scholarly journals Sparsity and Geometry Preserving Graph Embedding for Dimensionality Reduction

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 75748-75766 ◽  
Author(s):  
Jianping Gou ◽  
Zhang Yi ◽  
David Zhang ◽  
Yongzhao Zhan ◽  
Xiangjun Shen ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Graph Embedding

Discriminative globality and locality preserving graph embedding for dimensionality reduction

2020 ◽  
Vol 144 ◽  
pp. 113079 ◽  
Author(s):  
Jianping Gou ◽  
Yuanyuan Yang ◽  
Zhang Yi ◽  
Jiancheng Lv ◽  
Qirong Mao ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Graph Embedding ◽  
Locality Preserving

scholarly journals More faithfulness graph embedding

2015 ◽  
Vol 4 (2) ◽  
pp. 336
Author(s):  
Alaa Najim
Keyword(s):  
Dimensionality Reduction ◽  
Graph Embedding ◽  
New Method ◽  
Graph Representation ◽  
Data Sets ◽  
Graph Visualization ◽  
Graph Data ◽  
Original Space ◽  
Data Points ◽  
Effectiveness And Efficiency

<p><span lang="EN-GB">Using dimensionality reduction idea to visualize graph data sets can preserve the properties of the original space and reveal the underlying information shared among data points. Continuity Trustworthy Graph Embedding (CTGE) is new method we have introduced in this paper to improve the faithfulness of the graph visualization. We will use CTGE in graph field to find new understandable representation to be more easy to analyze and study. Several experiments on real graph data sets are applied to test the effectiveness and efficiency of the proposed method, which showed CTGE generates highly faithfulness graph representation when compared its representation with other methods.</span></p>

A generalized least-squares approach regularized with graph embedding for dimensionality reduction

2020 ◽  
Vol 98 ◽  
pp. 107023 ◽  
Author(s):  
Xiang-Jun Shen ◽  
Si-Xing Liu ◽  
Bing-Kun Bao ◽  
Chun-Hong Pan ◽  
Zheng-Jun Zha ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Least Squares ◽  
Graph Embedding ◽  
Generalized Least Squares ◽  
Least Squares Approach

scholarly journals Robust Graph Dimensionality Reduction

2018 ◽  
Author(s):  
Xiaofeng Zhu ◽  
Cong Lei ◽  
Hao Yu ◽  
Yonggang Li ◽  
Jiangzhang Gan ◽  
...  
Keyword(s):  
Dimensionality Reduction ◽  
Optimization Algorithm ◽  
Graph Embedding ◽  
Original Data ◽  
Transformation Matrix ◽  
High Dimensional ◽  
Local Similarity ◽  
Robust Estimators ◽  
Classification Tasks ◽  
Low Dimensional

In this paper, we propose conducting Robust Graph Dimensionality Reduction (RGDR) by learning a transformation matrix to map original high-dimensional data into their low-dimensional intrinsic space without the influence of outliers. To do this, we propose simultaneously 1) adaptively learning three variables, \ie a reverse graph embedding of original data, a transformation matrix, and a graph matrix preserving the local similarity of original data in their low-dimensional intrinsic space; and 2) employing robust estimators to  avoid outliers involving the processes of optimizing these three matrices. As a result, original data are cleaned by two strategies, \ie a prediction of original data based on three resulting variables and robust estimators, so that the transformation matrix can be learnt from accurately estimated intrinsic space with the helping of the reverse graph embedding and the graph matrix. Moreover, we propose a new optimization algorithm to the resulting objective function as well as theoretically prove the convergence of our optimization algorithm. Experimental results indicated that our proposed method outperformed all the comparison methods in terms of different classification tasks.

scholarly journals Semi-supervised Orthogonal Graph Embedding with Recursive Projections

2017 ◽  
Author(s):  
Hanyang Liu ◽  
Junwei Han ◽  
Feiping Nie
Keyword(s):  
Dimensionality Reduction ◽  
Orthogonal Projection ◽  
Graph Embedding ◽  
Feature Space ◽  
Linear Mapping ◽  
Projection Matrix ◽  
Data Matrix ◽  
Stiefel Manifold ◽  
Projection Direction ◽  
Number Of Classes

Many graph based semi-supervised dimensionality reduction algorithms utilize the projection matrix to linearly map the data matrix from the original feature space to a lower dimensional representation. But the dimensionality after reduction is inevitably restricted to the number of classes, and the learned non-orthogonal projection matrix usually fails to preserve distances well and balance the weight on different projection direction. This paper proposes a novel dimensionality reduction method, called the semi-supervised orthogonal graph embedding with recursive projections (SOGE). We integrate the manifold smoothness and label fitness as well as the penalization of the linear mapping mismatch, and learn the orthogonal projection on the Stiefel manifold that empirically demonstrates better performance. Moreover, we recursively update the projection matrix in its orthocomplemented space to continuously learn more projection vectors, so as to better control the dimension of reduction. Comprehensive experiment on several benchmarks demonstrates the significant improvement over the existing methods.

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