In this work, we introduce theaverage top-$k$k($\mathrm {AT}_k$) loss, which is the average over the$k$largest individual losses over a training data, as a new aggregate loss for supervised learning. We show that the$\mathrm {AT}_k$loss is a natural generalization of the two widely used aggregate losses, namely the average loss and the maximum loss. Yet, the$\mathrm {AT}_k$loss can better adapt to different data distributions because of the extra flexibility provided by the different choices of$k$. Furthermore, it remains a convex function over all individual losses and can be combined with different types of individual loss without significant increase in computation. We then provide interpretations of the$\mathrm {AT}_k$loss from the perspective of the modification of individual loss and robustness to training data distributions. We further study the classification calibration of the$\mathrm {AT}_k$loss and the error bounds of$\mathrm {AT}_k$-SVM model. We demonstrate the applicability of minimum average top-$k$learning for supervised learning problems including binary/multi-class classification and regression, using experiments on both synthetic and real datasets.

Great progress has been achieved in domain adaptation in decades. Existing works are always based on an ideal assumption that testing target domains are independent and identically distributed with training target domains. However, due to unpredictable corruptions (e.g., noise and blur) in real data, such as web images and real-world object detection, domain adaptation methods are increasingly required to be corruption robust on target domains. We investigate a new task, corruption-agnostic robust domain adaptation (CRDA), to be accurate on original data and robust against unavailable-for-training corruptions on target domains. This task is non-trivial due to the large domain discrepancy and unsupervised target domains. We observe that simple combinations of popular methods of domain adaptation and corruption robustness have suboptimal CRDA results. We propose a new approach based on two technical insights into CRDA, as follows: (1) an easy-to-plug module called domain discrepancy generator (DDG) that generates samples that enlarge domain discrepancy to mimic unpredictable corruptions; (2) a simple but effective teacher-student scheme with contrastive loss to enhance the constraints on target domains. Experiments verify that DDG maintains or even improves its performance on original data and achieves better corruption robustness than baselines. Our code is available at: https://github.com/YifanXu74/CRDA .

Distinguishing aesthetically pleasing food photos from others is an important visual analysis task for social media and ranking systems related to food. Nevertheless, aesthetic assessment of food images remains a challenging and relatively unexplored task, largely due to the lack of related food image datasets and practical knowledge. Thus, we present the Gourmet Photography Dataset (GPD), the first large-scale dataset for aesthetic assessment of food photos. It contains 24,000 images with corresponding binary aesthetic labels, covering a large variety of foods and scenes. We also provide a non-stationary regularization method to combat over-fitting and enhance the ability of tuned models to generalize. Quantitative results from extensive experiments, including a generalization ability test, verify that neural networks trained on the GPD achieve comparable performance to human experts on the task of aesthetic assessment. We reveal several valuable findings to support further research and applications related to visual aesthetic analysis of food images. To encourage further research, we have made the GPD publicly available at https://github.com/Openning07/GPA .

The ability to learn more concepts from incrementally arriving data over time is essential for the development of a lifelong learning system. However, deep neural networks often suffer from forgetting previously learned concepts when continually learning new concepts, which is known as the catastrophic forgetting problem. The main reason for catastrophic forgetting is that past concept data are not available, and neural weights are changed during incrementally learning new concepts. In this article, we propose an incremental concept learning framework that includes two components, namely, ICLNet and RecallNet. ICLNet, which consists of a trainable feature extractor and a dynamic concept memory matrix, aims to learn new concepts incrementally. We propose a concept-contrastive loss to alleviate the magnitude of neural weight changes and mitigate the catastrophic forgetting problems. RecallNet aims to consolidate old concepts memory and recall pseudo samples, whereas ICLNet learns new concepts. We propose a balanced online memory recall strategy to reduce the information loss of old concept memory. We evaluate the proposed approach on the MNIST, Fashion-MNIST, and SVHN data sets and compare it with other pseudorehearsal-based approaches. Extensive experiments demonstrate the effectiveness of our approach.

Visual aesthetic assessment has been an active research field for decades. Although latest methods have achieved promising performance on benchmark datasets, they typically rely on a large number of manual annotations including both aesthetic labels and related image attributes. In this paper, we revisit the problem of image aesthetic assessment from the self-supervised feature learning perspective. Our motivation is that a suitable feature representation for image aesthetic assessment should be able to distinguish different expert-designed image manipulations, which have close relationships with negative aesthetic effects. To this end, we design two novel pretext tasks to identify the types and parameters of editing operations applied to synthetic instances. The features from our pretext tasks are then adapted for a one-layer linear classifier to evaluate the performance in terms of binary aesthetic classification. We conduct extensive quantitative experiments on three benchmark datasets and demonstrate that our approach can faithfully extract aesthetics-aware features and outperform alternative pretext schemes. Moreover, we achieve comparable results to state-of-the-art supervised methods that use 10 million labels from ImageNet.

