Proposed Error Function Research Articles

Synchronized Data Collection for Human Group Recognition.

It is commonplace for people to perform various kinds of activities in groups. The recognition of human groups is of importance in many applications including crowd evacuation, teamwork coordination, and advertising. Existing group recognition approaches require snapshots of human trajectories, which is often impossible in the reality due to different data collection start time and frequency, and the inherent time deviations of devices. This study proposes an approach to synchronize the data of people for group recognition. All people’s trajectory data are aligned by using data interpolating. The optimal interpolating points are computed based on our proposed error function. Moreover, the time deviations among devices are estimated and eliminated by message passing. A real-life data set is used to validate the effectiveness of the proposed approach. The results show that 97.7% accuracy of group recognition can be achieved. The approach proposed to deal with time deviations was also proven to lead to better performance compared to that of the existing approaches.

Improved small‐signal hybrid parameter‐extraction technique for AlGaN / GaN high electron mobility transistors

An improved hybrid parameter-extraction technique is proposed for the small-signal modeling application in AlGaN/GaN high electron mobility transistors (HEMTs). The capacitance partitioning characteristics of cold pinch-off GaN device with non-field-plate and field-plate structures are reinvestigated and the scanning range of parasitic capacitances Cpg and Cpd is determined. A systematic optimization approach is proposed to obtain the initial values of Cpg and Cpd. By using the global optimization algorithm, particle swarm optimization, the reliable parasitic parameters can be acquired based on the proposed error function. The validity of the developed hybrid parameter-extraction method is verified by 2 × 100 μm AlGaN/GaN HEMT with source-connected FP structure from 0.1 to 40 GHz among the 442 biasing points.

Multi-objective Cartesian Genetic Programming optimization of morphological filters in navigation systems for Visually Impaired People

Navigation systems for Visually Impaired People (VIP) have improved in the last decade, incorporating many features to ensure navigation safety. Such systems often use grayscale depth images to segment obstacles and paths according to distances. However, this approach has the common problem of unknown distances. While this can be solved with good quality morphological filters, these might be too complex and power demanding. Considering navigation systems for VIP rely on limited energy sources that have to run multiple tasks, fixing unknown distance areas without major impacts on power consumption is a definite concern. Multi-objective optimization algorithms might improve filters’ energy efficiency and output quality, which can be accomplished by means of different quality vs. complexity trade-offs. This study presents NSGA2CGP, a multi-objective optimization method that employs the NSGA-II algorithm on top of Cartesian Genetic Programming to optimize morphological filters for incomplete depth images used by navigation systems for VIP. Its goal is to minimize output errors and structuring element complexity, presenting several feasible alternatives combining different levels of filter quality and complexity—both of which affect power consumption. NSGA2CGP-optimized filters were deployed into an actual embedded platform, so as to experimentally measure power consumption and execution time. We also propose two new fitness functions based on existing approaches from literature. Results showed improvements in visual quality, performance, speed and power consumption, thanks to our proposed error function, proving NSGA2CGP as a solid method for developing and evolving efficient morphological filters.

The Synchronization of Data Collection for Real-time Group Recognition

It is commonplace for people to perform various kinds of activities in groups. The recognition of groups is of importance in many applications including crowd evacuation, teamwork coordination, and advertising for groups. Existing group recognition approaches require snapshots of human trajectories, which is often impossible in real life situation due to the differences of data collection start time and frequency. This paper proposes an approach to synchronize the trajectory data of people by interpolation based on Catmull-Rom Spline. The optimal interpolating points are computed based on our proposed error function. Moreover, we propose an approach to assign the groups proper colors and then uses the hot map to show the dynamic changes of groups graphically. A real-life data set is used to validate the effectiveness of the proposed approach. The results show that 97.9% accuracy of group recognition can be achieved and the dynamic changes of groups is well shown.

PRINCIPAL GEODESIC ANALYSIS BOUNDARY DELINEATION WITH SUPERPIXEL-BASED CONSTRAINTS

In this paper an algorithm for accurate delineation of object boundaries is proposed. The method employs a superpixel algorithm to obtain an oversegmentation of the input image, used as a constraint in the task. A shape model is built by applying Principal Geodesic Analysis on angular representation of automatically placed uniformly distant landmark points. The shape model is used to detect the boundaries of an object on a given image by iterative elongation of a partial boundary along borders of superpixels. Contrary to many state-of-the-art methods, the proposed approach does not need an initial boundary. The algorithm was tested on two natural and two synthetic sets of images. Mean Dice coefficients between 0.91 and 0.97 were obtained. In almost all cases the object was found. In areas of relatively high gradient magnitude the borders are delineated very accurately, though further research is needed to improve the accuracy in areas of low gradient magnitude and automatically select the parameters of the proposed error function.

