Facial expression classification: An approach based on the fusion of facial deformations using the transferable belief model

A method for the classification of facial expressions from the analysis of facial deformations is presented. This classification process is based on the transferable belief model (TBM) framework. Facial expressions are related to the six universal emotions, namely Joy, Surprise, Disgust, Sadness, Anger, Fear, as well as Neutral. The proposed classifier relies on data coming from a contour segmentation technique, which extracts an expression skeleton of facial features (mouth, eyes and eyebrows) and derives simple distance coefficients from every face image of a video sequence. The characteristic distances are fed to a rule-based decision system that relies on the TBM and data fusion in order to assign a facial expression to every face image. In the proposed work, we first demonstrate the feasibility of facial expression classification with simple data (only five facial distances are considered). We also demonstrate the efficiency of TBM for the purpose of emotion classification. The TBM based classifier was compared with a Bayesian classifier working on the same data. Both classifiers were tested on three different databases.     

Belief Scheduler based on model failure detection in the TBM framework. Application to human activity recognition

A tool called Belief Scheduler is proposed for state sequence recognition in the Transferable Belief Model (TBM) framework. This tool makes noisy temporal belief functions smoother using a Temporal Evidential Filter (TEF). The Belief Scheduler makes belief on states smoother, separates the states (assumed to be true or false) and synchronizes them in order to infer the sequence. A criterion is also provided to assess the appropriateness between observed belief functions and a given sequence model. This criterion is based on the conflict information appearing explicitly in the TBM when combining observed belief functions with predictions. The Belief Scheduler is part of a generic architecture developed for on-line and automatic human action and activity recognition in videos of athletics taken with a moving camera. In experiments, the system is assessed on a database composed of 69 real athletics video sequences. The goal is to automatically recognize running, jumping, falling and standing-up actions as well as high jump, pole vault, triple jump and long jump activities of an athlete. A comparison with Hidden Markov Models for video classification is also provided.     

Combination of partially non-distinct beliefs: The cautious-adaptive rule

The combination rule is critical in an evidence based fusion process. The conjunctive rule is most common eventhough when the cognitive independence – distinctness – assumption is often questionable. A new combination rule is tested here in both discrete and continuous cases, accounting for a partial non-distinctness between evidences. It is based on ‘generalized discounting’, that we define for separable basic belief assignments (bbas) or basic belief densities (bbds), to be applied to the source correlation derived from the cautious rule. This correlation can be specified in both considered cases of consonant bbas/bbds (as proposed by Dubois et al.) and separable bbas/bbds (as proposed by Denœux). Then, the so-called ‘cautious-adaptive’ rule varies between the conjunctive rule and the cautious one, depending on the discounting level. In the Gaussian case with standard deviation σ, the evidence non-distinctness will be parameterized by a factor [0,1] dividing σ. It leads to the generalized discounting needed in the cautious-adaptive formulation.     

Inference in directed evidential networks based on the transferable belief model

Inference algorithms in directed evidential networks (DEVN) obtain their efficiency by making use of the represented independencies between variables in the model. This can be done using the disjunctive rule of combination (DRC) and the generalized Bayesian theorem (GBT), both proposed by Smets [Ph. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal of Approximate Reasoning 9 (1993) 1–35]. These rules make possible the use of conditional belief functions for reasoning in directed evidential networks, avoiding the computations of joint belief function on the product space. In this paper, new algorithms based on these two rules are proposed for the propagation of belief functions in singly and multiply directed evidential networks.     

Minimum classification error training in example based speech and pattern recognition using sparse weight matrices

The Minimum Classification Error (MCE) criterion is a well-known criterion in pattern classification systems. The aim of MCE training is to minimize the resulting classification error when trying to classify a new data set. Usually, these classification systems use some form of statistical model to describe the data. These systems usually do not work very well when this underlying model is incorrect. Speech recognition systems traditionally use Hidden Markov Models (HMM) with Gaussian (or Gaussian mixture) probability density functions as their basic model. It is well known that these models make some assumptions that are not correct. In example based approaches, these statistical models are absent and are replaced by the pure data. The absence of statistical models has created the need for parameters to model the data space accurately. For this work, we use the MCE criterion to create a system that is able to work together with this example based approach. Moreover, we extend the locally scaled distance measure with sparse, block diagonal weight matrices resulting in a better model for the data space and avoiding the computational load caused by using full matrices. We illustrate the approach with some example experiments on databases from pattern recognition and with speech recognition.     

