Nr. doc. | Classificazioni |
114 | 1 Contributo su Rivista |
64 | 2 Contributo in Volume |
14 | 4 Contributo in Atti di Convegno (Proceeding) |
Anno | Risorsa |
---|---|
2020 |
Minimal control effort and time Lie-group synchronisation design based on proportional-derivative control
INTERNATIONAL JOURNAL OF CONTROL Autore/i: Fiori, S.; Del Rossi, L. Classificazione: 1 Contributo su Rivista Abstract: The present paper introduces a novel minimal control-effort and control-time, proportional-derivative feedback control theory for second-order dynamical systems on Lie groups. The devised control theory is particularised to achieve time-synchronisation of rotational systems, with special reference to a master-slave pair of quad-rotor drones. Minimal control-effort and control-time regulation is achieved through an empirical algorithm to infer the optimal values of the proportional and derivative gain. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286585 |
2020 |
First order and second order learning algorithms on the special orthogonal group to compute the SVD of data matrices
ELECTRONICS Autore/i: Fiori, S.; Rossi, L. D.; Gigli, M.; Saccuti, A. Classificazione: 1 Contributo su Rivista Abstract: The present paper deals with neural algorithms to learn the singular value decomposition (SVD) of data matrices. The neural algorithms utilized in the present research endeavor were developed by Helmke and Moore (HM) and appear under the form of two continuous-time differential equations over the special orthogonal group of matrices. The purpose of the present paper is to develop and compare different numerical schemes, under the form of two alternating learning rules, to learn the singular value decomposition of large matrices on the basis of the HM learning paradigm. The numerical schemes developed here are both first-order (Euler-like) and second-order (Runge-like). Moreover, a reduced Euler scheme is presented that consists of a single learning rule for one of the factors involved in the SVD. Numerical experiments performed to estimate the optical-flow (which is a component of modern IoT technologies) in real-world video sequences illustrate the features of the novel learning schemes. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286576 |
2020 |
Extension of a PID control theory to Lie groups applied to synchronising satellites and drones
IET CONTROL THEORY & APPLICATIONS Autore/i: Fiori, S.; Cervigni, I.; Ippoliti, M.; Menotta, C. Classificazione: 1 Contributo su Rivista Abstract: The authors tackle time synchronisation of two (possibly non-identical) second-order dynamical systems whose state space possess the structure of a Lie group. Synchronisation is treated as a non-linear control problem on Lie groups. They present a control theory inspired by the proportional–integral–derivative (PID) regulation principle. The resulting L-PID control scheme is applied to sync the rotational component of motions in physical systems. A model-dependent version of the L-PID, equipped with a dynamics-cancelling component, is theoretically proven to converge to zero control error by a Lyapunov stability analysis. Furthermore, they present Lie-group-tailored numerical techniques to implement the devised PID regulation theory and test such numerical schemes on two dynamical systems, namely, a gyrostat satellite and a quadrotor drone. As a further extension, they present an empirical translational synchronisation algorithm for two drones based on a pair of concurring L-PID and projected-PID controllers. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286583 |
2020 |
Gradient-based learning methods extended to smooth manifolds applied to automated clustering
THE JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH Autore/i: Koudounas, A.; Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: Grassmann manifold based sparse spectral clustering is a classification technique that consists in learning a latent representation of data, formed by a subspace basis, which is sparse. In order to learn a latent representation, spectral clustering is formulated in terms of a loss minimization problem over a smooth manifold known as Grassmannian. Such minimization problem cannot be tackled by one of traditional gradient-based learning algorithms, which are only suitable to perform optimization in absence of constraints among parameters. It is, therefore, necessary to develop specific optimization/learning algorithms that are able to look for a local minimum of a loss function under smooth constraints in an efficient way. Such need calls for manifold optimization methods. In this paper, we extend classical gradient-based learning algorithms on flat parameter spaces (from classical gradient descent to adaptive momentum) to curved spaces (smooth manifolds) by means of tools from manifold calculus. We compare clustering performances of these methods and known methods from the scientific literature. The obtained results confirm that the proposed learning algorithms prove lighter in computational complexity than existing ones without detriment in clustering efficacy. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286582 |
2020 |
A control-theoretic approach to the synchronization of second-order continuous-time dynamical systems on real connected Riemannian manifolds
SIAM JOURNAL ON CONTROL AND OPTIMIZATION Autore/i: Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: In the present paper, we consider the synchronization of a pair of deterministic, second-order dynamical systems whose states evolve on a connected Riemannian manifold. The ``slave"" system has access to the state/momentum pair of the ``master"" system and is driven by a control vector field designed to make the former system sync in time to the latter. The paper also presents a theoretical analysis of a modified control scheme aimed at limiting the ``control efforts"" needed to achieve synchronization. An alternative version of the equations is also introduced that represents the case that the master system's state is observable under additive-exponential disturbances. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286579 |
2020 |
A novel non-isotonic statistical bivariate regression method-application to stratigraphic data modeling and interpolation
MATHEMATICAL AND COMPUTATIONAL APPLICATIONS Autore/i: Polucci, D.; Marchetti, M.; Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: The present paper deals with nonlinear, non-monotonic data regression. This paper introduces an efficient algorithm to perform data transformation from non-monotonic to monotonic to be paired with a statistical bivariate regression method. The proposed algorithm is applied to a number of synthetic and real-world non-monotonic data sets to test its effectiveness. The proposed novel non-isotonic regression algorithm is also applied to a collection of data about strontium isotope stratigraphy and compared to a LOWESS regression tool. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286577 |
2020 |
Anisotropic Gaussian kernel adaptive filtering by Lie-group dictionary learning
PLOS ONE Autore/i: Wada, T.; Fukumori, K.; Tanaka, T.; Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: The present paper proposes a novel kernel adaptive filtering algorithm, where each Gaussian kernel is parameterized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of scalar width parameter. In fact, different from conventional kernel adaptive systems, the proposed filter is structured as a superposition of non-isotropic Gaussian kernels, whose non-isotropy makes the filter more flexible. The adaptation algorithm will search for optimal parameters in a wider parameter space. This generalization brings the need of special treatment of parameters that have a geometric structure. In fact, the main contribution of this paper is to establish update rules for precision matrices on the Lie group of SPD matrices in order to ensure their symmetry and positive-definiteness. The parameters of this filter are adapted on the basis of a least-squares criterion to minimize the filtering error, together with an ℓ1-type regularization criterion to avoid overfitting and to prevent the increase of dimensionality of the dictionary. Experimental results confirm the validity of the proposed method. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/286580 |
2019 |
Statistical modeling of trivariate static systems: Isotonic models
DATA Autore/i: Fiori, S.; Vitali, A. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/270372 |
2019 |
A Comprehensive Comparison of Algorithms for the Statistical Modeling of Non-Monotone Relationships via Isotonic Regression of Transformed Data