Modeling of a greenhouse prototype using PSO and differential evolution algorithms based on a real-time LabView™ application

In general, to obtain an adequate mathematical model of a greenhouse is a difficult task due to the complexity of the involved equations that describe the dynamics of the system, and the required high number of physical parameters, which are complicated or even impossible to measure. In these situations, estimation methods are commonly used to obtain a suitable approximation for those parameters. This paper presents the application and comparison of a collection of methods based on Particle Swarm Optimization (PSO) and Differential Evolution (DE), using them as the tools to identify the parameters that complete a proposed mathematical model for a greenhouse. These parameters are sought aiming to approximate the dynamic behavior of a greenhouse physical prototype building in CINVESTAV Campus Guadalajara, by using the heuristic algorithms in order to minimize a proposed error function, which considers as arguments estimations and measurements of the two more representative dynamics of the climate conditions inside a greenhouse: namely, the air temperature and relative humidity. Different forms of PSO and DE algorithms are considered and applied in order to select the one that achieves the set of parameters with the lowest evaluation error. The comparison of the selected algorithms is carried out in an offline optimization schedule using real data recorded through the LabView™ SignalExpress application, and a real-time implementation in a LabView™ code, implemented to optimize the model in a sample to sample execution. The proposed model, with its corresponding computed parameters, is validated comparing its results against the real dynamic behavior of the temperature and relative humidity, that are measured directly from the greenhouse prototype, showing a good agreement between real and estimated values. Several tests were executed in order to find PSO and DE best calibration conditions. Experimental results allow us to propose an efficient way to deal with numerical optimization problems of high complexity, applying a two stages scheme based on a first offline pre-identification, where the obtained results are used as initial condition for an online, real-time refinement process.

A modified regularized scheme for isochromatic demodulation in RGB photoelasticity

Red-Green-Blue (RGB) photoelasticity has become popular recently owing to its ability for determining the isochromatic fringe orders by processing a single photoelastic color image. This technique employs an a priori calibrated RGB look-up table (LUT) for demodulation of colors in the analyzed image based on an error function. The demodulation is based on the minimization of the error function, which sometimes produce ambiguous fringe orders. Therefore, the initially proposed error function was improved by regularized (or refined) schemes for ambiguity-free isochromatic demodulation. The simplest regularized scheme employs horizontal scanning and left pixel fringe order continuity to remove ambiguity. This particular scheme cannot produce noise-free fringe maps in the presence of color abberations (discontinuities or noise) at the starting pixels of the rows. The available literature mostly deals with the removal of ambiguities produced due to minimization of the error function. This paper highlights the noise produced in the fringe maps due to the presence of color abberations at the starting pixels. To address this issue, an alternative scheme is proposed, wherein a modified regularized algorithm and an improved LUT calibration have been employed in tandem. Moreover, two other schemes, which are meant for ambiguity removal, have been explored for removing the color noise. The present work is observed to produce smooth and accurate fringe maps without any manual intervention to the fringe map.

A hybrid learning method composed by the orthogonal least-squares and the back-propagation learning algorithms for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic systems

The purpose of this paper is to present a hybrid learning method for interval A2-C1 type-1 non-singleton type-2 TSK fuzzy logic system that uses the recursive orthogonal least-squares algorithm to tune the type-1 consequent parameters, and the back-propagation algorithm to tune the interval type-2 antecedent parameters. Based on the combination of these two training algorithms the new hybrid learning method changes the interval type-2 fuzzy model parameters adaptively and minimizes the proposed error function as the new type-1 non-singleton input---output data pairs are processed. Its antecedent sets are interval type-2 fuzzy sets, its consequent sets are type-1 fuzzy sets, and its inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations. Comparison with the non-hybrid interval A2-C1 type-1 non-singleton type-2 Takagi---Sugeno---Kang fuzzy logic system that only uses the back-propagation algorithm for both antecedent and consequent parameter's adaptation demonstrates that the proposed hybrid algorithm is a well-performing nonlinear adaptation that enables the interval type-2 fuzzy model to optimally match the nonlinear behavior of the process. The application of the interval type-2 fuzzy logic as adaptable predictor using the proposed hybrid learning method was constructed for the modeling and prediction of the transfer bar surface temperature in an industrial hot strip mill facility. Experimental results demonstrated that this method improves the temperature prediction performance of the interval A2-C1 type-1 non-singleton type-2 Takagi---Sugeno---Kang fuzzy logic system.

