Probabilistic PCA Self-Organizing Maps

López‐Rubio, Ezequiel; Ortiz-de-Lazcano-Lobato, Juan Miguel; López-Rodríguez, Domingo

doi:10.1109/tnn.2009.2025888

Cited by 31 publications

(9 citation statements)

References 57 publications

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“…can also be seen in [17] which proposed an online PPCA. Since the all parameters can be achieved by summing information from each data in the summing variant, we can develop a DEM for the MPPCA model.…”

Section: A Summing Variant Of Em In Mppcamentioning

confidence: 90%

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Distributed clustering using distributed mixture of probabilistic PCA

Yin

Zhang

2014

2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

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This paper considers the clustering algorithm based on mixture of probabilistic principle component analyzers in distributed environments. The EM procedure of it is first transformed to a summing variant. Following the classic distributed EM framework for mixture of exponential family distributions and utilizing the summing variant, we propose the distributed EM for mixture of probabilistic principle component analyzers. The proposed algorithm avoids transferring all data from distributed nodes to a central node. Experiment verifies the validity and feasibility of the proposed method. For some datasets, the proposed method can even enhance the log-likelihood as well as the clustering performance.

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Section: A Summing Variant Of Em In Mppcamentioning

confidence: 90%

“…The basic idea of DEM is that in node m, ( , ) t m Q θ θ will be increased or kept unchanged (when convergence is reached) and all the other parts of the summation ( , ), [17]. Concretely, the expectation of latent variable should be firstly computed as well as the conditional secondary moment:…”

Section: A Summing Variant Of Em In Mppcamentioning

confidence: 99%

Distributed clustering using distributed mixture of probabilistic PCA

Yin

Zhang

2014

2014 11th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

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“…3) Pattern Recognition: Our last set of experiments is devoted to the well-known problem of handwritten digit recognition, which is also managed with the help of selforganizing models [7], [43], [50], [67], [69]. We selected a standard benchmark, namely the MNIST handwritten digit database [35].…”

Section: B Real Datamentioning

confidence: 99%

Improving the Quality of Self-Organizing Maps by Self-Intersection Avoidance

López‐Rubio

2013

IEEE Trans. Neural Netw. Learning Syst.

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The quality of self-organizing maps is always a key issue to practitioners. Smooth maps convey information about input data sets in a clear manner. Here a method is presented to modify the learning algorithm of self-organizing maps to reduce the number of topology errors, hence the obtained map has better quality at the expense of increased quantization error. It is based on avoiding maps that self-intersect or nearly so, as these states are related to low quality. Our approach is tested with synthetic data and real data from visualization, pattern recognition and computer vision applications, with satisfactory results.

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“…Let i = π i , μ i , C i be a vector comprising the parameters for mixture component i. The following derivation relies on the methodology proposed in [41] and [42]. Let ϕ ( i , t) be an arbitrary function of i and the input sample t. Then we define the weighted mean of ϕ ( i , t) as…”

Section: Appendix Stochastic Approximationmentioning

confidence: 99%

Growing Hierarchical Probabilistic Self-Organizing Graphs

López‐Rubio

Palomo

2011

IEEE Trans. Neural Netw.

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Since the introduction of the growing hierarchical self-organizing map, much work has been done on self-organizing neural models with a dynamic structure. These models allow adjusting the layers of the model to the features of the input dataset. Here we propose a new self-organizing model which is based on a probabilistic mixture of multivariate Gaussian components. The learning rule is derived from the stochastic approximation framework, and a probabilistic criterion is used to control the growth of the model. Moreover, the model is able to adapt to the topology of each layer, so that a hierarchy of dynamic graphs is built. This overcomes the limitations of the self-organizing maps with a fixed topology, and gives rise to a faithful visualization method for high-dimensional data.

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Probabilistic PCA Self-Organizing Maps

Cited by 31 publications

References 57 publications

Distributed clustering using distributed mixture of probabilistic PCA

Distributed clustering using distributed mixture of probabilistic PCA

Improving the Quality of Self-Organizing Maps by Self-Intersection Avoidance

Growing Hierarchical Probabilistic Self-Organizing Graphs

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