In this letter, we present a new hierarchical clustering approach based on the evolutionary process of Amari's dynamical neural field model. Dynamical neural field theory provides a theoretical framework macroscopically describing the activity of neuron ensemble. Based on it, our clustering approach is essentially close to the neurophysiological nature of perception. It is also computationally stable, insensitive to noise, flexible, and tractable for data with complex structure. Some examples are given to show the feasibility.
In this letter, using methods proposed by E. Kaslik, St. Balint, and their colleagues, we develop a new method, expansion approach, for estimating the attraction domain of asymptotically stable equilibrium points of Hopfield-type neural networks. We prove theoretically and demonstrate numerically that the proposed approach is feasible and efficient. The numerical results that obtained in the application examples, including the network system considered by E. Kaslik, L. Brăescu, and St. Balint, indicate that the proposed approach is able to achieve better attraction domain estimation.
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We propose a novel neural model with lateral interaction for learning tasks. The model consists of two functional fields: an elementary field to extract features and a high-level field to store and recognize patterns. Each field is composed of some neurons with lateral interaction, and the neurons in different fields are connected by the rules of synaptic plasticity. The model is established on the current research of cognition and neuroscience, making it more transparent and biologically explainable. Our proposed model is applied to data classification and clustering. The corresponding algorithms share similar processes without requiring any parameter tuning and optimization processes. Numerical experiments validate that the proposed model is feasible in different learning tasks and superior to some state-of-the-art methods, especially in small sample learning, one-shot learning, and clustering.
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