Clustering decomposed belief functions using generalized weights of conflict

We develop a method for clustering all types of belief functions, in particular non-consonant belief functions. Such clustering is done when the belief functions concern multiple events, and all belief functions are mixed up. Clustering is performed by decomposing all belief functions into simple support and inverse simple support functions that are clustered based on their pairwise generalized weights of conflict, constrained by weights of attraction assigned to keep track of all decompositions. The generalized conflict c(-∞,∞) and generalized weight of conflict J^-(-∞,∞) are derived in the combination of simple support and inverse simple support functions.     

A joint SSPDF–CMC method for simulating turbulent methane–air jet combustion

A joint single scalar probability density function and conditional moment closure (SSPDF–CMC) method is proposed for modeling a turbulent methane–air jet flame. In general, the probability density function (PDF) of passive scalar (such as mixture fraction) is non-Gaussian and not fully determined by the advecting velocity field, therefore the presumed shape of PDF of mixture fraction assumed as clipped Gaussian distribution or beta function in normal conditional moment closure (CMC) method is incorrect. In SSPDF–CMC method, the PDF of mixture fraction is obtained using a Monte-Carlo method to solve a PDF transport equation. An assumption that the averaged scalar advection is approximately equal to the averaged scalar dissipation in the wake of a grid-generated turbulence flow is adopted to model the averaged scalar dissipation. The predictions using the proposed method are compared with those using the conventional CMC method and the experimental data. It is seen that the predicted Favre conditional averaged statistics and Favre unconditional averaged statistics using the proposed method are in better agreement with the measurement data than those using the conventional CMC method. The predicted conditional or unconditional mean NO even using the SSPDF model is only in fair agreement with the experiments. It shows that the first-order closure for the conditional reaction rate of NO should be improved.     

Belief functions on real numbers

We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbers , under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The mathematics of belief functions become essentially the mathematics of probability density functions on .     

Tail Dependence from a Distributional Point of View

The dependence structure in the tails of bivariate random variables is studied by means of appropriate copulae. Weak convergence results show that these copulae are natural dependence structures for joint tail events. The results obtained apply to particular types of copulae such as archimedean copulae and the Gaussian copula. Further, connections to multivariate extreme value theory are investigated and a two-dimensional Pickands–Balkema–de Haan Theorem type is derived. Finally, a counterexample showing that the tail dependence coefficients do not completely determine the dependence structure of bivariate rare events is provided.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

Decision making in the TBM: the necessity of the pignistic transformation

In the transferable belief model (TBM), pignistic probabilities are used for decision making. The nature of the pignistic transformation is justified by a linearity requirement. We justify the origin of this requirement showing it is not ad hoc but unavoidable provides one accepts expected utility theory.     

Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process

We address estimation of parametric coefficients of a pure-jump Lévy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study (Masuda, 2013) that adopting the conventional Gaussian quasi-maximum likelihood estimator then leads to an inconsistent estimator. In this paper, under the assumption that the driving Lévy process is locally stable, we extend the Gaussian framework into a non-Gaussian counterpart, by introducing a novel quasi-likelihood function formally based on the small-time stable approximation of the unknown transition density. The resulting estimator turns out to be asymptotically mixed normally distributed without ergodicity and finite moments for a wide range of the driving pure-jump Lévy processes, showing much better theoretical performance compared with the Gaussian quasi-maximum likelihood estimator. Extensive simulations are carried out to show good estimation accuracy. The case of large-time asymptotics under ergodicity is briefly mentioned as well, where we can deduce an analogous asymptotic normality result.     

