IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v15y2021i4d10.1007_s11634-020-00434-3.html
   My bibliography  Save this article

PCA-KL: a parametric dimensionality reduction approach for unsupervised metric learning

Author

Listed:
  • Alexandre L. M. Levada

    (Federal University of São Carlos)

Abstract

Dimensionality reduction algorithms are powerful mathematical tools for data analysis and visualization. In many pattern recognition applications, a feature extraction step is often required to mitigate the curse of the dimensionality, a collection of negative effects caused by an arbitrary increase in the number of features in classification tasks. Principal Component Analysis (PCA) is a classical statistical method that creates new features based on linear combinations of the original ones through the eigenvectors of the covariance matrix. In this paper, we propose PCA-KL, a parametric dimensionality reduction algorithm for unsupervised metric learning, based on the computation of the entropic covariance matrix, a surrogate for the covariance matrix of the data obtained in terms of the relative entropy between local Gaussian distributions instead of the usual Euclidean distance between the data points. Numerical experiments with several real datasets show that the proposed method is capable of producing better defined clusters and also higher classification accuracy in comparison to regular PCA and several manifold learning algorithms, making PCA-KL a promising alternative for unsupervised metric learning.

Suggested Citation

  • Alexandre L. M. Levada, 2021. "PCA-KL: a parametric dimensionality reduction approach for unsupervised metric learning," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 829-868, December.
  • Handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-020-00434-3
    DOI: 10.1007/s11634-020-00434-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-020-00434-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11634-020-00434-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Daniel D. Lee & H. Sebastian Seung, 1999. "Learning the parts of objects by non-negative matrix factorization," Nature, Nature, vol. 401(6755), pages 788-791, October.
    2. Ding, Chris & Li, Tao & Peng, Wei, 2008. "On the equivalence between Non-negative Matrix Factorization and Probabilistic Latent Semantic Indexing," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3913-3927, April.
    3. Lan Huong Nguyen & Susan Holmes, 2019. "Ten quick tips for effective dimensionality reduction," PLOS Computational Biology, Public Library of Science, vol. 15(6), pages 1-19, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nicolas Jouvin & Pierre Latouche & Charles Bouveyron & Guillaume Bataillon & Alain Livartowski, 2021. "Greedy clustering of count data through a mixture of multinomial PCA," Computational Statistics, Springer, vol. 36(1), pages 1-33, March.
    2. Bastian Schaefermeier & Gerd Stumme & Tom Hanika, 2021. "Topic space trajectories," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 5759-5795, July.
    3. Travis R Meyer & Daniel Balagué & Miguel Camacho-Collados & Hao Li & Katie Khuu & P Jeffrey Brantingham & Andrea L Bertozzi, 2019. "A year in Madrid as described through the analysis of geotagged Twitter data," Environment and Planning B, , vol. 46(9), pages 1724-1740, November.
    4. Triss Ashton & Nicholas Evangelopoulos & Victor Prybutok, 2014. "Extending monitoring methods to textual data: a research agenda," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 2277-2294, July.
    5. Zhang, Zhong-Yuan & Gai, Yujie & Wang, Yu-Fei & Cheng, Hui-Min & Liu, Xin, 2018. "On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 687-697.
    6. Sun, Lijun & Axhausen, Kay W., 2016. "Understanding urban mobility patterns with a probabilistic tensor factorization framework," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 511-524.
    7. Ma, Xiaoke & Wang, Bingbo & Yu, Liang, 2018. "Semi-supervised spectral algorithms for community detection in complex networks based on equivalence of clustering methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 786-802.
    8. Pau Figuera & Alfredo Cuzzocrea & Pablo García Bringas, 2024. "Clustering Validation Inference," Mathematics, MDPI, vol. 12(15), pages 1-31, July.
    9. Del Corso, Gianna M. & Romani, Francesco, 2019. "Adaptive nonnegative matrix factorization and measure comparisons for recommender systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 164-179.
    10. P Fogel & C Geissler & P Cotte & G Luta, 2022. "Applying separative non-negative matrix factorization to extra-financial data," Working Papers hal-03689774, HAL.
    11. Xiao-Bai Li & Jialun Qin, 2017. "Anonymizing and Sharing Medical Text Records," Information Systems Research, INFORMS, vol. 28(2), pages 332-352, June.
    12. Naiyang Guan & Lei Wei & Zhigang Luo & Dacheng Tao, 2013. "Limited-Memory Fast Gradient Descent Method for Graph Regularized Nonnegative Matrix Factorization," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    13. Spelta, A. & Pecora, N. & Rovira Kaltwasser, P., 2019. "Identifying Systemically Important Banks: A temporal approach for macroprudential policies," Journal of Policy Modeling, Elsevier, vol. 41(1), pages 197-218.
    14. M. Moghadam & K. Aminian & M. Asghari & M. Parnianpour, 2013. "How well do the muscular synergies extracted via non-negative matrix factorisation explain the variation of torque at shoulder joint?," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 16(3), pages 291-301.
    15. Markovsky, Ivan & Niranjan, Mahesan, 2010. "Approximate low-rank factorization with structured factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3411-3420, December.
    16. Paul Fogel & Yann Gaston-Mathé & Douglas Hawkins & Fajwel Fogel & George Luta & S. Stanley Young, 2016. "Applications of a Novel Clustering Approach Using Non-Negative Matrix Factorization to Environmental Research in Public Health," IJERPH, MDPI, vol. 13(5), pages 1-14, May.
    17. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    18. Zhaoyu Xing & Yang Wan & Juan Wen & Wei Zhong, 2024. "GOLFS: feature selection via combining both global and local information for high dimensional clustering," Computational Statistics, Springer, vol. 39(5), pages 2651-2675, July.
    19. Chae, Bongsug (Kevin), 2018. "The Internet of Things (IoT): A Survey of Topics and Trends using Twitter Data and Topic Modeling," 22nd ITS Biennial Conference, Seoul 2018. Beyond the boundaries: Challenges for business, policy and society 190376, International Telecommunications Society (ITS).
    20. Jingfeng Guo & Chao Zheng & Shanshan Li & Yutong Jia & Bin Liu, 2022. "BiInfGCN: Bilateral Information Augmentation of Graph Convolutional Networks for Recommendation," Mathematics, MDPI, vol. 10(17), pages 1-16, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:15:y:2021:i:4:d:10.1007_s11634-020-00434-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.