Probabilistic PCA self-organizing maps

Neural networks

Principal component analysis

Authors

Ezequiel López-Rubio

Juan Miguel Ortiz-de-Lazcano-Lobato

Domingo López Rodríguez

Published

19 August 2009

Publication details

IEEE Transactions on Neural Networks vol 20 (9), 1474-1489

Links

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.

BibTeX

@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}
}

Bibliometric data

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Citations
CrossRef - Citation Indexes: 29
PubMed - Citation Indexes: 1
Scopus - Citation Indexes: 30

Captures
Mendeley - Readers: 24

Cites

The following graph plots the number of cites received by this work from its publication, on a yearly basis.

Papers citing this work

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

[1] Y. Cao, H. He, and H. Man. “SOMKE: Kernel Density Estimation Over Data Streams by Sequences of Self-Organizing Maps”. In: IEEE Transactions on Neural Networks and Learning Systems 23.8 (Aug. 2012), p. 1254–1268. ISSN: 2162-2388. DOI: 10.1109/tnnls.2012.2201167. URL: http://dx.doi.org/10.1109/tnnls.2012.2201167.

[2] L. Chen, Y. Liu, Z. Huang, et al. “An improved SOM algorithm and its application to color feature extraction”. In: Neural Computing and Applications 24.7–8 (Apr. 2013), p. 1759–1770. ISSN: 1433-3058. DOI: 10.1007/s00521-013-1416-9. URL: http://dx.doi.org/10.1007/s00521-013-1416-9.

[3] K. Du and M. N. S. Swamy. “Probabilistic and Bayesian Networks”. In: Neural Networks and Statistical Learning. Springer London, Dec. 2013, p. 563–619. ISBN: 9781447155713. DOI: 10.1007/978-1-4471-5571-3_19. URL: http://dx.doi.org/10.1007/978-1-4471-5571-3_19.

[4] M. N. Florentín-Núñez, E. López-Rubio, and F. J. López-Rubio. “Adaptive kernel regression and probabilistic self-organizing maps for JPEG image deblocking”. In: Neurocomputing 121 (Dec. 2013), p. 32–39. ISSN: 0925-2312. DOI: 10.1016/j.neucom.2012.10.029. URL: http://dx.doi.org/10.1016/j.neucom.2012.10.029.

[5] M. Gruszczynski, A. Klos, and J. Bogusz. “A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis”. In: Pure and Applied Geophysics 175.5 (Apr. 2018), p. 1841–1867. ISSN: 1420-9136. DOI: 10.1007/s00024-018-1856-3. URL: http://dx.doi.org/10.1007/s00024-018-1856-3.

[6] M. Gruszczynski, A. Klos, and J. Bogusz. “A Filtering of Incomplete GNSS Position Time Series with Probabilistic Principal Component Analysis”. In: Geodynamics and Earth Tides Observations from Global to Micro Scale. Springer International Publishing, Aug. 2018, p. 247–273. ISBN: 9783319962771. DOI: 10.1007/978-3-319-96277-1_19. URL: http://dx.doi.org/10.1007/978-3-319-96277-1_19.

[7] I. E. Kaya, A. Ç. Pehlivanlı, E. G. Sekizkardeş, et al. “PCA based clustering for brain tumor segmentation of T1w MRI images”. In: Computer Methods and Programs in Biomedicine 140 (Mar. 2017), p. 19–28. ISSN: 0169-2607. DOI: 10.1016/j.cmpb.2016.11.011. URL: http://dx.doi.org/10.1016/j.cmpb.2016.11.011.

[8] E. Lopez-Rubio. “Improving the Quality of Self-Organizing Maps by Self-Intersection Avoidance”. In: IEEE Transactions on Neural Networks and Learning Systems 24.8 (Aug. 2013), p. 1253–1265. ISSN: 2162-2388. DOI: 10.1109/tnnls.2013.2254127. URL: http://dx.doi.org/10.1109/tnnls.2013.2254127.

[9] E. López-Rubio. “Probabilistic Self-Organizing Maps for Continuous Data”. In: IEEE Transactions on Neural Networks 21.10 (Oct. 2010), p. 1543–1554. ISSN: 1941-0093. DOI: 10.1109/tnn.2010.2060208. URL: http://dx.doi.org/10.1109/tnn.2010.2060208.

[10] E. López-Rubio. “Probabilistic self-organizing maps for qualitative data”. In: Neural Networks 23.10 (Dec. 2010), p. 1208–1225. ISSN: 0893-6080. DOI: 10.1016/j.neunet.2010.07.002. URL: http://dx.doi.org/10.1016/j.neunet.2010.07.002.

[11] E. López-Rubio. “Restoration of images corrupted by Gaussian and uniform impulsive noise”. In: Pattern Recognition 43.5 (May. 2010), p. 1835–1846. ISSN: 0031-3203. DOI: 10.1016/j.patcog.2009.11.017. URL: http://dx.doi.org/10.1016/j.patcog.2009.11.017.

[12] E. López-Rubio, E. José Palomo-Ferrer, J. Miguel Ortiz-de-Lazcano-Lobato, et al. “Dynamic topology learning with the probabilistic self-organizing graph”. In: Neurocomputing 74.16 (Sep. 2011), p. 2633–2648. ISSN: 0925-2312. DOI: 10.1016/j.neucom.2011.03.020. URL: http://dx.doi.org/10.1016/j.neucom.2011.03.020.

