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Bivariate regression allows inferring a model underlying two data-sets. We consider the case of regression from possibly incomplete data sets, namely the case that data in the two sets do not necessarily correspond in size and might come... more
Bivariate regression allows inferring a model underlying two data-sets. We consider the case of regression from possibly incomplete data sets, namely the case that data in the two sets do not necessarily correspond in size and might come unmatched/unpaired. The paper proposes to tackle the problem of bivariate regression through a non-parametric neural-learning method that is able to match the statistics of the available data sets. The devised neural algorithm is based on a look-up-table representation of the involved functions. A numerical experiment, performed on a real-world data set, serves to illustrate the features of the proposed statistical regression procedure.
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In the present paper, we treat the problem of learning averages out of a set of unitary matrices. We discuss a possible learning technique based on the differential geometrical properties of the Lie group of unitary matrices. We first... more
In the present paper, we treat the problem of learning averages out of a set of unitary matrices. We discuss a possible learning technique based on the differential geometrical properties of the Lie group of unitary matrices. We first recall some relevant notions from differential geometry, mainly related to Lie group theory, and then we propose a scheme for learning averages. Some numerical experiments will illustrate the features of the learnt averages.
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Research Interests: Engineering, Mathematics, Computer Science, Artificial Intelligence, Signal Processing, and 15 morePrincipal Component Analysis, Pattern Recognition, Independent Component Analysis, Unsupervised Learning, Learning Theory, Theoretical Analysis, Eddy Current, Neurocomputing, Rigid Body, Lyapunov function, Rigid Body Dynamics, Non Destructive Evaluation, Rule Based, parameter space, and Psychology and Cognitive Sciences
The purpose of this work is to give a neural algorithm that allows a controller to determine robot's location within an environment like a building, by observing through a camera some elements of the rooms, as... more
The purpose of this work is to give a neural algorithm that allows a controller to determine robot's location within an environment like a building, by observing through a camera some elements of the rooms, as for instance the ceiling or the floor; it is natural to suppose that different parts of the digital image sequence coming from the camera
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ABSTRACT
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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... more
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 anal...
Research Interests: Cognitive Science, Mathematics, Computer Science, Algorithms, Artificial Intelligence, and 14 moreInformation Theory, Principal Component Analysis, Nonlinear dynamics, Independent Component Analysis, Medicine, Linear models, Learning, Humans, Computer Simulation, Theoretical Models, Spacecraft, Computer Science Neural Networks, neural systems, and submanifold
Research Interests: Computer Science, Artificial Intelligence, Signal Processing, Principal Component Analysis, Independent Component Analysis, and 9 moreNeural Networks, Blind Source Separation, Algorithm, Hebbian learning, Vectors, Nonlinear system, Source Separation, Artificial Neural Network, and Blind Signal Separation
One of the most commonly known algorithm to perform neural Principal Component Analysis of real-valued random signals is the Kung-Diamantaras' Adaptive Principal component EXtractor (APEX) for a laterally-connected neural... more
One of the most commonly known algorithm to perform neural Principal Component Analysis of real-valued random signals is the Kung-Diamantaras' Adaptive Principal component EXtractor (APEX) for a laterally-connected neural architecture. In this paper we present a new approach to obtain an APEX-like PCA procedure as a special case of a more general class of learning rules, by means of an optimization theory specialized for the laterally-connected topology. Through simulations we show the new algorithms can be faster than the original one
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The aim of this paper is to examine the performance of an independent component analysis algorithm based on neural networks applied to the solution of an electrical engineering problem related to non-destructive evaluation of conductive... more
The aim of this paper is to examine the performance of an independent component analysis algorithm based on neural networks applied to the solution of an electrical engineering problem related to non-destructive evaluation of conductive objects. The proposed application is assessed through computer experiments carried out on real-world data, which prove the usefulness of this non-destructive evaluation technique.
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Research Interests: Mathematics, Computer Science, Artificial Intelligence, Image Processing, Remote Sensing, and 14 moreSignal Processing, Radar, Independent Component Analysis, Neural Networks, Neural Network, Medicine, Multidisciplinary, Space flight, Synthetic Aperture Radar, SAR, Inverse Synthetic Aperture Radar, Artificial Neural Network, Computer Science Neural Networks, and Radar Imaging
In recent work, we introduced nonlinear adaptive activation function (FAN) artificial neuron models, which learn their activation functions in an unsupervised way by information-theoretic adapting rules. We also applied networks of these... more
In recent work, we introduced nonlinear adaptive activation function (FAN) artificial neuron models, which learn their activation functions in an unsupervised way by information-theoretic adapting rules. We also applied networks of these neurons to some blind signal processing problems, such as independent component analysis and blind deconvolution. The aim of this letter is to study some fundamental aspects of FAN units' learning by investigating the properties of the associated learning differential equation systems.
Research Interests: Mathematics, Computer Science, Algorithms, Artificial Intelligence, Nonlinear dynamics, and 15 moreIndependent Component Analysis, Medicine, Multidisciplinary, Entropy, Brain, Humans, Animals, Neurons, Blind Deconvolution, Nonlinear system, Neural Computation, Differential equation, Action Potentials, Artificial Neural Network, and Activation Function
Research Interests: Mathematics, Applied Mathematics, Computational Complexity, Independent Component Analysis, Geometric Numerical Integration, and 10 moreNeural Network, Applied Mathematics and Computational Science, Component Analysis, Rigid Body, Numerical Analysis and Computational Mathematics, Numerical Stability, Point of View, Artificial Neural Network, Electrical And Electronic Engineering, and Reaserch In a Field of Applied Mathematics and Mathematical Physics
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In a previous work (S. Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based... more
In a previous work (S. Fiori, 2006), we proposed a random number generator based on a tunable non-linear neural system, whose learning rule is designed on the basis of a cardinal equation from statistics and whose implementation is based on look-up tables (LUTs). The aim of the present manuscript is to improve the above-mentioned random number generation method by changing the learning principle, while retaining the efficient LUT-based implementation. The new method proposed here proves easier to implement and relaxes some previous limitations.