Facial action unit (AU) intensity is an index to characterize human expressions. Accurate AU intensity estimation depends on three major elements: image representation, intensity estimator, and supervisory information. Most existing methods learn intensity estimator with fixed image representation, and rely on the availability of fully annotated supervisory information. In this paper, a novel general framework for AU intensity estimation is presented, which differs from traditional estimation methods in two aspects. First, rather than keeping image representation fixed, it simultaneously learns representation and intensity estimator to achieve an optimal solution. Second, it allows incorporating weak supervisory training signal from human knowledge (e.g. feature smoothness, label smoothness, label ranking, and positive label), which makes our model trainable even fully annotated information is not available. More specifically, human knowledge is represented as either soft or hard constraints which are encoded as regularization terms or equality/inequality constraints, respectively. On top of our novel framework, we additionally propose an efficient algorithm for optimization based on Alternating Direction Method of Multipliers (ADMM). Evaluations on two benchmark databases show that our method outperforms competing methods under different ratios of AU intensity annotations, especially for small ratios.

In this work, we propose a novel meta-learning approach for few-shot classification, which learns transferable prior knowledge across tasks and directly produces network parameters for similar unseen tasks with training samples. Our approach, called LGM-Net, includes two key modules, namely, TargetNet and MetaNet. The TargetNet module is a neural network for solving a specific task and the MetaNet module aims at learning to generate functional weights for TargetNet by observing training samples. We also present an intertask normalization strategy for the training process to leverage common information shared across different tasks. The experimental results on Omniglot and miniImageNet datasets demonstrate that LGM-Net can effectively adapt to similar unseen tasks and achieve competitive performance, and the results on synthetic datasets show that transferable prior knowledge is learned by the MetaNet module via mapping training data to functional weights. LGM-Net enables fast learning and adaptation since no further tuning steps are required compared to other meta-learning approaches

Facial action unit (AU) intensity estimation plays an important role in affective computing and human-computer interaction. Recent works have introduced deep neural networks for AU intensity estimation, but they require a large amount of intensity annotations. AU annotation needs strong domain expertise and it is expensive to construct a large database to learn deep models. We propose a novel knowledge-based semi-supervised deep convolutional neural network for AU intensity estimation with extremely limited AU annotations. Only the intensity annotations of peak and valley frames in training sequences are needed. To provide additional supervision for model learning, we exploit naturally existing constraints on AUs, including relative appearance similarity, temporal intensity ordering, facial symmetry, and contrastive appearance difference. Experimental evaluations are performed on two public benchmark databases. With around 2% of intensity annotations in FERA 2015 and around 1% in DISFA for training, our method can achieve comparable or even better performance than the state-of-the-art methods which use 100% of intensity annotations in the training set.

Facial action units (AUs) play an important role in human emotion understanding. One big challenge for data-driven AU recognition approaches is the lack of enough AU annotations, since AU annotation requires strong domain expertise. To alleviate this issue, we propose a knowledge-driven method for jointly learning multiple AU classifiers without any AU annotation by leveraging prior probabilities on AUs, including expression-independent and expression-dependent AU probabilities. These prior probabilities are drawn from facial anatomy and emotion studies, and are independent of datasets. We incorporate the prior probabilities on AUs as the constraints into the objective function of multiple AU classifiers, and develop an efficient learning algorithm to solve the formulated problem. Experimental results on five benchmark expression databases demonstrate the effectiveness of the proposed method, especially its generalization ability, and the power of the prior probabilities.

Automatic intensity estimation of facial action units (AUs) is challenging in two aspects. First, capturing subtle changes of facial appearance is quite difficult. Second, the annotation of AU intensity is scarce and expensive. Intensity annotation requires strong domain knowledge thus only experts are qualified. The majority of methods directly apply supervised learning techniques to AU intensity estimation while few methods exploit unlabeled samples to improve the performance. In this paper, we propose a novel weakly supervised regression model-Bilateral Ordinal Relevance Multi-instance Regression (BORMIR), which learns a frame-level intensity estimator with weakly labeled sequences. From a new perspective, we introduce relevance to model sequential data and consider two bag labels for each bag. The AU intensity estimation is formulated as a joint regressor and relevance learning problem. Temporal dynamics of both relevance and AU intensity are leveraged to build connections among labeled and unlabeled image frames to provide weak supervision. We also develop an efficient algorithm for optimization based on the alternating minimization framework. Evaluations on three expression databases demonstrate the effectiveness of the proposed method.