INTERNATIONAL JOURNAL OF DATA ANALYSIS TECHNIQUES AND STRATEGIES Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/270371 |
2019 |
Synchronization of first-order autonomous oscillators on Riemannian manifolds
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. Autore/i: Fiori, S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/270374 |
2019 |
Digital Signal Processing for Audio Applications: Then, Now and the Future
The First Outstanding 50 Years of “Università Politecnica delle Marche” Autore/i: Piazza, Francesco; Squartini, Stefano; Cecchi, Stefania; Fiori, Simone; Orcioni, Simone; Spinsante, Susanna; Pirani, Stefano Editore: Springer Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/272643 |
2019 |
Model formulation over Lie groups and numerical methods to simulate the motion of gyrostats and quadrotors
MATHEMATICS Autore/i: Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: The present paper recalls a formulation of non-conservative system dynamics through the Lagrange-d'Alembert principle expressed through a generalized Euler-Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler-Poincaré equations on the rotation groups to a gyrostat satellite and a quadcopter drone. The numerical solution of the dynamical equations on the rotation groups is tackled via a generalized forward Euler method and an explicit Runge-Kutta integration method tailored to Lie groups. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/274508 |
2019 |
Empirical means on pseudo-orthogonal groups
MATHEMATICS Autore/i: Wang, J.; Sun, H.; Fiori, S. Classificazione: 1 Contributo su Rivista Abstract: The present article studies the problemof computing empiricalmeans on pseudo-orthogonal groups. To design numerical algorithms to compute empirical means, the pseudo-orthogonal group is endowed with a pseudo-Riemannian metric that affords the computation of the exponential map in closed forms. The distance between two pseudo-orthogonal matrices, which is an essential ingredient, is computed by both the Frobenius norm and the geodesic distance. The empirical-mean computation problem is solved via a pseudo-Riemannian-gradient-stepping algorithm. Several numerical tests are conducted to illustrate the numerical behavior of the devised algorithm. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/274509 |
2019 |
A Closed-Form Expression of the Instantaneous Rotational Lurch Index to Evaluate Its Numerical Approximation
SYMMETRY Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/274510 |
2019 |
Glomerular filtration rate estimation by a novel numerical binning-less isotonic statistical bivariate numerical modeling method
INFORMATION Autore/i: Giles, S. N.; Fiori, S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/270373 |
2018 |
An experimental study to compare CSP and TSM techniques to extract features during motor imagery tasks
Signal Processing and Machine Learning for Brain-Machine Interfaces Autore/i: Sartori, M.; Fiori, S.; Tanaka, T. Editore: The Institution of Engineering and Technology (IET) Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/270370 |
2018 |
A Riemannian-steepest-descent approach for optimization on the real symplectic group
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Autore/i: Wang, Jing; Sun, Huafei; Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: In this paper, we first give the geodesic in closed form on the real symplectic group endowed with a Riemannian metric and then study a geodesic‐based Riemannian‐steepest‐descent approach to compute the empirical average out of a set of symplectic matrices. The devised averaging algorithm is compared with the Euclidean gradient algorithm and the extended Hamiltonian algorithm. Simulation examples show that the convergence of the geodesic‐based Riemannian‐steepest‐descent algorithm is the fastest among the 3 considered algorithms. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/264712 |
2018 |
Smooth statistical modeling of bivariate non-monotonic data by a three-stage LUT neural system
NEURAL COMPUTING & APPLICATIONS Autore/i: Fiori, Simone; Fioranelli, Nicola Classificazione: 1 Contributo su Rivista Abstract: The present paper introduces a new statistical data modeling algorithm based on artificial neural systems. This procedure allows abstracting from datasets by working on their probability density functions. The proposed method strives to capture the overall structure of the analyzed data, exhibits competitive computational runtimes and may be applied to non-monotonic real-world data (building on a previously developed isotonic neural modeling algorithm). An outstanding feature of the proposed method is the ability to return a smoother model compared to other modeling algorithms. Smooth models could have applications in the fields of engineering and computer science. In fact, the present research was motivated by an image contour resampling problem that arises in shape analysis. The features of the proposed algorithm are illustrated and compared to the features of existing algorithms by means of numerical tests on shape resampling. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/264713 |
2018 |
Non-delayed synchronization of non-autonomous dynamical systems on Riemannian manifolds and its applications
NONLINEAR DYNAMICS Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The present paper aims at tackling the non-delayed synchronization of two first-order, nonautonomous dynamical systems whose state spaces are (curved) Riemannian manifolds. The present research endeavor borrows notions from system theory, differential geometry, control theory and numerical calculus to design a general synchronization theory and a set of numerical methods to implement the devised synchronization theory on a computing platform. The features of these synchronization algorithms are illustrated by means of five sets of numerical experiments including the synchronization of the attitude of a fleet of flying bodies and the secure transmission of a message by the modulation of a system-generated carrier. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/264714 |
2018 |
A mobile acquisition system and a method for hips sway fluency assessment
INFORMATION Autore/i: Civita, Andrea; Fiori, Simone; Romani, Giuseppe Classificazione: 1 Contributo su Rivista Abstract: The present contribution focuses on the estimation of the Cartesian kinematic jerk of the hips’ orientation during a full three-dimensional movement in the context of enabling eHealth applications of advanced mathematical signal analysis. The kinematic jerk index is estimated on the basis of gyroscopic signals acquired offline through a smartphone. A specific free mobile application is used to acquire the gyroscopic signals and to transmit them to a personal computer through a wireless network. The personal computer elaborates the acquired data and returns the kinematic jerk index associated with a motor task. A comparison of the kinematic jerk index value on a number of data sets confirms that such index can be used to evaluate the fluency of hips orientation during motion. The present research confirms that the proposed gyroscopic data acquisition/processing setup constitutes an inexpensive and portable solution to motion fluency analysis. The proposed data-acquisition and data-processing setup may serve as a supporting eHealth technology in clinical bio-mechanics as well as in sports science. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/264715 |
2017 |
Robust averaging of covariances for EEG recordings classification in motor imagery brain-computer interfaces
NEURAL COMPUTATION Autore/i: Uehara, Takashi; Sartori, Matteo; Tanaka, Toshihisa; Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The estimation of covariance matrices is of prime importance to analyze the distribution of multivariate signals. In motor imagery based brain-computer interfaces (MI-BCI), covariance matrices play a central role in the extraction of features from recorded electroencephalograms (EEGs), therefore, estimating covariances properly is crucial for EEG classification. The paper discusses algorithms to average sample covariance matrices (SCMs) for the selection of the reference matrix in tangent space mapping (TSM) based MI-BCI. Tangent space mapping is a powerful method of feature extraction and strongly depends on the selection of a reference covariance matrix. In general, the observed signals may include outliers, therefore, taking the geometric mean of SCMs as the reference matrix may not be the best choice. In order to deal with the effects of outliers, robust estimators have to be used. In particular, we discuss and test the use of geometric medians and trimmed averages (defined on the basis of several metrics) as robust estimators. The main idea behind trimmed averages is to eliminate those data that exhibit the largest distance from the average covariance calculated on the basis of all available data. The results of the experiments show that, while the geometric medians show little differences from conventional methods in terms of classification accuracy in the classification of electroencephalographic recordings, the trimmed averages show a significant improvement for all subjects. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/249279 |