[13] E. López-Rubio and R. M. Luque-Baena. “An adaptive system for compressed video deblocking”. In: Signal Processing 103 (Oct. 2014), p. 415–425. ISSN: 0165-1684. DOI: 10.1016/j.sigpro.2013.12.033. URL: http://dx.doi.org/10.1016/j.sigpro.2013.12.033.

[14] E. López-Rubio and R. M. Luque-Baena. “Stochastic approximation for background modelling”. In: Computer Vision and Image Understanding 115.6 (Jun. 2011), p. 735–749. ISSN: 1077-3142. DOI: 10.1016/j.cviu.2011.01.007. URL: http://dx.doi.org/10.1016/j.cviu.2011.01.007.

[15] E. LÓPEZ-RUBIO, R. M. LUQUE-BAENA, and E. DOMÍNGUEZ. “FOREGROUND DETECTION IN VIDEO SEQUENCES WITH PROBABILISTIC SELF-ORGANIZING MAPS”. In: International Journal of Neural Systems 21.03 (Jun. 2011), p. 225–246. ISSN: 1793-6462. DOI: 10.1142/s012906571100281x. URL: http://dx.doi.org/10.1142/s012906571100281x.

[16] E. Lopez-Rubio and E. J. Palomo. “Growing Hierarchical Probabilistic Self-Organizing Graphs”. In: IEEE Transactions on Neural Networks 22.7 (Jul. 2011), p. 997–1008. ISSN: 1941-0093. DOI: 10.1109/tnn.2011.2138159. URL: http://dx.doi.org/10.1109/tnn.2011.2138159.

[17] E. LÓPEZ-RUBIO, E. J. PALOMO, and E. DOMÍNGUEZ. “BREGMAN DIVERGENCES FOR GROWING HIERARCHICAL SELF-ORGANIZING NETWORKS”. In: International Journal of Neural Systems 24.04 (Apr. 2014), p. 1450016. ISSN: 1793-6462. DOI: 10.1142/s0129065714500166. URL: http://dx.doi.org/10.1142/s0129065714500166.

[18] F. J. López-Rubio, E. Domínguez, E. J. Palomo, et al. “Selecting the Color Space for Self-Organizing Map Based Foreground Detection in Video”. In: Neural Processing Letters 43.2 (May. 2015), p. 345–361. ISSN: 1573-773X. DOI: 10.1007/s11063-015-9431-8. URL: http://dx.doi.org/10.1007/s11063-015-9431-8.

[19] F. J. Lopez-Rubio, E. Lopez-Rubio, R. M. Luque-Baena, et al. “Color space selection for self-organizing map based foreground detection in video sequences”. In: 2014 International Joint Conference on Neural Networks (IJCNN). IEEE, Jul. 2014, p. 3347–3354. DOI: 10.1109/ijcnn.2014.6889404. URL: http://dx.doi.org/10.1109/ijcnn.2014.6889404.

[20] E. J. Palomo, M. A. Molina-Cabello, E. Lopez-Rubio, et al. “A New Self-Organizing Neural Gas Model based on Bregman Divergences”. In: 2018 International Joint Conference on Neural Networks (IJCNN). IEEE, Jul. 2018, p. 1–8. DOI: 10.1109/ijcnn.2018.8489545. URL: http://dx.doi.org/10.1109/ijcnn.2018.8489545.

[21] T. C. Silva and L. Zhao. “Network-Based Stochastic Semisupervised Learning”. In: IEEE Transactions on Neural Networks and Learning Systems 23.3 (Mar. 2012), p. 451–466. ISSN: 2162-2388. DOI: 10.1109/tnnls.2011.2181413. URL: http://dx.doi.org/10.1109/tnnls.2011.2181413.

[22] T. C. Silva and L. Zhao. “Stochastic Competitive Learning in Complex Networks”. In: IEEE Transactions on Neural Networks and Learning Systems 23.3 (Mar. 2012), p. 385–398. ISSN: 2162-2388. DOI: 10.1109/tnnls.2011.2181866. URL: http://dx.doi.org/10.1109/tnnls.2011.2181866.

[23] A. Soltani and M. Akbarzadeh-T. “Confabulation-Inspired Association Rule Mining for Rare and Frequent Itemsets”. In: IEEE Transactions on Neural Networks and Learning Systems 25.11 (Nov. 2014), p. 2053–2064. ISSN: 2162-2388. DOI: 10.1109/tnnls.2014.2303137. URL: http://dx.doi.org/10.1109/tnnls.2014.2303137.

[24] D. Sovilj, T. Raiko, and E. Oja. “Extending Self-Organizing Maps with uncertainty information of probabilistic PCA”. In: The 2010 International Joint Conference on Neural Networks (IJCNN). IEEE, Jul. 2010, p. 1–7. DOI: 10.1109/ijcnn.2010.5596578. URL: http://dx.doi.org/10.1109/ijcnn.2010.5596578.

[25] H. Yin, C. Zhang, and Y. Ji. “Distributed clustering using distributed mixture of probabilistic PCA”. In: 2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, Aug. 2014, p. 352–357. DOI: 10.1109/fskd.2014.6980859. URL: http://dx.doi.org/10.1109/fskd.2014.6980859.