Probabilistic PCA self-organizing maps

 

Abstract

In this paper, we present a probabilistic neural model, which extends Kohonen’s self-organizing map (SOM) by performing a probabilistic principal component analysis (PPCA) at each neuron. Several SOMs have been proposed in the literature to capture the local principal subspaces, but our approach offers a probabilistic model while it has a low complexity on the dimensionality of the input space. This allows to process very high-dimensional data to obtain reliable estimations of the probability densities which are based on the PPCA framework. Experimental results are presented, which show the map formation capabilities of the proposal with high-dimensional data, and its potential in image and video compression applications.

Citation

Please, cite this work as:

[LOL09] E. López-Rubio, J. M. Ortiz-de-Lazcano-Lobato, and D. López-Rodríguez. “Probabilistic PCA Self-Organizing Maps”. In: IEEE Trans. Neural Networks 20.9 (2009), pp. 1474-1489. DOI: 10.1109/TNN.2009.2025888. URL: https://doi.org/10.1109/TNN.2009.2025888.

NoteBibTeX

@article{Lopez-RubioOL09,
     author = {Ezequiel López{-}Rubio and
     Juan Miguel Ortiz{-}de{-}Lazcano{-}Lobato and
     Domingo López{-}Rodríguez},
     title = {Probabilistic {PCA} Self-Organizing Maps},
     journal = {{IEEE} Trans. Neural Networks},
     volume = {20},
     number = {9},
     pages = {1474–1489},
     year = {2009},
     url = {https://doi.org/10.1109/TNN.2009.2025888},
     doi = {10.1109/TNN.2009.2025888},
     timestamp = {Wed, 14 Nov 2018 10:32:52 +0100},
     biburl = {https://dblp.org/rec/journals/tnn/Lopez-RubioOL09.bib},
     bibsource = {dblp computer science bibliography, https://dblp.org}
}

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Probabilistic PCA self-organizing maps

Cites

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

1. Maciej Gruszczynski, Anna Kłos, Janusz Bogusz (2018). A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis. Pure and Applied Geophysics DOI
2. Esteban J. Palomo, Miguel A. Molina‐Cabello, Ezequiel López‐Rubio, et al. (2018). A New Self-Organizing Neural Gas Model based on Bregman Divergences. DOI
3. Maciej Gruszczynski, Anna Kłos, Janusz Bogusz (2018). A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis. Pageoph topical volumes DOI
4. İrem Ersöz Kaya, Ayça Çakmak Pehlivanlı, Emine Gezmez Sekizkardeş, et al. (2016). PCA based clustering for brain tumor segmentation of T1w MRI images. Computer Methods and Programs in Biomedicine DOI
5. Thiago Christiano Silva, Liang Zhao (2016). Case Study of Network-Based Unsupervised Learning: Stochastic Competitive Learning in Networks. DOI
6. Francisco Javier López-Rubio, Enrique Domínguez, Esteban J. Palomo, et al. (2015). Selecting the Color Space for Self-Organizing Map Based Foreground Detection in Video. Neural Processing Letters DOI
7. Azadeh Soltani, Mohammad-R. Akbarzadeh-T (2014). Confabulation-Inspired Association Rule Mining for Rare and Frequent Itemsets. IEEE Transactions on Neural Networks and Learning Systems DOI
8. Ezequiel López‐Rubio, Esteban J. Palomo, Enrique Domínguez (2014). BREGMAN DIVERGENCES FOR GROWING HIERARCHICAL SELF-ORGANIZING NETWORKS. International Journal of Neural Systems DOI
9. Francisco Javier López-Rubio, Ezequiel López‐Rubio, Rafael Marcos Luque‐Baena, et al. (2014). Color space selection for self-organizing map based foreground detection in video sequences. DOI
10. Ezequiel López‐Rubio, Rafael Marcos Luque‐Baena (2014). An adaptive system for compressed video deblocking. Signal Processing DOI
11. Hang Yin, Chunhong Zhang, Yang Ji (2014). Distributed clustering using distributed mixture of probabilistic PCA. DOI
12. Ezequiel López‐Rubio, Rafael Marcos Luque‐Baena (2014). Online Learning by Stochastic Approximation for Background Modeling. DOI
13. María Nieves Florentín-Núñez, Ezequiel López‐Rubio, Francisco Javier López-Rubio (2013). Adaptive kernel regression and probabilistic self-organizing maps for JPEG image deblocking. Neurocomputing DOI
14. Ezequiel López‐Rubio (2013). Improving the Quality of Self-Organizing Maps by Self-Intersection Avoidance. IEEE Transactions on Neural Networks and Learning Systems DOI
15. Liping Chen, Yiguang Liu, Zengxi Huang, et al. (2013). An improved SOM algorithm and its application to color feature extraction. Neural Computing and Applications DOI
16. Ke-Lin Du, M. N. S. Swamy (2013). Probabilistic and Bayesian Networks. DOI
17. Thiago Christiano Silva, Liang Zhao (2012). Stochastic Competitive Learning in Complex Networks. IEEE Transactions on Neural Networks and Learning Systems DOI
18. Yuan Cao, Haibo He, Hong Man (2012). SOMKE: Kernel Density Estimation Over Data Streams by Sequences of Self-Organizing Maps. IEEE Transactions on Neural Networks and Learning Systems DOI
19. Thiago Christiano Silva, Liang Zhao (2012). Network-Based Stochastic Semisupervised Learning. IEEE Transactions on Neural Networks and Learning Systems DOI
20. Thiago Christiano Silva (2012). Machine learning in complex networks: modeling, analysis, and applications. DOI
21. Ezequiel López‐Rubio, Rafael Marcos Luque‐Baena, Enrique Domínguez (2011). FOREGROUND DETECTION IN VIDEO SEQUENCES WITH PROBABILISTIC SELF-ORGANIZING MAPS. International Journal of Neural Systems DOI
22. Ezequiel López‐Rubio, Rafael Marcos Luque‐Baena (2011). Stochastic approximation for background modelling. Computer Vision and Image Understanding DOI
23. Ezequiel López‐Rubio, Esteban J. Palomo (2011). Growing Hierarchical Probabilistic Self-Organizing Graphs. IEEE Transactions on Neural Networks DOI
24. Ezequiel López‐Rubio, Esteban J. Palomo, Juan Miguel Ortiz-de-Lazcano-Lobato, et al. (2011). Dynamic topology learning with the probabilistic self-organizing graph. Neurocomputing DOI
25. Latifa Oukhellou, Étienne Côme, Patrice Aknin, et al. (2011). Semi-supervised Feature Extraction Using Independent Factor Analysis. DOI
26. Haibo He, Yuan Cao (2011). Kernel density estimation with stream data based on self-organizing map. DOI
27. María Nieves Florentín-Núñez, Ezequiel López‐Rubio, Francisco Javier López-Rubio (2011). Reduction of JPEG Compression Artifacts by Kernel Regression and Probabilistic Self-Organizing Maps. Lecture notes in computer science DOI
28. Ezequiel López‐Rubio (2010). Probabilistic self-organizing maps for qualitative data. Neural Networks DOI
29. Ezequiel López‐Rubio (2010). Probabilistic Self-Organizing Maps for Continuous Data. IEEE Transactions on Neural Networks DOI
30. Dušan Sovilj, Tapani Raiko, Erkki Oja (2010). Extending Self-Organizing Maps with uncertainty information of probabilistic PCA. DOI
31. Ezequiel López‐Rubio (2009). Restoration of images corrupted by Gaussian and uniform impulsive noise. Pattern Recognition DOI
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