2017 |
Gyroscopic signal smoothness assessment by geometric jolt estimation
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The present contribution focuses on the estimation of the geometric acceleration and of the geometric jolt (namely, the derivative of the acceleration) of a multidimensional, structured gyroscopic signal. A gyroscopic signal encodes the instantaneous orientation of a rigid body during a full 3-dimensional rotation, that is regarded as a trajectory in the curved space SO(3) of the special orthogonal matrices. The geometric acceleration and jolt associated to a gyroscopic signal are evaluated through the rules of calculus prescribed by differential geometry. Such an endeavor is motivated by recent studies on the smoothness of human body movement in bio-mechanical engineering, sports science and rehabilitation neuro-engineering. Two indexes of smoothness are compared, namely, a normalized proper geometric acceleration index and a normalized proper geometric jolt index. Our investigation concludes that, in the considered experiments with measured signals, for relatively low values of the acceleration and of the jolt indexes, such indexes are strongly positively correlated. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/252286 |
2017 |
Exact low-order polynomial expressions to compute the Kolmogoroff–Nagumo mean in the affine symplectic group of optical transference matrices
LINEAR & MULTILINEAR ALGEBRA Autore/i: Fiori, Simone; Prifti, Stilian Classificazione: 1 Contributo su Rivista Abstract: The current contribution presents exact third-order polynomial expressions of matrix functions that arise in the computation of the Kolmogoroff-Nagumo mean of a set of optical transference matrices, that belong to the affine symplectic group ASp(4). Scheda della pubblicazione: https://iris.univpm.it/handle/11566/238960 |
2017 |
Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation
COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: Nonlinear oscillators are ubiquitous in sciences, being able to model the behavior of com- plex nonlinear phenomena, as well as in engineering, being able to generate repeating (i.e., periodic) or non-repeating (i.e., chaotic) reference signals. The state of the classical oscillators known from the literature evolves in the space R^n , typically with n = 1 (e.g., the famous van der Pol vacuum-tube model), n = 2 (e.g., the FitzHugh–Nagumo model of spiking neurons) or n = 3 (e.g., the Lorenz simplified model of turbulence). The aim of the current paper is to present a general scheme for the numerical differential-geometry-based integration of a general second-order, nonlinear oscillator model on Riemannian manifolds and to present several instances of such model on manifolds of interest in sciences and engineering, such as the Stiefel manifold and the space of symmetric, positive-definite matrices. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/252284 |
2017 |
An Improved Chaotic Optimization Algorithm Applied to a DC Electrical Motor Modeling
ENTROPY Autore/i: Fiori, Simone; Di Filippo, Ruben Classificazione: 1 Contributo su Rivista Abstract: The chaos-based optimization algorithm (COA) is a method to optimize possibly non-linear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by means of nonlinear, discrete-time dynamical systems to explore the search space while looking for the global minimum of a complex criterion function. The aim of the present research is to investigate the numerical properties of the COA, both on complex optimization test-functions from the literature and on a real-world problem, to contribute to the understanding of its global-search features. Also, the present research suggests a refinement of the original COA algorithm in order to improve its optimization performances. In particular, the real-world optimization problem tackled within the paper is the estimation of six electro-mechanical parameters of a model of a direct-current (DC) electrical motor. A large number of test results prove that the algorithm achieves an excellent numerical precision at a little expense in the computational complexity, which appears as extremely limited, compared to the complexity of other benchmark optimization algorithms, namely, the \emph{genetic algorithm} and the \emph{simulated annealing algorithm}. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/252287 |
2016 |
Robust averaging of covariance matrices by Riemannian geometry for motor-imagery brain–computer interfacing
Advances in Cognitive Neurodynamics (V) Autore/i: Uehara, Takashi; Tanaka, Toshihisa; Fiori, Simone Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/238958 |
2016 |
A Riemannian steepest descent approach over the inhomogeneous symplectic group: Application to the averaging of linear optical systems
APPLIED MATHEMATICS AND COMPUTATION Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The present manuscript describes a Riemannian-steepest-descent approach to compute the average out of a set of optical system transference matrices on the basis of a Lie-group av- eraging criterion function. The devised averaging algorithm is compared with the Harris’ exponential-mean-logarithm averaging rule, especially developed in computational oph- thalmology to compute the average character of a set of biological optical systems. Results of numerical experiments show that the iterative algorithm based on gradient steepest de- scent implemented by exponential-map stepping converges to solutions that are in good agreement with those obtained by the application of Harris’ exponential-mean-logarithm averaging rule. Such results seem to confirm that Harris’ exponential-mean-logarithm av- eraging rule is numerically optimal in a Lie-group averaging sense. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/238959 |
2016 |
In-Lab Drone’s Attitude Maneuvering Fluency Evaluation by a Gyroscopic Lurch Index
Recent Advances in Circuits, Systems, Signal Processing and Communications Autore/i: Fiori, Simone; Sabino, Nicola; Bonci, Andrea Editore: WSEAS Press Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: The present paper reports on the current progress about the laboratory-based assessment of the fluency of attitude maneuvering of a quadcopter. The manuscript illustrates a laboratory-based data-acquisition setup and a mathematical data-processing algorithm to test a novel attitude maneuvering fluency estimation index termed geometric lurch. The geometric lurch index is defined in terms of angular variables’ values as returned by gyroscopic sensors that a quadcopter vehicle is equipped with. The results of several numerical tests, conducted on both synthetic and real-world gyroscopic signals, show that the geometric lurch index is fairly sensitive to the fluency of attitude maneuvering. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/247023 |
2016 |
Nonlinear damped oscillators on Riemannian manifolds: Fundamentals
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The classical theory of mass-spring-damper-type dynamical systems on the ordinary flat space R^3 may be generalized to higher-dimensional Riemannian manifolds by reformulating the basic underlying physical principles through differential geometry. Nonlinear dynamical systems have been studied in the scientific literature because they arise naturally from the modeling of complex physical structures and because such dynamical systems constitute the basis for several modern applications such as the secure transmission of information. The flows of nonlinear dynamical systems may evolve over time in complex, non-repeating (although deterministic) patterns. The focus of the present paper is on formulating the general equations that describe the dynamics of a point-wise particle sliding on a Riemannian manifold in a coordinate-free manner. The paper shows how the equations particularize in the case of some manifolds of interest in the scientific literature, such as the Stiefel manifold and the manifold of symmetric positive-definite matrices. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/238957 |
