Guoqi Li

Identification of a Class of Nonlinear Autoregressive Models With Exogenous Inputs Based on Kernel Machines

In this paper, we propose a new approach to identify a new class of nonlinear autoregressive models with exogenous inputs (NARX) based on kernel machine and space projection (KMSP). The well-known Hammerstein-Wiener model which includes blocks of nonlinear static functions in series with a linear dynamic block is a subset of the NARX models considered. In the KMSP based approach, kernel machine is used to represent the functions and space projection to separate the represented functions. We also discuss two possible ambiguities and give conditions to avoid such ambiguities. The asymptotic behavior of the proposed approach is analyzed. The performance of the proposed method is verified by simulation studies.

Continuous and Noninvasive Blood Pressure Measurement: A Novel Modeling Methodology of the Relationship Between Blood Pressure and Pulse Wave Velocity

In this paper, we aim to establish a new mathematical model that relates pulse wave velocity (PWV) to blood pressure (BP) for continuous and noninvasive BP measurement. For the first time, we derive an ordinary differential equation (ODE) expressing the fundamental relation between BP, elastic modulus G and PWV. The general solution of this ODE is the mathematical BP-PWV model. In our model, the elastic modulus G is included in model parameters, unlike the existing theoretical models. This enables us to express the BP-PWV relationship for subjects of different ages and genders. A family of BP-PWV functions for specific age and gender groups can be obtained using statistical methods based on clinical trial data, which serve as the calibrated benchmark models for continuous and noninvasive BP measurement. To illustrate the modeling methodology, we construct benchmark models for people aged 19 and 60 and apply them to continuous diastolic blood pressure (DBP) measurement without individual calibration. The results of clinical tests meet the test standard in ANSI/AAMI SP10, which attests the feasibility of the modeling methodology.

Enabling an Integrated Rate-temporal Learning Scheme on Memristor

Learning scheme is the key to the utilization of spike-based computation and the emulation of neural/synaptic behaviors toward realization of cognition. The biological observations reveal an integrated spike time- and spike rate-dependent plasticity as a function of presynaptic firing frequency. However, this integrated rate-temporal learning scheme has not been realized on any nano devices. In this paper, such scheme is successfully demonstrated on a memristor. Great robustness against the spiking rate fluctuation is achieved by waveform engineering with the aid of good analog properties exhibited by the iron oxide-based memristor. The spike-time-dependence plasticity (STDP) occurs at moderate presynaptic firing frequencies and spike-rate-dependence plasticity (SRDP) dominates other regions. This demonstration provides a novel approach in neural coding implementation, which facilitates the development of bio-inspired computing systems.

Model-Based Online Learning With Kernels

New optimization models and algorithms for online learning with Kernels (OLK) in classification, regression, and novelty detection are proposed in a reproducing Kernel Hilbert space. Unlike the stochastic gradient descent algorithm, called the naive online Reg minimization algorithm (NORMA), OLK algorithms are obtained by solving a constrained optimization problem based on the proposed models. By exploiting the techniques of the Lagrange dual problem like Vapniks support vector machine (SVM), the solution of the optimization problem can be obtained iteratively and the iteration process is similar to that of the NORMA. This further strengthens the foundation of OLK and enriches the research area of SVM. We also apply the obtained OLK algorithms to problems in classification, regression, and novelty detection, including real time background substraction, to show their effectiveness. It is illustrated that, based on the experimental results of both classification and regression, the accuracy of OLK algorithms is comparable with traditional SVM-based algorithms, such as SVM and least square SVM (LS-SVM), and with the state-ofthe-art algorithms, such as Kernel recursive least square (KRLS) method and projectron method, while it is slightly higher than that of NORMA. On the other hand, the computational cost of the OLK algorithm is comparable with or slightly lower than existing online methods, such as above mentioned NORMA, KRLS, and projectron methods, but much lower than that of SVM-based algorithms. In addition, different from SVM and LS-SVM, it is possible for OLK algorithms to be applied to non-stationary problems. Also, the applicability of OLK in novelty detection is illustrated by simulation results.

