embedding simply takes the reconstruction weights obtained from the data space as the weights of the embedding space. This paper proposes an improved method for sparse data sets, a united locally linear embedding, to make the reconstruction more robust to sparse data sets. In the proposed method, the neighborhood correlation matrix presenting the position information of the points constructed from the embedding space is added to the correlation matrix in the original space, thus the reconstruction weights can be adjusted. As the reconstruction weights adjusted gradually, the position information of sparse points can also be changed continually and the local geometry of the data manifolds in the embedding space can be well preserved. Experimental results on both synthetic and real-world data show that the proposed approach is very robust against sparse data sets.

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An improved locally linear embedding for sparse data sets

2010 IEEE International Conference on Image Processing ◽

10.1109/icip.2010.5651452 ◽

2010 ◽

Cited By ~ 1

Author(s):

Ying Wen ◽

Zhenyu Zhou ◽

Xunheng Wang ◽

Yudong Zhang ◽

Renhua Wu

Keyword(s):

Sparse Data ◽

Locally Linear Embedding ◽

Data Sets ◽

Linear Embedding ◽

Sparse Data Sets ◽

Locally Linear

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Self-Regulation of Neighborhood Parameter for Locally Linear Embedding

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.677.436 ◽

2013 ◽

Vol 677 ◽

pp. 436-441 ◽

Cited By ~ 1

Author(s):

Kang Hua Hui ◽

Chun Li Li ◽

Xin Zhong Xu ◽

Xiao Rong Feng

Keyword(s):

Dimensionality Reduction ◽

Self Regulation ◽

Evaluation Criteria ◽

Locally Linear Embedding ◽

Nonlinear Dimensionality Reduction ◽

Data Sets ◽

Powerful Method ◽

Local Patch ◽

Linear Embedding ◽

Locally Linear

The locally linear embedding (LLE) algorithm is considered as a powerful method for the problem of nonlinear dimensionality reduction. In this paper, a new method called Self-Regulated LLE is proposed. It achieves to solve the problem of deciding appropriate neighborhood parameter for LLE by finding the local patch which is close to be a linear one. The experiment results show that LLE with self-regulation performs better in most cases than LLE based on different evaluation criteria and spends less time on several data sets.

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A Dynamic Neighborhood Selection Approach for Locally Linear Embedding

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1033-1034.1369 ◽

2014 ◽

Vol 1033-1034 ◽

pp. 1369-1372

Author(s):

Gui Jun Shan

Keyword(s):

Geodesic Distance ◽

Distance Matrix ◽

Locally Linear Embedding ◽

Neighborhood Size ◽

Data Sets ◽

Euclidean Distance Matrix ◽

Local Neighborhood ◽

Linear Embedding ◽

Dynamic Neighborhood Selection ◽

Locally Linear

Locally linear embedding is based on the assumption that the whole data manifolds are evenly distributed so that they determine the neighborhood for all points with the same neighborhood size. Accordingly, they fail to nicely deal with most real problems that are unevenly distributed. This paper presents a new approach that takes the general conceptual framework of Hessian locally linear embedding so as to guarantee its correctness in the setting of local isometry to an open connected subset but dynamically determines the local neighborhood size for each point. This approach estimates the approximate geodesic distance between any two points by the shortest path in the local neighborhood graph, and then determines the neighborhood size for each point by using the relationship between its local estimated geodesic distance matrix and local Euclidean distance matrix. This approach has clear geometry intuition as well as the better performance and stability to deal with the sparsely sampled or noise contaminated data sets that are often unevenly distributed. The conducted experiments on benchmark data sets validate the proposed approach.

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CLASSIFICATION-ORIENTED LOCALLY LINEAR EMBEDDING

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001410008159 ◽

2010 ◽

Vol 24 (05) ◽

pp. 737-762 ◽

Cited By ~ 1

Author(s):

PI-FUEI HSIEH ◽

MING-HUA YANG ◽

YI-JAY GU ◽

YU-CHENG LIANG

Keyword(s):

Dimensional Space ◽

Linear Method ◽

Real Data ◽

Data Representation ◽

Classification Performance ◽

Locally Linear Embedding ◽

Real World Data ◽

Label Information ◽

Linear Embedding ◽

Locally Linear

The locally linear embedding (LLE) algorithm is hypothetically able to find a lower dimensional space than a linear method for preserving a data manifold originally embedded in a high dimensional space. However, uneven sampling over the manifold in real-world data ultimately causes LLE to suffer from the disconnected-neighborhood problem. Consequently, the final dimensionality required for the data manifold is multiplied by the number of disjoint groups in the complete data representation. In addition, LLE as an unsupervised method is unable to suppress between-class connections. This means that samples from different classes are mixed during reconstruction. This study presents CLLE, a classification-oriented LLE method that uses class label information from training samples to guide unsupervised LLE. The criterion for neighbor selection is redesigned using class-conditional likelihood as well as Euclidean distance. This algorithm largely eliminates fractured classes and lowers the incidence of connections between classes. Also, a reconnection technique is proposed as a supporting method for ensuring a fully connected neighborhood graph, so that CLLE is able to extract the fewest features. Experiments with simulated and real data show that CLLE exceeds the performance of linear methods. Comparable classification performance can be achieved by CLLE using fewer features. In comparison with LLE, CLLE demonstrates a higher aptitude for and flexibility towards classification.

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