2015 |
Bivariate Nonisotonic Statistical Regression by a Lookup Table Neural System
COGNITIVE COMPUTATION Autore/i: Fiori, Simone; Gong, Tianxia; Lee, Hwee Kuan Classificazione: 1 Contributo su Rivista Abstract: Linear data regression is a fundamental mathematical tool in engineering and applied sciences. However, for complex non-linear phenomena, the standard linear least-squares regression may prove ineffective, hence calling for more involved data modeling techniques. The current research work investigates, in particular, non-linear statistical regression of bivariate data that do not exhibit a monotonic dependency. The current contribution proposes a neural-network-based data processing method, termed data monotonization, followed by neural isotonic statistical regression. Such data monotonization processing is performed by means of an adaptive neural network that learns its non-linear transfer function from the training set. The artificial neural system that performs data monotonization is implemented through a look-up table (LUT), which entails few computationally-inexpensive algebraic operations to adapt and to compute the output from the input data-set. A number of learning rules to adapt such LUT-based neural system are introduced and compared, in order to elucidate their relative merits and drawbacks. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/233662 |
2015 |
Tangent-Bundle Maps on the Grassmann Manifold: Application to Empirical Arithmetic Averaging
IEEE TRANSACTIONS ON SIGNAL PROCESSING Autore/i: Fiori, Simone; Kaneko, Tetsuya; Tanaka, Toshihisa Classificazione: 1 Contributo su Rivista Abstract: The present paper elaborates on tangent-bundle maps on the Grassmann manifold, with application to subspace arithmetic averaging. In particular, the present contribution elaborates on the work about retraction/lifting maps devised for the Stiefel manifold in the recently published paper T. Kaneko, S. Fiori and T. Tanaka, “Empirical arithmetic averaging over the compact Stiefel manifold,” IEEE Trans. Signal Process., Vol. 61, No. 4, pp. 883-894, February 2013, and discusses the extension of such maps to the Grassmann manifold. Tangent-bundle maps are devised on the basis of the thin QR matrix decomposition, the polar matrix decomposition and the exponential map. Also, tangent-bundle pseudo-maps based on the matrix Cayley transform are devised. Theoretical and numerical comparisons about the devised tangent-bundle maps are performed in order to get an insight into their relative merits and demerits, with special emphasis to their computational burden. The averaging algorithm based on the thin-QR decomposition maps stands out as it exhibits the best trade off between numerical precision and computational burden. Such algorithm is further compared with two Grassmann averaging algorithms drawn from the scientific literature on an handwritten digits recognition data set. The thin-QR tangent-bundle maps-based algorithm exhibits again numerical features that make it preferable over such algorithms. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/225174 |
2015 |
Kolmogoroff-Nagumo mean over the affine symplectic group of matrices
APPLIED MATHEMATICS AND COMPUTATION Autore/i: Fiori, Simone Classificazione: 1 Contributo su Rivista Abstract: The present work shows that Harris' exponential-mean-log averaging rule over the space of optical transference matrices may be regarded as an instance of the Kolmogoroff-Nagumo averaging rule over the affine symplectic group. As such, Harris' averaging rule may be generalized to a phi-mean-phi^{-1} rule that can be implemented by different phi maps. The present work also shows that the involved maps may be computed in closed form by low-degree polynomial expressions. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/227815 |
2015 |
Nonlinear Second-Order Dynamical Systems on Riemannian Manifolds
International Conference on Modeling, Simulation and Visualization Methods Autore/i: Simone, Fiori; Andrea, Bonci Editore: CSREA Press Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: Linear as well as non-linear mathematical systems that exhibit an oscillatory behavior are ubiquitous in sciences and engineering. Such mathematical systems have been used to model the behavior of biological structures, such as the pulsating contraction of cardiac cells, as well as the behavior of electrical and mechanical components. Chaotic oscillators are currently being used in the secure transmission of information. The state of such classical dynamical systems evolve in the Euclidean space R^n (typically, n=1,2,3). The current paper aims at proposing a principled mathematical technique to design second-order nonlinear dynamical systems over curved Riemannian manifolds and to discuss a numerical simulation framework that is compatible with the structure of such spaces. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/227816 |
2014 |
A two-dimensional Poisson equation formulation of non-parametric statistical non-linear modeling
COMPUTERS & MATHEMATICS WITH APPLICATIONS Autore/i: S. Fiori Classificazione: 1 Contributo su Rivista Abstract: The present paper deals with a Poisson equation arising in statistical modeling of semi-deterministic non-linear systems with two independent (input) variables and one dependent (output) variable. Statistical modeling is formulated in terms of a differential equation that relates the second-order joint probability density functions of the model's input/output random variables with the sought nonlinear model transference. The discussed modeling procedure makes no prior assumptions on the functional structure of the model, except for monotonicity and continuity with respect to both input variables. In particular, the method is non-parametric. Results of numerical tests are presented and discussed in order to get an insight into the behavior of the devised statistical modeling procedure. The results of numerical tests confirm that the proposed statistical modeling approach is able to cope with both synthetic and real-world data sets and, in particular, with underlying systems and data that exhibit strong hidden nuisance variables and measurement disturbances. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/204113 |
2014 |
Auto-Regressive Moving Average Models on Complex-Valued Matrix Lie Groups
CIRCUITS SYSTEMS AND SIGNAL PROCESSING Autore/i: Simone Fiori Classificazione: 1 Contributo su Rivista Abstract: The present contribution aims at extending the classical scalar ARMA (auto-regressive moving-average) model to generate random (as well as deterministic) paths on complex-valued matrix Lie groups. The numerical properties of the developed ARMA model are studied by recurring to a tailored version of the Z-transform on Lie groups and to statistical indicators tailored to Lie groups, such as correlation functions on tangent bundles. The numerical behavior of the devised ARMA model is also illustrated by numerical simulations. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/204114 |
2014 |
Fast closed-form trivariate statistical isotonic modelling
ELECTRONICS LETTERS Autore/i: S. Fiori Classificazione: 1 Contributo su Rivista Abstract: The present Letter introduces a non-iterative, closed-form solution to the problem of statistically modeling the monotonic relationship between a dependent variable and two independent variables through a probability conservation principle. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/204115 |
2014 |
Mixed maps for learning a Kolmogoroff-Nagumo-type average element on the compact Stiefel manifold
2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) Autore/i: S. Fiori; T. Kaneko; T. Tanaka Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: The present research work proposes a new fast fixed-point average-value learning algorithm on the compact Stiefel manifold based on a mixed retraction/lifting pair. Numerical comparisons between fixed-point algorithms based on the proposed non-associated retraction/lifting map pair and two associated retraction/lifting pairs confirm that the averaging algorithm based on a combination of mixed maps is remarkably less computationally demanding than the same averaging algorithm based on any of the constituent associated retraction/lifting pairs. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/204116 |
2014 |
Auto-regressive moving-average discrete-time dynamical systems and autocorrelation functions on real-valued Riemannian matrix manifolds
