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Graph-dual Laplacian principal component analysis

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Abstract

Principal component analysis is the most widely used method for linear dimensionality reduction, due to its effectiveness in exploring low-dimensional global geometric structures embedded in data. To preserve the intrinsic local geometrical structures of data, graph-Laplacian PCA (gLPCA) incorporates Laplacian embedding into PCA framework for learning local similarities between data points, which leads to significant performance improvement in clustering and classification. Some recent works showed that not only the high dimensional data reside on a low-dimensional manifold in the data space, but also the features lie on a manifold in feature space. However, both PCA and gLPCA overlook the local geometric information contained in the feature space. By considering the duality between data manifold and feature manifold, graph-dual Laplacian PCA (gDLPCA) is proposed, which incorporates data graph regularization and feature graph regularization into PCA framework to exploit local geometric structures of data manifold and feature manifold simultaneously. The experimental results on four benchmark data sets have confirmed its effectiveness and suggested that gDLPCA outperformed gLPCA on classification and clustering tasks.

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Notes

  1. http://www-stat.stanford.edu/~tibs/ElemStatLearn/data.html.

  2. https://archive.ics.uci.edu/ml/datasets/ISOLET.

  3. http://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

  4. http://archive.ics.uci.edu/ml/datasets/Semeion+Handwritten+Digit.

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Acknowledgements

The authors would like to thank the anonymous reviewers and the editor for their helpful comments and suggestions to improve the quality of this paper. We also thank Zhaolu Guo of Jiangxi University of Science and Technology for helpful discussions and Jie Su of College of Information Engineering in Northwest A&F University for his much experimental works. This work was supported in part by National Natural Science Foundation of China under Grant 61602388, the China Postdoctoral Science Foundation under Grant 2018M633585, Natural Science Basic Research Plan in Shaanxi Province of China under Grant 2018JQ6060, Doctoral Starting up Foundation of Northwest A&F University under Grant 2452015302, and the Open Project Program of the National Laboratory of Pattern Recognition (NLPR) under Grant 201700009.

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Authors and Affiliations

  1. College of Information Engineering, Northwest A&F University, Yangling, 712100, Shaanxi, China

    Jinrong He & Bin Liu

  2. Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture, People’s Republic of China, Yangling, 712100, China

    Jinrong He & Bin Liu

  3. Science Computing and Intelligent Information Processing of Guangxi Higher Education Key Laboratory, Guangxi Teachers Education University, Nanning, 530001, Guangxi, China

    Yingzhou Bi

  4. College of Computer and Communication, Hunan University of Technology, Hunan, 412000, China

    Zhigao Zeng

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  1. Jinrong He
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  2. Yingzhou Bi
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  4. Zhigao Zeng
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Correspondence to Jinrong He.

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He, J., Bi, Y., Liu, B. et al. Graph-dual Laplacian principal component analysis. J Ambient Intell Human Comput 10, 3249–3262 (2019). https://doi.org/10.1007/s12652-018-1096-5

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