Aggregation structures with explicit information, such as image attributes and scene semantics, are effective and popular for intelligent systems for assessing aesthetics of visual data. However, useful information may not be available due to the high cost of manual annotation and expert design. In this paper, we present a novel multi-patch (MP) aggregation method for image aesthetic assessment. Different from state-of-the-art methods, which augment an MP aggregation network with various visual attributes, we train the model in an end-to-end manner with aesthetic labels only (i.e., aesthetically positive or negative). We achieve the goal by resorting to an attention-based mechanism that adaptively adjusts the weight of each patch during the training process to improve learning efficiency. In addition, we propose a set of objectives with three typical attention mechanisms (i.e., average, minimum, and adaptive) and evaluate their effectiveness on the Aesthetic Visual Analysis (AVA) benchmark. Numerical results show that our approach outperforms existing methods by a large margin. We further verify the effectiveness of the proposed attention-based objectives via ablation studies and shed light on the design of aesthetic assessment systems.

The correntropy-induced loss (C-loss) function has the nice property of being robust to outliers. In this paper, we study the C-loss kernel classifier with the Tikhonov regularization term, which is used to avoid overfitting. After using the half-quadratic optimization algorithm, which converges much faster than the gradient optimization algorithm, we find out that the resulting C-loss kernel classifier is equivalent to an iterative weighted least square support vector machine (LS-SVM). This relationship helps explain the robustness of iterative weighted LS-SVM from the correntropy and density estimation perspectives. On the large-scale data sets which have low-rank Gram matrices, we suggest to use incomplete Cholesky decomposition to speed up the training process. Moreover, we use the representer theorem to improve the sparseness of the resulting C-loss kernel classifier. Experimental results confirm that our methods are more robust to outliers than the existing common classifiers.

Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by the minimizer function. Existing methods usually pursue this by artificially designing the explicit form of SPL regularizer. In this paper, we study a group of new regularizer (named self-paced implicit regularizer) that is deduced from robust loss function. Based on the convex conjugacy theory, the minimizer function for self-paced implicit regularizer can be directly learned from the latent loss function, while the analytic form of the regularizer can be even unknown. A general framework (named SPL-IR) for SPL is developed accordingly. We demonstrate that the learning procedure of SPL-IR is associated with latent robust loss functions, thus can provide some theoretical insights for its working mechanism. We further analyze the relation between SPL-IR and half-quadratic optimization and provide a group of self-paced implicit regularizer. Finally, we implement SPL-IR to both supervised and unsupervised tasks, and experimental results corroborate our ideas and demonstrate the correctness and effectiveness of implicit regularizers.

In this work, we introduce the average top-$k$ (\atk) loss as a new ensemble loss for supervised learning. The \atk loss provides a natural generalization of the two widely used ensemble losses, namely the average loss and the maximum loss. Furthermore, the \atk loss combines the advantages of them and can alleviate their corresponding drawbacks to better adapt to different data distributions. We show that the \atk loss affords an intuitive interpretation that reduces the penalty of continuous and convex individual losses on correctly classified data. The \atk loss can lead to convex optimization problems that can be solved effectively with conventional sub-gradient based method. We further study the Statistical Learning Theory of \matk by establishing its classification calibration and statistical consistency of \matk which provide useful insights on the practical choice of the parameter $k$. We demonstrate the applicability of \matk learning combined with different individual loss functions for binary and multi-class classification and regression using synthetic and real datasets.

This review examines the relevance of parameter identifiability for statistical models used in machine learning. In addition to defining main concepts, we address several issues of identifiability closely related to machine learning, showing the advantages and disadvantages of state-of-the-art research and demonstrating recent progress. First, we review criteria for determining the parameter structure of models from the literature. This has three related issues: parameter identifiability, parameter redundancy, and reparameterization. Second, we review the deep influence of identifiability on various aspects of machine learning from theoretical and application viewpoints. In addition to illustrating the utility and influence of identifiability, we emphasize the interplay among identifiability theory, machine learning, mathematical statistics, information theory, optimization theory, information geometry, Riemann geometry, symbolic computation, Bayesian inference, algebraic geometry, and others. Finally, we present a new perspective together with the associated challenges.

This paper presents a data-driven approach for automatically generating cartoon faces in different styles from a given portrait image. Our stylization pipeline consists of two steps: an offline analysis step to learn about how to select and compose facial components from the databases; a runtime synthesis step to generate the cartoon face by assembling parts from a database of stylized facial components. We propose an optimization framework that, for a given artistic style, simultaneously considers the desired image-cartoon relationships of the facial components and a proper adjustment of the image composition. We measure the similarity between facial components of the input image and our cartoon database via image feature matching, and introduce a probabilistic framework for modeling the relationships between cartoon facial components. We incorporate prior knowledge about image-cartoon relationships and the optimal composition of facial components extracted from a set of cartoon faces to maintain a natural, consistent, and attractive look of the results. We demonstrate generality and robustness of our approach by applying it to a variety of portrait images and compare our output with stylized results created by artists via a comprehensive user study.