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B. Autore/i: Simone Fiori Classificazione: 1 Contributo su Rivista Abstract: The present research paper proposes an extension of the classical scalar Auto-Regressive Moving-Average (ARMA) model to real-valued Riemannian matrix manifolds. The resulting ARMA model on matrix manifolds is expressed as a non-linear discrete-time dynamical system in state-space form whose state evolves on the tangent bundle associated with the underlying manifold. A number of examples are discussed within the present contribution that aim at illustrating the numerical behavior of the proposed ARMA model. In order to measure the degree of temporal dependency between the state-values of the ARMA model, an extension of the classical autocorrelation function for scalar sequences is suggested on the basis of the geometrical features of the underlying real-valued matrix manifold. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/204117 |
2013 |
Empirical Arithmetic Averaging over the Compact Stiefel Manifold
IEEE TRANSACTIONS ON SIGNAL PROCESSING Autore/i: T. Kaneko; S. Fiori; T. Tanaka Classificazione: 1 Contributo su Rivista Abstract: The aim of the present research work is to investigate algorithms to compute empirical averages of finite sets of sample-points over the Stiefel manifold by extending the notion of Pythagoras' arithmetic averaging over the real line to a curved manifold. The idea underlying the developed algorithms is that sample-points on the Stiefel manifold get mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is brought back to the Stiefel manifold, via appropriate maps. Numerical experimental results are shown and commented on in order to illustrate the numerical behaviour of the proposed procedure. The obtained numerical results confirm that the developed algorithms converge steadily and in a few iterations and that they are able to cope with relatively large-size problems. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/82412 |
2013 |
An isotonic trivariate statistical regression method
ADVANCES IN DATA ANALYSIS AND CLASSIFICATION Autore/i: Simone Fiori Classificazione: 1 Contributo su Rivista Abstract: The present research work outlines the main ideas behind statistical regression by a 2-independent-variates and 1-dependent-variate model based on the invariance of measures in probabilistic spaces. The principle of probabilistic measure invariance, applied under the assumption that the model be isotonic, leads to a system of differential equations. Such differential system is reformulated in terms of an integral equation that affords an iterative numerical solution. Numerical tests performed on the devised statistical regression procedure illustrate its features. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/138464 |
2013 |
Fast statistical regression in presence of a dominant independent variable
NEURAL COMPUTING & APPLICATIONS Autore/i: Simone Fiori Classificazione: 1 Contributo su Rivista Abstract: Bivariate statistical regression is a statisti- cal tool that allows performing regression on a multi- variate data set under the hypothesis that one of the independent variables is dominant. Statistical regres- sion is profitable when the amount of available data is enough to explain the relevant statistical features of the phenomenon underlying the data. The present pa- per suggests a fast statistical regression method based on a neural system that is able to match its input- output statistic to the marginal statistic of the avail- able data sets. A key point of the implementation pro- posed in the present paper is that it is based on purely numerical-algebraic operations, which guarantee a com- putationally advantageous way of implementing neu- ral systems. A number of numerical experiments, per- formed on real-world data sets, provide some insights into the behaviour of the devised neural-system-based statistical regression method and its limitations. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75355 |
2013 |
Random Clouds on Matrix Lie Groups
» Geometric Science of Information Autore/i: Simone Fiori Editore: Springer Berlin Heidelberg Luogo di pubblicazione: Berlin Classificazione: 2 Contributo in Volume Abstract: In the development of information processing algorithms that insist on matrix-manifold-type parameter spaces, testing is a fundamental step. The present paper aims at providing an overview about the generation of random matrices on Lie groups. A random matrix is an array of random numbers. Imposing symmetry constraints on random matrices leads to relationships with differential geometry. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/138463 |
2013 |
Neural System Learning on Complex-Valued Manifolds
Complex-Valued Neural Networks: Advances and Applications Autore/i: S. Fiori Editore: Wiley-IEEE Press Classificazione: 2 Contributo in Volume Abstract: An instance of artificial neural learning is by criterion optimization, where the criterion to optimize measures the learning ability of the neural network either in supervised learning (the adaptation is supervised by a teacher) or in unsupervised learning (the adaptation of network parameters proceeds on the basis of the information that the neural system is able to extract from the inputs). In some circumstances of interest, the space of parameters of the neural system is restricted to a particular feasible space via suitable bounds, which represent the constraint imposed by the learning problem at hand. In this case, the optimization rules to adapt the parameters of the neural network must be designed according to the known constraints. If the set of feasible parameters form a smooth continuous set, namely, a differentiable manifold, the design of adaptation rules falls in the realm of differential geometrical methods for neural networks and learning and of the numerical geometric integration of learning equations. The present chapter deals with complex-valued parameter-manifolds and with applications of complex-valued artificial neural networks whose connection-parameters live in complex-valued manifolds. The successful applications of such neural networks, which are described within the present chapter, are to blind source separation of complex-valued sources and to multichannel blind deconvolution of signals in telecommunications, to nondestructive evaluation of materials in industrial metallic slabs production and to the purely algorithmic problem of averaging the parameters of a pool of cooperative complex-valued neural networks. The present chapter recalls those notions of differential geometry that are instrumental in the definition of a consistent learning theory over complex-valued differentiable manifolds and introduces some learning problems and their solutions. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/138462 |
2013 |
Blind deconvolution by a Newton method on the non-unitary hypersphere
INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Autore/i: S. Fiori Classificazione: 1 Contributo su Rivista Abstract: Blind deconvolution is an inverse filtering technique that has received increasing attention from academia as well industry because of its theoretical implications and practical applications, such as in speech dereverberation, nondestructive testing and seismic exploration. An effective blind deconvolution technique is known as Bussgang , which relies on the iterative Bayesian estimation of the source sequence. Automatic gain control in blind deconvolution keeps constant the energy of the inverse filter impulse response and controls the magnitude of the estimated source sequence. The aim of the present paper is to introduce a class of Newton-type algorithms to optimize the Bussgang cost function on the inverse-filter parameter space whose geometrical structure is induced by the automatic-gain-control constraint. As the parameter space is a differentiable manifold, the Newton-like optimization method is formulated in terms of differential-geometrical concepts. The present paper also discusses convergence issues related to the introduced Newton-type optimization algorithms and illustrates their performance on a comparative basis. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/81594 |
2012 |
Extended Hamiltonian Learning on Riemannian Manifolds: Numerical Aspects
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS Autore/i: Simone Fiori Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75352 |
2012 |
Learning on the Compact Stiefel Manifold by a Cayley-Transform-Based Pseudo-Retraction Map