A continuous-time stochastic model for the mortality surface of multiple populations

We formulate, study and calibrate a continuous-time model for the joint evolution of the mortality surface of multiple populations. We model the mortality intensity by age and population as a mixture of stochastic latent factors, that can be either population-specific or common to all populations. These factors are described by affine time-(in)homogeneous stochastic processes. Traditional, deterministic mortality laws can be extended to multi-population stochastic counterparts within our framework. We detail the calibration procedure when factors are Gaussian, using centralized data-fusion Kalman filter. We provide an application based on the joint mortality of UK and Dutch males and females. Although parsimonious, the specification we calibrate provides a good fit of the observed mortality surface (ages 0–89) of both sexes and populations between 1960 and 2013.     

联合订货下基于ø-散度的多产品库存鲁棒优化模型

针对多产品联合库存决策问题,在市场需求不确定条件下,建立了考虑联合订货成本的多产品库存鲁棒优化模型。针对不确定市场需求,采用一系列未知概率的离散情景进行描述,给出了基于最小最大准则的鲁棒对应模型,并证明了(s,S)库存策略的最优性。进一步,在仅知多产品市场需求历史数据基础上,采用基于ø-散度的数据驱动方法构建了满足一定置信度要求的关于未知需求概率分布的不确定集。在此基础上,为获得(s,S)库存策略的相关参数,运用拉格朗日对偶方法将所建模型等价转化为易于求解的数学规划问题。最后,通过数值计算分析了Kullback-Leibler散度和Cressie-Read散度以及不同的置信水平下的多产品库存绩效,并将其与真实分布下应用鲁棒库存策略得到的库存绩效进行对比。结果表明,需求分布信息的缺失虽然会导致一定的库存绩效损失,但损失值很小,表明基于文中方法得到的库存策略能够有效抑制需求不确定性扰动,具有良好的鲁棒性。     

Bias phenomenon and compensation for PDA/JPDA algorithms

Probabilistic Data Association (PDA) and Joint PDA (JPDA) algorithms are approaches for target tracking which have received considerable attention. It has been observed for some years that they both yield biased tracks in a multitarget environment. However, most work assumes no false alarms and the rejection phenomenon of the JPDA algorithm has not been reported. In this paper, the general procedure of multitarget tracking and the PDA/JPDA algorithms are first described. Their bias phenomenon is simulated and investigated. It is observed that

(1) the JPDA algorithm has less bias than the PDA algorithm in a clean environment. Both of them yield coalescence

(2) the JPDA algorithm has coalescence and rejection bias phenomenon while the PDA algorithm has only coalescence phenomenon in a clutter environment.

Bias compensated algorithms are then presented using the polynomial regression method. Simulations are carried out to select the order of polynomial regression. Monte Carlo simulations also demonstrate the effectiveness of the compensated PDA/JPDA algorithms.     

A numerical method to price European derivatives based on the one factor LIBOR Market Model of interest rates

We consider the problem of pricing European interest rate derivatives based on the LIBOR Market Model (LMM) with one driving factor. We derive a closed-form approximation of the transition probability density functions associated to the stochastic dynamical systems that describe the behaviour of the forward LIBOR interest rates in the LMM. These approximate formulae are based on a truncated power series expansion of the solutions of the Fokker–Planck equations associated to the LMM. The approximate probability density functions obtained are used to price European interest rate derivatives using the method of discounted expectations. The resulting integrals are low dimensional when the most commonly traded European interest rate derivatives are considered, and they can be computed efficiently using elementary numerical quadrature schemes (i.e. Simpson’s rule). The algorithm obtained is very well suited for parallel computing and is tested on the problem of pricing several derivatives including an European swaption and an interest rate spread option. In both cases, the method proposed in this paper appears to be accurate (i.e. relative error of order 10⁻², 10⁻³, or even 10⁻⁴) and approximately between 278 and 63 000 times faster than previous methods based on the Monte Carlo simulation of the LMM stochastic dynamical systems.

The website http://www.econ.univpm.it/pacelli/ballestra/finance/w2 contains material that helps the understanding of this paper and makes available to the interested users the computer programs that implement the numerical method proposed.     