Optimality of transmitter location in a wireless network with RAKE receivers

In this study, the authors consider a transmitter location finding problem in a wireless network equipped with RAKE receivers. In these types of receivers, fading is mitigated in the wireless communication channel. This fading is due to multiple versions of the transmitted signal at a spread of arrival times. In the RAKE receiver, a certain number of them are needed – called strongest – to have received signal strength above a threshold. In the optimum location finding problem, the number of bad receiving points determined based on a proposed error function is minimised. Two different criteria, which are defined through the RAKE receiver architecture, form this error function. Thus, a multi-objective optimisation problem is herein solved in order to solve transmitter location finding problem. The proposed optimisation method contains a jointly designed ray tracing engine (RTE) and genetic algorithm (GA). The algorithm is applied on a sample environment, which is fully simulated with RTE. The GA, which is integrated to RTE, determines optimum location(s) of transmitters. The results show that the proposed method perfectly finds the best locations of the minimum number of transmitters.

Optimal control problem via neural networks

This paper attempts to propose a new method based on capabilities of artificial neural networks, in function approximation, to attain the solution of optimal control problems. To do so, we try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. In the proposed error function, we used trial solutions for the trajectory function, control function and the Lagrange multipliers. These trial solutions are constructed by using neurons. Then, we minimize the error function that contains just the weights of the trial solutions. Substituting the optimal values of the weights in the trial solutions, we obtain the optimal trajectory function, optimal control function and the optimal Lagrange multipliers.

Optimum synthesis of path generating four-bar mechanisms using differential evolution and a modified error function

This paper proposes a new error function that can be used for optimum synthesis of path generating mechanisms. The proposed error function is formulated in a way that makes it suitable for use in applications when the primary requirement is that the synthesized path should match closely with the prescribed path. The proposed error function is used in the optimum synthesis of four-bar mechanisms. The method of differential evolution is used to carry out the optimization. Results for three path synthesis problems are presented. Results obtained by using the proposed error function are compared with those obtained by using the commonly used cumulative squares of Euclidean distance error function, on the basis of the values of transverse and longitudinal errors between the prescribed and synthesized paths. The usefulness of the proposed error function is established on the basis of the comparative results.

Use of a fuzzy granulation–degranulation criterion for assessing cluster validity

The identification of a suitable clustering algorithm to partition data and assessment of the validity of the resultant partitioning are ongoing quests in unsupervised learning. In this study, a fuzzy granulation–degranulation criterion is proposed to evaluate the goodness of a fuzzy partitioning of the data. This, in turn, is used to determine the appropriate clustering algorithm suitable for a particular data set. In general, the quality of a partitioning is measured by computing the variance within it, which is a measure of compactness of the obtained partitioning. Here a new error function, which reflects how well the computed cluster centers represent the whole data set, is used as the goodness measure of the obtained partitioning. Thus a clustering algorithm, providing a good set of cluster centers which approximate well the whole data set, is considered to be the most suited. Thereafter this new fuzzy granulation–degranulation criterion is used to develop six new cluster validity indices. These indices mimic the definitions of the existing and well-known cluster validity indices, such as PBM-index, XB-index, PS-index, FS-index, K-index and SV-index, but use the new fuzzy granulation–degranulation based error function instead of cluster compactness. In order to evaluate the effectiveness of the proposed error function in correctly identifying the appropriate clustering algorithm for a particular data set, eight well-known clustering algorithms, K-means, Fuzzy C-means, GAK-means (genetic algorithm based K-means algorithm), a newly developed genetic point symmetry based clustering technique (GAPS-clustering), Average Linkage clustering algorithm, Expectation Maximization (EM) clustering algorithm, Self-Organizing Map (SOM) and Spectral clustering technique are evaluated on a set of six artificially generated and six real-life data sets. Results show that GAK-means is the most appropriate for most of the data sets used for the experiments. Thereafter the effectiveness of the proposed cluster validity indices in identifying the appropriate number of clusters automatically from different data sets are shown for above mentioned 12 data sets. For the purpose of comparison, results obtained with the original versions of the proposed cluster validity indices and results obtained by a density based clustering technique are also presented.