Proceedings of the International Joint Conference on Neural Networks (WCCI-IJCNN 2012) Autore/i: S. Fiori; T. Kaneko; T. Tanaka Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: The present research takes its moves from previous contributions by the present authors on two topics, namely, neural learning on differentiable manifolds by manifold retractions and averaging over differentiable manifolds. Learning on differentiable manifolds is a general theory that allows a neural system that insists on curved smooth spaces to adapt its parameters without violating the constraints on the geometry of the parameter spaces. In particular, the present contribution focuses on learning on the compact Stiefel manifold by manifold retraction with application to averaging `tall-skinny' matrices and generalizes some contributions recently appeared in the scientific literature about such a topic. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75354 |
2012 |
A Method to Compute Averages over the Compact Stiefel Manifold
Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2012) Autore/i: T. Kaneko; T. Tanaka; S. Fiori Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: The aim of the present contribution is to extend the algorithm introduced in the paper S. Fiori and T. Tanaka, “An algorithm to compute averages on matrix Lie groups,” IEEE Transactions on Signal Processing, Vol. 57, No. 12, pp. 4734 - 4743, December 2009, to compute averages over the Stiefel manifold. The idea underlying the developed algorithms is that points on the Stiefel manifold are mapped onto a tangent space, where the average is taken, and then the average point on the tangent space is projected back to the Stiefel manifold. Based on this idea, a fixed-point algorithm is developed, and numerical examples are shown to support the analysis. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75353 |
2011 |
Extended Hamiltonian Learning on Riemannian Manifolds: Theoretical Aspects
IEEE TRANSACTIONS ON NEURAL NETWORKS Autore/i: Fiori S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/66089 |
2011 |
Solving Minimal-Distance Problems over the Manifold of Real Symplectic Matrices
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS Autore/i: Fiori S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/66090 |
2011 |
Riemannian-Gradient-Based Learning on the Complex Matrix-Hypersphere
IEEE TRANSACTIONS ON NEURAL NETWORKS Autore/i: Fiori S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/66091 |
2011 |
Visualization of Riemannian-Manifold-Valued Elements by Multidimensional Scaling
NEUROCOMPUTING Autore/i: Fiori S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/66088 |
2011 |
Averaging matrices over the Stifel manifold
Proceeding of the 26th Signal Processing Symposium in Japan Autore/i: T. Kaneko; T. Tanaka; S. Fiori Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75351 |
2011 |
Averaging over the Lie Group of Optical Systems Transference Matrices
FRONTIERS OF ELECTRICAL AND ELECTRONIC ENGINEERING IN CHINA Autore/i: Fiori S. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/69922 |
2011 |
Statistical Nonparametric Bivariate Isotonic Regression by Look-Up-Table-Based Neural NetworksNeural Information Processing
Lecture Notes in Computer ScienceNeural Information Processing Autore/i: Simone Fiori Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75350 |
2010 |
A pseudo-Riemannian-gradient approach to the least-squares problem on the real symplectic group
Proceedings of the 2010 International Conference on Acoustics, Speech and Signal Processing (ICASSP 2010) Autore/i: S. Fiori Classificazione: 2 Contributo in Volume Abstract: The present paper discusses the problem of geodesic least squares over the real symplectic group of matrices Sp(2n,ℝ). As the space Sp(2n,ℝ) is a non-compact Lie group, it is convenient to endow it with a pseudo-Riemannian geometry instead of a Riemannian one. Indeed, a pseudo-Riemannian metric allows the computation of geodesic arcs and geodesic distances in closed form. ©2010 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73860 |
2010 |
Optimal stepsize schedule for a projection-based blind deconvolution algorithm
Proceedings of the 2nd Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC 2010) Autore/i: S. Fiori Classificazione: 4 Contributo in Atti di Convegno (Proceeding) Abstract: The present paper illustrates a gradient-update-type projection-based adaptation algorithm over a curved parameter-space (namely, the unit hypershpere) for blind deconvolution application. The deconvolving structure is an FIR adaptive filter whose adaptation rule arises from criterion-function minimization over the smooth parameter-manifold of unit-norm vectors. In particular, the present paper explains an adaptive stepsize theory for the algorithm at hand. The blind deconvolution performances of the algorithm as well as its computational burden are discussed. Also, a numerical comparison with seven blinddeconvolution algorithms known from the scientific literature is illustrated and discussed. Results of numerical tests conducted on a noiseless as well as a noisy channel will confirm that the algorithm discussed in the present paper performs in a satisfactory way. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73862 |
2010 |
Learning by Natural Gradient on Noncompact Matrix-type Pseudo-Riemannian Manifolds
IEEE TRANSACTIONS ON NEURAL NETWORKS Autore/i: S. FIORI Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/35784 |
2010 |
A closed-form solution to the problem of averaging over the lie group of special orthogonal matrices
Proceedings of the 2010 International Symposium on Neural Networks (ISNN 2010) Autore/i: S. Fiori Editore: Springer-Verlag, Berlin, Heidelber Classificazione: 2 Contributo in Volume Abstract: Averaging over the Lie group SO(p) of special orthogonal matrices has several applications in the neural network field. The problem of averaging over the group SO(3) has been studied in details and, in some specific cases, it admits a closed form solution. Averaging over a generic-dimensional group SO(p) has also been studied recently, although the common formulation in terms of Riemannian mean leads to a matrix-type non-linear problem to solve, which, in general, may be tackled via iterative algorithms only. In the present paper, we propose a novel formulation of the problem that gives rise to a closed form solution for the average SO(p)-matrix. © 2010 Springer-Verlag. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73859 |
2009 |
Learning the Fréchet Mean over the Manifold of Symmetric Positive-Definite Matrices
COGNITIVE COMPUTATION Autore/i: S. FIORI Editore: New York : Springer New York Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/34029 |
2009 |
An Algorithm to Compute Averages on Matrix Lie Groups
IEEE TRANSACTIONS ON SIGNAL PROCESSING Autore/i: S. FIORI; TANAKA T Classificazione: 1 Contributo su Rivista Abstract: Averaging is a common way to alleviate errors and random fluctuations in measurements and to smooth out data. Averaging also provides a way to merge structured data in a smooth manner. The present paper describes an algorithm to compute averages on matrix Lie groups. In particular, we discuss the case of averaging over the special orthogonal group of matrices, the unitary group of matrices and the group of symmetric positive-definite matrices. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/34030 |
2009 |
Approximate Joint Matrix Diagonalization by Riemannian-Gradient-Based Optimization over the Unitary Group (With Application to Neural Multichannel Blind Deconvolution)
Neural Computation and Particle Accelerators: Research, Technology and Applications Autore/i: S. Fiori; P. Baldassarri Editore: Nova publisher Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75349 |
2009 |
Learning averages over the Lie group of symmetric positive-definite matrices
Proceedings of the 2009 International Joint Conference on Neural Networks Autore/i: S. Fiori; T. Tanaka Classificazione: 2 Contributo in Volume Abstract: In the present paper, we treat the problem of learning averages out of a set of symmetric positive-definite matrices (SPDMs). We discuss a possible learning technique based on the differential geometrical properties of the SPDM- manifold which was recently shown to possess a Lie-group structure under appropriate group definition. We first recall some relevant notions from differential geometry, mainly related to Lie-group theory, and then we propose a scheme of learning averages. Some numerical experiments will serve to illustrate the features of the learnt averages. ©2009 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73857 |