Convergence of normalized iterative identification of Hammerstein systems

Abstract An iterative identification algorithm of Hammerstein systems needs a proper initial condition to guarantee its convergence. In this paper, we propose a new algorithm by fixing the norm of the parameter estimates. The normalized algorithm ensures the convergence property under arbitrary nonzero initial conditions. The proofs of the property also give a geometrical explanation on why the normalization guarantees the convergence. An additional contribution is that the static function in the Hammerstein system is extended to square-integrable functions.

PRESYNAPTIC LEARNING AND MEMORY WITH A PERSISTENT FIRING NEURON AND A HABITUATING SYNAPSE: A MODEL OF SHORT TERM PERSISTENT HABITUATION

Our paper explores the interaction of persistent firing axonal and presynaptic processes in the generation of short term memory for habituation. We first propose a model of a sensory neuron whose axon is able to switch between passive conduction and persistent firing states, thereby triggering short term retention to the stimulus. Then we propose a model of a habituating synapse and explore all nine of the behavioral characteristics of short term habituation in a two neuron circuit. We couple the persistent firing neuron to the habituation synapse and investigate the behavior of short term retention of habituating response. Simulations show that, depending on the amount of synaptic resources, persistent firing either results in continued habituation or maintains the response, both leading to longer recovery times. The effectiveness of the model as an element in a bio-inspired memory system is discussed.

Error tolerance based support vector machine for regression

Most existing online algorithms in support vector machines (SVM) can only grow support vectors. This paper proposes an online error tolerance based support vector machine (ET-SVM) which not only grows but also prunes support vectors. Similar to least square support vector machines (LS-SVM), ET-SVM converts the original quadratic program (QP) in standard SVM into a group of easily solved linear equations. Different from LS-SVM, ET-SVM remains support vectors sparse and realizes a compact structure. Thus, ET-SVM can significantly reduce computational time while ensuring satisfactory learning accuracy. Simulation results verify the effectiveness of the newly proposed algorithm.

Minimum-cost control of complex networks

Finding the solution for driving a complex network at the minimum energy cost with a given number of controllers, known as the minimum-cost control problem, is critically important but remains largely open. We propose a projected gradient method to tackle this problem, which works efficiently in both synthetic and real-life networks. The study is then extended to the case where each controller can only be connected to a single network node to have the lowest connection complexity. We obtain the interesting insight that such connections basically avoid high-degree nodes of the network, which is in resonance with recent observations on controllability of complex networks. Our results provide the first technical path to enabling minimum-cost control of complex networks, and contribute new insights to locating the key nodes from a minimum-cost control perspective.

Identification of Wiener Systems With Clipped Observations

In this paper, we consider the parametric version of Wiener systems where both the linear and nonlinear parts are identified with clipped observations in the presence of internal and external noises. Also the static functions are allowed noninvertible. We propose a classification based support vector machine (SVM) and formulate the identification problem as a convex optimization. The solution to the optimization problem converges to the true parameters of the linear system if it is an finite-impulse-response (FIR) system, even though clipping reduces a great deal of information about the system characteristics. In identifying a Wiener system with a stable infinite-impulse-response (IIR) system, an FIR system is used to approximate it and the problem is converted to identifying the FIR system together with solving a set of nonlinear equations. This leads to biased estimates of parameters in the IIR system while the bias can be controlled by choosing the order of the approximated FIR system.

Iterative identification of block-oriented nonlinear systems based on biconvex optimization

Abstract We investigate the identification of a class of block-oriented nonlinear systems which is represented by a common model in this paper. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. By applying the results to Hammerstein–Wiener systems with an invertible nonlinear function, the long-standing problem on the convergence of iteratively identifying such systems under arbitrary nonzero initial conditions is also now solved.