Robust Finite-Time Consensus Tracking Algorithm for Multirobot Systems

This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Trajectory Association across Multiple Airborne Cameras

A camera mounted on an aerial vehicle provides an excellent means for monitoring large areas of a scene. Utilizing several such cameras on different aerial vehicles allows further flexibility, in terms of increased visual scope and in the pursuit of multiple targets. In this paper, we address the problem of associating objects across multiple airborne cameras. Since the cameras are moving and often widely separated, direct appearance-based or proximity-based constraints cannot be used. Instead, we exploit geometric constraints on the relationship between the motion of each object across cameras, to test multiple association hypotheses, without assuming any prior calibration information. Given our scene model, we propose a likelihood function for evaluating a hypothesized association between observations in multiple cameras that is geometrically motivated. Since multiple cameras exist, ensuring coherency in association is an essential requirement, e.g. that transitive closure is maintained between more than two cameras. To ensure such coherency we pose the problem of maximizing the likelihood function as a k-dimensional matching and use an approximation to find the optimal assignment of association. Using the proposed error function, canonical trajectories of each object and optimal estimates of inter-camera transformations (in a maximum likelihood sense) are computed. Finally, we show that as a result of associating objects across the cameras, a concurrent visualization of multiple aerial video streams is possible and that, under special conditions, trajectories interrupted due to occlusion or missing detections can be repaired. Results are shown on a number of real and controlled scenarios with multiple objects observed by multiple cameras, validating our qualitative models, and through simulation quantitative performance is also reported.

FEEDFORWARD NEURAL NETWORK MODELS FOR HANDLING CLASS OVERLAP AND CLASS IMBALANCE

This paper proposes a framework for training feedforward neural network models capable of handling class overlap and imbalance by minimizing an error function that compensates for such imperfections of the training set. A special case of the proposed error function can be used for training variance-controlled neural networks (VCNNs), which are developed to handle class overlap by minimizing an error function involving the class-specific variance (CSV) computed at their outputs. Another special case of the proposed error function can be used for training class-balancing neural networks (CBNNs), which are developed to handle class imbalance by relying on class-specific correction (CSC). VCNNs and CBNNs are compared with conventional feedforward neural networks (FFNNs), quantum neural networks (QNNs), and resampling techniques. The properties of VCNNs and CBNNs are illustrated by experiments on artificial data. Various experiments involving real-world data reveal the advantages offered by VCNNs and CBNNs in the presence of class overlap and class imbalance.

Adaptive fuzzy PIMD controller for systems with uncertain deadzones

In this paper, a new adaptive fuzzy Proportional-Integral (of a modified error function)-Derivative (PIMD) controller is designed for systems with uncertain deadzones. Instead of using the summation of the system output error to be one of the input variables, the fuzzy mechanism in PIMD controller takes the summation of a proposed error function as one essential part of the output fuzzy singleton. Together, with the linearly combined error and difference of the error as the only input variables, the complexity reduced fuzzy mechanism of the fuzzy PIMD controller is constructed. The adaptation processes are provided to determine the parameters of the PIMD controller to reduce the overshoot and to accelerate the system with deadzone to the desired output. The fuzzy PIMD controller is indicated to be flexible to the variations of deadzone parameters. Also, the proposed fuzzy PIMD controller is flexible to the change of deadzone model to contain jump discontinuity points. Moreover, the fuzzy PIMD controller can perform well for the system with time-varying deadzone model. Simulation results are included to indicate the effectiveness of the adaptive fuzzy PIMD controller.

A new error function at hidden layers for fast training of multilayer perceptrons

This letter proposes a new error function at hidden layers to speed up the training of multilayer perceptrons (MLP's). With this new hidden error function, the layer-by-layer (LBL) algorithm approximately converges to the error backpropagation algorithm with optimum learning rates. Especially, the optimum learning rate for a hidden weight vector appears approximately as a multiplication of two optimum factors, one for minimizing the new hidden error function and the other for assigning hidden targets. Effectiveness of the proposed error function was demonstrated for handwritten digit recognition and isolated-word recognition tasks. Very fast learning convergence was obtained for MLP's without the stalling problem experienced in conventional LBL algorithms.

Model reduction for continuous- and discrete-time systems via squared-magnitude responses matching by linear programming

The use of linear programming technique for the model reduction of continuous-and discrete-time systems is discussed. Based on squared-magnitude responses between the original system and its reduced model, a novel error function is presented. Two linear programming formulations are presented that use the L1-norm and the L∞;-norm of the proposed error function as respective criteria to solve the squared-magnitude matching problem. Finally, the reduced model is obtained by applying the factorization technique. Since the poles of the obtained squared-magnitude function are prevented from occurring on the JΩ axis (continuous-time case) or unit circle (discrete-time case) by constraint, this approach ensures the stability of the reduced model. Some examples illustrate its applicability.