Nonlinear Modeling and Tracking Control of a Hydraulic Rotary Vane Actuator

Rotary vane actuators as rotational drives provide rotational movements directly because they are constructed as a joint and actuator in one. So it is possible to pass on the disadvantageous transmission kinematics used with the so far usual differential cylinders at the arms of large manipulators. However, the use of hydraulic rotary vane actuators is associated with high internal oil leakage and/or high friction. Therefore, a nonlinear dynamic model for such an actuator, driving a rigid robot arm, as well as its nonlinear control are derived. To achieve tracking control a model based control law is set up using fundamental linear differential equations for the tracking error. The control law is implemented and tested on a testbed, the produced experimental results are presented. The same control algorithm can also be used to realize nonlinear disturbance attenuation for hydraulic rotary vane actuators via tracking control. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forecasting using belief functions: An application to marketing econometrics

A method is proposed to quantify uncertainty on statistical forecasts using the formalism of belief functions. The approach is based on two steps. In the estimation step, a belief function on the parameter space is constructed from the normalized likelihood given the observed data. In the prediction step, the variable Y to be forecasted is written as a function of the parameter θ and an auxiliary random variable Z with known distribution not depending on the parameter, a model initially proposed by Dempster for statistical inference. Propagating beliefs about θ and Z through this model yields a predictive belief function on Y. The method is demonstrated on the problem of forecasting innovation diffusion using the Bass model, yielding a belief function on the number of adopters of an innovation in some future time period, based on past adoption data.     

Theory of evidence for face detection and tracking

This paper deals with face detection and tracking by computer vision for multimedia applications. Contrary to current techniques that are based on huge learning databases and complex algorithms to get generic face models (e.g., active appearance models), the proposed method handles simple contextual knowledge representative of the application background thanks to a quick supervised initialization. The transferable belief model is used to counteract the incompleteness of the prior model due first to a lack of exhaustiveness of the learning stage and secondly to the subjectivity of the task of face segmentation. The algorithm contains two main steps: detection and tracking. In the detection phase, an evidential face model is estimated by merging basic beliefs elaborated from Viola and Jones face detector and from a skin colour detector, for the assignment of mass functions. These functions are computed as the merging of sources in a specific nonlinear colour space. In order to deal with colour information dependence in the fusion process, the Den?ux cautious rule is used. The pignistic probabilities stemming from the face model guarantee the compatibility between the belief framework and the probabilistic framework. They are the entries of a bootstrap particle filter which yields face tracking at video rate. We show that the proper tuning of the evidential model parameters improves the tracking performance in real-time. Quantitative evaluation of the proposed method gives a detection rate reaching 80%, comparable to what can be found in the literature. However the proposed method requires only a weak initialization.     

Solitary waves of the EW and RLW equations

Eight finite difference methods are employed to study the solitary waves of the equal-width (EW) and regularized long–wave (RLW) equations. The methods include second-order accurate (in space) implicit and linearly implicit techniques, a three-point, fourth-order accurate, compact operator algorithm, an exponential method based on the local integration of linear, second-order ordinary differential equations, and first- and second-order accurate temporal discretizations. It is shown that the compact operator method with a Crank–Nicolson discretization is more accurate than the other seven techniques as assessed for the three invariants of the EW and RLW equations and the L₂-norm errors when the exact solution is available. It is also shown that the use of Gaussian initial conditions may result in the formation of either positive or negative secondary solitary waves for the EW equation and the formation of positive solitary waves with or without oscillating tails for the RLW equation depending on the amplitude and width of the Gaussian initial conditions. In either case, it is shown that the creation of the secondary wave may be preceded by a steepening and an narrowing of the initial condition. The creation of a secondary wave is reported to also occur in the dissipative RLW equation, whereas the effects of dissipation in the EW equation are characterized by a decrease in amplitude, an increase of the width and a curving of the trajectory of the solitary wave. The collision and divergence of solitary waves of the EW and RLW equations are also considered in terms of the wave amplitude and the invariants of these equations.