2009 |
Learning averages over the Lie group of unitary matrices
Proceedings of the 2009 International Joint Conference on Neural Networks Autore/i: S. Fiori Classificazione: 2 Contributo in Volume Abstract: 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. © 2009 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73858 |
2009 |
Computation of the Fréchet mean, variance and interpolation for a pool of neural networks over the manifold of special orthogonal matrices
INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE STUDIES Autore/i: S. FIORI Editore: Inderscience Enterprises Limited. Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33969 |
2009 |
On Vector Averaging over the Unit Hyphersphere
DIGITAL SIGNAL PROCESSING Autore/i: S. FIORI Editore: Academic Press Incorporated:6277 Sea Harbor Drive:Orlando, FL 32887:(800)543-9534, (407)345-4100, EMAIL: ap@acad.com, INTERNET: http://www.idealibrary.com, Fax: (407)352-3445 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33968 |
2009 |
Learning-machines-committee averages over the unitary group of matrices
Proceedings of the 2009 International Symposium on Circuits and Systems Autore/i: S. Fiori; T. Tanaka Editore: IEEE Classificazione: 2 Contributo in Volume Abstract: A committee of learning machines may be conceived of as a group of adaptive systems that adapt independently of each other and whose goal is to solve a common learning problem. Each machine in a committee computes a set of parameter-patterns belonging to a curved space. A natural question is how to combine the learnt patterns in order to obtain a better solution to the learning problem. In the present paper, we treat the case that the parameter space is the Lie group of unitary matrices. In order to combine the learnt patterns, we discuss a possible merging technique based on the differential geometrical structure of the parameter manifold. ©2009 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73856 |
2008 |
Geodesic-Based and Projection-Based Neural Blind Deconvolution Algorithms
SIGNAL PROCESSING Autore/i: S. FIORI Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33962 |
2008 |
A Study on Neural Learning on Manifold Foliations: The case of the Lie Group SU(3)
NEURAL COMPUTATION Autore/i: S. FIORI Editore: Berkeley Electronic Press:805 Camelia Street, Second Floor:Berkeley, CA 94710:(510)559-1500, EMAIL: info@bepress.com, INTERNET: http://www.bepress.com, Fax: (510)559-1550 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33961 |
2008 |
Learning by Criterion Optimization on a Unitary Unimodular Matrix Group
INTERNATIONAL JOURNAL OF NEURAL SYSTEMS Autore/i: S. FIORI Editore: World Scientific Publishing Company:PO Box 128, Farrer Road, Singapore 912805 Singapore:011 65 6 4665775, EMAIL: journal@wspc.com.sg, INTERNET: http://www.wspc.com.sg, http://www.worldscinet.com, Fax: 011 65 6 4677667 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33963 |
2008 |
Leap-Frog-Type Learning Algorithms over the Lie Group of Unitary Matrices
NEUROCOMPUTING Autore/i: S. FIORI Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33965 |
2008 |
Engineering of Intelligent Systems (Editorial)
NEUROCOMPUTING Autore/i: HUSSAIN A; S. FIORI; QURESHI I.M; DURRANI T.S; AHMED M.M; FUKUSHIMA K Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/35783 |
2008 |
Lie-Group-Type Neural System Learning by Manifold Retractions
NEURAL NETWORKS Autore/i: S. FIORI Editore: Elsevier Science Limited:Oxford Fulfillment Center, PO Box 800, Kidlington Oxford OX5 1DX United Kingdom:011 44 1865 843000, 011 44 1865 843699, EMAIL: asianfo@elsevier.com, tcb@elsevier.co.UK, INTERNET: http://www.elsevier.com, http://www.elsevier.com/locate/shpsa/, Fax: 011 44 1865 843010 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33967 |
2008 |
Learning stepsize selection for the geodesic-based neural blind deconvolution algorithm
Proceedings of the International Joint Conference on Neural Networks Autore/i: S. Fiori Editore: IEEE Classificazione: 2 Contributo in Volume Abstract: The present paper illustrates a geodesic-based learning algorithm over a curved parameter space for blind deconvolution application. The chosen deconvolving structure appears as a single neuron model whose learning rule arises from criterion-function minimization over a smooth manifold. In particular, we propose here a learning stepsize selection theory for the algorithm at hand. We consider the blind deconvolution performances of the algorithm as well as its computational burden. Also, a numerical comparison with seven blind-deconvolution algorithms known from the scientific literature is illustrated and discussed. Results of numerical tests conducted on a noiseless as well as a noisy system will confirm that the algorithm discussed in the present paper performs in a satisfactory way. Also, the performances of the presented algorithm will be compared with those exhibited by other blind deconvolution algorithms known from the literature. © 2008 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73851 |
2008 |
Descent Methods for Optimization on Homogeneous Manifolds
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTERS IN SIMULATION Autore/i: CELLEDONI E; S. FIORI Editore: NAUN NORTH ATLANTIC UNIVERSITY UNION - United States - http://www.naun.org/journals/mcs/ Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33966 |
2008 |
Generation of pseudorandom numbers with arbitrary distribution by learnable look-up-table-type neural networks
Proceedings of the International Joint Conference on Neural Networks Autore/i: S. Fiori Editore: IEEE Classificazione: 2 Contributo in Volume Abstract: The aim of the present manuscript is to propose a pseudo-random number generation algorithm based on a learnable non-linear neural network whose implementation is based on look-up tables. The proposed neural network is able to generate pseudo-random numbers with arbitrary distribution on the basis of standard variate generators available within programming environments. The proposed method is not computationally demanding and easy to implement on a computer. Numerical tests confirm the agreement between the desired and obtained distributions of the generated pseudo-random number batches. © 2008 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73853 |
2008 |
An averaging method for a committee of special-orthogonal-group machines
Proceedings of the International Symposium on Circuits and Systems Autore/i: S. Fiori; T. Tanaka Classificazione: 2 Contributo in Volume Abstract: The present paper aims at introducing a novel procedure for designing an averaging algorithm for a committee of learning machines under the assumption that the machines share a common parameter-space, namely, the group of special orthogonal matrices SO(p). The averaging procedure inputs the patterns learnt by the machines in the committee and outputs a mean-matrix that represents an average of machines' patterns. Since the space SO(p) is a curved manifold, averaging does not carry on the usual (Euclidean) meaning and should be designed on the basis of the parameter-space's geometric properties. ©2008 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73849 |
2008 |
Estimating Independent Components by Mappings onto the Orthogonal Manifold
T.A.S.K. QUARTERLY Autore/i: S. Fiori Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75347 |
2008 |
Asymmetric Variate Generation via a Parameterless Dual Neural Learning Algorithm
COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE Autore/i: S. FIORI Editore: New York: Hindawi Publishing Corporation Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33964 |
2007 |
Neural learning by retractions on manifolds
IEEE International Symposium on Circuits and Systems Autore/i: S. Fiori Classificazione: 2 Contributo in Volume Abstract: Neural learning algorithms based on criterion optimization over differential manifolds have been devised over the few past years. Such learning algorithms mainly differ by the way the single learning steps are effected on the neural system's parameter space. We introduce a unifying view of these algorithms by recalling from the literature of differential geometry the concept of retraction on manifolds. It provides a general way of acting upon neural system's learnable parameters for learning criteria optimization purpose. © 2007 IEEE. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73848 |
2007 |
Learning Independent Components on the Orthogonal Group of Matrices by Retractions
