International Journal of Neural Systems

In previous contributions we presented a new class of algorithms for orthonormal learning of a linear neural network with p inputs and m outputs, based on the equations describing the dynamics of a massive rigid frame in a submanifold of ℛ^p. While exhibiting interesting features, such as intrinsic numerical stability, strongly binding to the orthonormal submanifolds, and good controllability of the learning dynamics, tested on principal/independent component analysis, the proposed algorithms were not completely satisfactory from a computational-complexity point of view. The main drawback was the need to repeatedly evaluate a matrix exponential map. With the aim to lessen the computational efforts pertaining to these algorithms, we propose here an improvement based on the closed-form Rodriguez formula for the exponential map. Such formula is available in the p=3 and m=3 case, which is discussed with details here. In particular, experimental results on independent component analysis (ICA), carried out with both synthetic and real-world data, help confirming the computational gain due to the proposed improvement.

In this paper, entropy is a term used in the learning phase of a neural network. As learning progresses, more hidden nodes get into saturation. The early creation of such hidden nodes may impair generalisation. Hence an entropy approach is proposed to dampen the early creation of such nodes by using a new computation called entropy cycle. Entropy learning also helps to increase the importance of relevant nodes while dampening the less important nodes. At the end of learning, the less important nodes can then be pruned to reduce the memory requirements of the neural network.

We present a noise robust PCA algorithm which is an extension of the Oja subspace algorithm and allows tuning the noise sensitivity. We derive a loss function which is minimized by this algorithm and interpret it in a noisy PCA setting. Results on the local stability analysis of this algorithm are given and it is shown that the locally stable equilibria are those which minimize the loss function.

This work investigates the nonlinear predictability of the Electro Telluric Field (ETF) variations data in order to develop new intelligent tools for the difficult task of earthquake prediction. Support Vector Machines trained on a signal window have been used to predict the next sample. We observe a significant increase at this short-term unpredictability of the ETF signal at about two weeks time period before the major earthquakes that took place in regions near the recording devices. The unpredictability increase can be attributed to a quick time variation of the dynamics that produce the ETF signal due to the earthquake generation process. Thus, this increase can be taken into advantage for signaling for an increased possibility of a large earthquake within the next few days in the neighboring region of the recording station.

A key problem in Binary Neural Network learning is to decide bigger linear separable subsets. In this paper we prove some lemmas about linear separability. Based on these lemmas, we propose Multi-Core Learning (MCL) and Multi-Core Expand-and-Truncate Learning (MCETL) algorithms to construct Binary Neural Networks. We conclude that MCL and MCETL simplify the equations to compute weights and thresholds, and they result in the construction of simpler hidden layer. Examples are given to demonstrate these conclusions.

The Self-Organizing Map (SOM) is an efficient tool for visualizing high-dimensional data. In this paper, an intuitive and effective SOM projection method is proposed for mapping high-dimensional data onto the two-dimensional grid structure with a growing self-organizing mechanism. In the learning phase, a growing SOM is trained and the growing cell structure is used as the baseline framework. In the ordination phase, the new projection method is used to map the input vector so that the input data is mapped to the structure of the SOM without having to plot the weight values, resulting in easy visualization of the data. The projection method is demonstrated on four different data sets, including a 118 patent data set and a 399 checical abstract data set related to polymer cements, with promising results and a significantly reduced network size.

In this paper, a new sufficient condition is given for the global asymptotic stability and global exponential output stability of a unique equilibrium points of delayed cellular neural networks (DCNNs) by using Lyapunov method. This condition imposes constraints on the feedback matrices and delayed feedback matrices of DCNNs and is independent of the delay. The obtained results extend and improve upon those in the earlier literature, and this condition is also less restrictive than those given in the earlier references. Two examples compared with the previous results in the literatures are presented and a simulation result is also given.