Learning Topologies with the Growing Neural Forest.

In this work, a novel self-organizing model called growing neural forest (GNF) is presented. It is based on the growing neural gas (GNG), which learns a general graph with no special provisions for datasets with separated clusters. On the contrary, the proposed GNF learns a set of trees so that each tree represents a connected cluster of data. High dimensional datasets often contain large empty regions among clusters, so this proposal is better suited to them than other self-organizing models because it represents these separated clusters as connected components made of neurons. Experimental results are reported which show the self-organization capabilities of the model. Moreover, its suitability for unsupervised clustering and foreground detection applications is demonstrated. In particular, the GNF is shown to correctly discover the connected component structure of some datasets. Moreover, it outperforms some well-known foreground detectors both in quantitative and qualitative terms.

Bregman divergences for growing hierarchical self-organizing networks.

Growing hierarchical self-organizing models are characterized by the flexibility of their structure, which can easily accommodate for complex input datasets. However, most proposals use the Euclidean distance as the only error measure. Here we propose a way to introduce Bregman divergences in these models, which is based on stochastic approximation principles, so that more general distortion measures can be employed. A procedure is derived to compare the performance of networks using different divergences. Moreover, a probabilistic interpretation of the model is provided, which enables its use as a Bayesian classifier. Experimental results are presented for classification and data visualization applications, which show the advantages of these divergences with respect to the classical Euclidean distance.

Growing hierarchical probabilistic self-organizing graphs.

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.