NEURAL PROCESSING LETTERS Autore/i: S. FIORI Editore: Kluwer Academic Publishers:Journals Department, PO Box 322, 3300 AH Dordrecht Netherlands:011 31 78 6576050, EMAIL: frontoffice@wkap.nl, kluweronline@wkap.nl, INTERNET: http://www.kluwerlaw.com, Fax: 011 31 78 6576254 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/35782 |
2007 |
Neural learning algorithms based on mappings: The case of the unitary group of matrices
International Conference on Artificial Neural Networks (ICANN'07) Autore/i: S. Fiori Editore: Springer Verlag Germany:Tiergartenstrasse 17, D 69121 Heidelberg Germany:011 49 6221 3450, EMAIL: g.braun@springer.de, INTERNET: http://www.springer.de, Fax: 011 49 6221 345229 Classificazione: 2 Contributo in Volume Abstract: Neural learning algorithms based on optimization on manifolds differ by the way the single learning steps are effected on the neural system's parameter space. In this paper, we present a class counting four neural learning algorithms based on the differential geometric concept of mappings from the tangent space of a manifold to the manifold itself. A learning stepsize adaptation theory is proposed as well under the hypothesis of additiveness of the learning criterion. The numerical performances of the discussed algorithms are illustrated on a learning task and are compared to a reference algorithm known from literature. © Springer-Verlag Berlin Heidelberg 2007. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/73868 |
2007 |
Least Squares Approximate Joint Diagonalization on the Orthogonal Group
2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07 Autore/i: Toshihisa Tanaka; Simone Fiori Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75346 |
2007 |
Neural Systems with Numerically-Matched Input-Output Statistic: Isotonic Bivariate Statistical Modeling
COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE Autore/i: S. FIORI Editore: New York: Hindawi Publishing Corporation Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33974 |
2006 |
Blind Adaptation of Stable Discrete-Time IIR Filters in State-Space Form
IEEE TRANSACTIONS ON SIGNAL PROCESSING Autore/i: S. FIORI Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33959 |
2006 |
Blind Equalization of Communication Channels for Equal Energy Sources: Energy Matching Approach
ELECTRONICS LETTERS Autore/i: A. NAVEED; A. HUSSAIN; I. M. QURESHI; S. FIORI Editore: Institution of Electrical Engineers:Michael Faraday House, 6 Hills Way, Stevenage Hertfordshire SG1 1AY United Kingdom:011 44 1438 313311, EMAIL: postmaster@iee.org, INTERNET: http://www.iee.org, Fax: 011 44 1438 313465 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33960 |
2006 |
Extrinsic Geometrical Methods for Neural Blind Deconvolution
AIP Conference Proceedings Autore/i: Simone Fiori Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75344 |
2006 |
Fixed-Point Neural Independent Component Analysis Algorithms on the Orthogonal Group
FUTURE GENERATION COMPUTER SYSTEMS Autore/i: S. FIORI Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/35780 |
2006 |
Simultaneous Tracking of the Best Basis in Reduced-Rank Wiener Filter
2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings Autore/i: T. Tanaka; S. Fiori Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75342 |
2006 |
Neural Systems with Numerically-Matched Input-Output Statistic: Variate Generation
NEURAL PROCESSING LETTERS Autore/i: S. FIORI Editore: Kluwer Academic Publishers:Journals Department, PO Box 322, 3300 AH Dordrecht Netherlands:011 31 78 6576050, EMAIL: frontoffice@wkap.nl, kluweronline@wkap.nl, INTERNET: http://www.kluwerlaw.com, Fax: 011 31 78 6576254 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/35781 |
2005 |
Formulation and Integration of Learning Differential Equations on the Stiefel Manifold
IEEE TRANSACTIONS ON NEURAL NETWORKS Autore/i: S. FIORI Editore: IEEE / Institute of Electrical and Electronics Engineers Incorporated:445 Hoes Lane:Piscataway, NJ 08854:(800)701-4333, (732)981-0060, EMAIL: subscription-service@ieee.org, INTERNET: http://www.ieee.org, Fax: (732)981-9667 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33958 |
2005 |
Editorial: Special issue on ''Geometrical Methods in Neural Networks and Learning''
NEUROCOMPUTING Autore/i: S. FIORI; AMARI S.-I Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33973 |
2005 |
Non-Linear Complex-Valued Extensions of Hebbian Learning: An Essay
NEURAL COMPUTATION Autore/i: S. FIORI Editore: Berkeley Electronic Press:805 Camelia Street, Second Floor:Berkeley, CA 94710:(510)559-1500, EMAIL: info@bepress.com, INTERNET: http://www.bepress.com, Fax: (510)559-1550 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33956 |
2005 |
Quasi-Geodesic Neural Learning Algorithms over the Orthogonal Group: A Tutorial
JOURNAL OF MACHINE LEARNING RESEARCH Autore/i: S. FIORI Classificazione: 1 Contributo su Rivista Abstract: The aim of this contribution is to present a tutorial on learning algorithms for a single neural layer whose connection matrix belongs to the orthogonal group. The algorithms exploit geodesics appropriately connected as piece-wise approximate integrals of the exact differential learning equation. The considered learning equations essentially arise from the Riemannian-gradient-based optimization theory with deterministic and diffusion-type gradient. The paper aims specifically at reviewing the relevant mathematics (and at presenting it in as much transparent way as possible in order to make it accessible to Readers that do not possess a background in differential geometry), at bringing together modern optimization methods on manifolds and at comparing the different algorithms on a common machine learning problem. As a numerical case-study, we consider an application to non-negative independent component analysis, although it should be recognized that Riemannian gradient methods are general-purpose algorithms, by no means limited to ICA-related applications. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33957 |
2004 |
Relative Uncertainty Learning Theory: An Essay
INTERNATIONAL JOURNAL OF NEURAL SYSTEMS Autore/i: S. FIORI Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33971 |
2004 |
Fast Fixed-Point Neural Blind Deconvolution Algorithm
IEEE TRANSACTIONS ON NEURAL NETWORKS Autore/i: S. FIORI Classificazione: 1 Contributo su Rivista Abstract: The aim of the present Letter is to introduce a new blind deconvolution algorithm based on fixed-point optimization of a `Bussgang'-type cost function. The cost function relies on approximate Bayesian estimation achieved by an adaptive neuron. The main feature of the presented algorithm is fast convergence that guarantees good deconvolution performances with limited computational demand compared to algorithms of the same class. Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33738 |
2004 |
Mechanical Properties of Polypropylene Matrix Composites Reinforced with Natural Fibers: A Statistical Approach
POLYMER COMPOSITES Autore/i: BIAGIOTTI J; S. FIORI; TORRE L; LÓPEZ-MANCHADO M.A; KENNY J.M Editore: Society of Plastics Engineers:14 Fairfield Drive, PO Box 0403:Brookfield, CT 06804:(203)775-0471, INTERNET: http://www.4spe.org, Fax: (203)775-8490 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33970 |
2004 |
Analysis of Modified `Bussgang' Algorithms (MBA) for Channel Equalization
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS. I, REGULAR PAPERS Autore/i: S. FIORI Editore: IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, USA, NJ, 08855 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33954 |
2004 |
One-Unit `Rigid-Bodies' Learning Rule for Principal/Independent Component Analysis with Application to ECT-NDE Signal Processing
NEUROCOMPUTING Autore/i: S. FIORI; BURRASCANO P Editore: Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598 Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/33972 |
2004 |
On Self-Consistency of Cost Functions for Blind Signal Processing Based on Neural Bayesian Estimators
23rd Annual Conference on Bayesian Methods and Maximum Entropy in Science and Engineering Autore/i: S. Fiori Editore: American Institute of Physics:2 Huntington Quadrangle, Suite 1NO1:Melville, NY 11747:(800)344-6902, (631)576-2287, EMAIL: subs@aip.org, INTERNET: http://www.aip.org, Fax: (516)349-9704 Classificazione: 2 Contributo in Volume Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75188 |
2004 |
Statistical Characterization of Some Electrical and Mechanical Phenomena by a Neural Probability Density Function Estimation Technique
NEURAL NETWORK WORLD Autore/i: S. Fiori; R. Rossi Classificazione: 1 Contributo su Rivista Scheda della pubblicazione: https://iris.univpm.it/handle/11566/75186 |
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