A Hopfield Neural Network for combining classifiers applied to textured images

In this paper we propose a new method for combining simple classifiers through the analogue Hopfield Neural Network (HNN) optimization paradigm for classifying natural textures in images. The base classifiers are the Fuzzy clustering (FC) and the parametric Bayesian estimator (BP). An initial unsupervised training phase determines the number of clusters and estimates the parameters for both FC and BP. Then a decision phase is carried out, where we build as many Hopfield Neural Networks as the available number of clusters. The number of nodes at each network is the number of pixels in the image which is to be classified. Each node at each network is initially loaded with a state value, which is the membership degree (provided by FC) that the node (pixel) belongs to the cluster associated to the network. Each state is later iteratively updated during the HNN optimization process taking into account the previous states and two types of external influences exerted by other nodes in its neighborhood. The external influences are mapped as consistencies. One is embedded in an energy term which considers the states of the node to be updated and the states of its neighbors. The other is mapped as the inter-connection weights between the nodes. From BP, we obtain the probabilities that the nodes (pixels) belong to a cluster (network). We define these weights as a relation between states and probabilities between the nodes in the neighborhood of the node which is being updated. This is the classifier combination, making the main finding of this paper. The proposed combined strategy based on the HNN outperforms the simple classifiers and also classical combination strategies.