Unsupervised ranking faces one critical challenge in evaluation applications, that is, no ground truth is available. While PageRank and its variants show a good solution in related objects, they are applicable only for ranking from link-structure data. In this work, we focus on unsupervised ranking from multi-attribute data which is also common in evaluation tasks. To overcome the challenge, we propose five essential meta-rules for the design and assessment of unsupervised ranking approaches: scale and translation invariance, strict monotonicity, compatibility of linearity and nonlinearity, smoothness, and explicitness of parameter size. These meta-rules are regarded as high level knowledge for unsupervised ranking tasks. Inspired by the works in [2] and [6], we propose a ranking principal curve (RPC) model, which learns a one-dimensional manifold function to perform unsupervised ranking tasks on multi-attribute observations. Furthermore, the RPC is modeled to be a cubic Bézier curve with control points restricted in the interior of a hypercube, complying with all the five meta-rules to infer a reasonable ranking list. With control points as model parameters, one is able to understand the learned manifold and to interpret and visualize the ranking results. Numerical experiments of the presented RPC model are conducted on two open datasets of different ranking applications. In comparison with the state-of-the-art approaches, the new model is able to show more reasonable ranking lists.

This work is a further study on the Generalized Constraint Neural Network (GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to embed any type of prior information and to select its imposing schemes. The work focuses on the second challenge and studies a new constraint imposing scheme for equality constraints. A new method called locally imposing function (LIF) is proposed to provide a local correction to the GCNN prediction function, which therefore falls within Locally Imposing Scheme (LIS). In comparison, the conventional Lagrange multiplier method is considered as Globally Imposing Scheme (GIS) because its added constraint term exhibits a global impact to its objective function. Two advantages are gained from LIS over GIS. First, LIS enables constraints to fire locally and explicitly in the domain only where they need on the prediction function. Second, constraints can be implemented within a network setting directly. We attempt to interpret several constraint methods graphically from a viewpoint of the locality principle. Numerical examples confirm the advantages of the proposed method. In solving boundary value problems with Dirichlet and Neumann constraints, the GCNN model with LIF is possible to achieve an exact satisfaction of the constraints.

In this paper, we propose to deal with the problems of logistic regression with outliers and class imbalance, which are common in a wide range of practical applications. The robust bounded logistic regression with different error costs is developed to reduce the combined influence of outliers and class imbalance. First, inspired by the Correntropy induced loss function, we develop the bounded logistic loss function which is a monotonic, bounded and nonconvex loss and thus robust to outliers. With the bounded logistic loss, we construct a new robust logistic regression. Second, under the principle of cost-sensitive learning, we assign different error costs for different classes in order to reduce the sensitiveness of the new robust logistic regression to class imbalance. Using the half-quadratic optimization method, it is easy to optimize the proposed logistic regression model. Experimental results demonstrate that our proposed method improves the performance of logistic regression on the datasets with outliers and class imbalance.

Marginal histograms provide valuable information for various computer vision problems. However, current image restoration methods do not fully exploit the potential of marginal histograms, in particular, their role as ensemble constraints on the marginal statistics of the restored image. In this paper, we introduce a new framework, UniHIST, to incorporate marginal histogram constraints into image restoration. The key idea of UniHIST is to minimize the discrepancy between the marginal histograms of the restored image and the reference histograms in pixel or gradient domains using the quadratic Wasserstein (W2) distance. The W2distance can be computed directly from data without resorting to density estimation. It provides a differentiable metric between marginal histograms and allows easy integration with existing image restoration methods. We demonstrate the effectiveness of UniHIST through denoising of pattern images and non-blind deconvolution of natural images. We show that UniHIST enhances restoration performance and leads to visual and quantitative improvements over existing state-of-the-art methods.

Several important classes of images such as text, barcode and pattern images have the property that pixels can only take a distinct subset of values. This knowledge can benefit the restoration of such images, but it has not been widely considered in current restoration methods. In this work, we describe an effective and efficient approach to incorporate the knowledge of distinct pixel values of the pristine images into the general regularized least squares restoration framework. We introduce a new regularizer that attains zero at the designated pixel values and becomes a quadratic penalty function in the intervals between them. When incorporated into the regularized least squares restoration framework, this regularizer leads to a simple and efficient step that resembles and extends the rounding operation, which we term as soft-rounding. We apply the soft-rounding enhanced solution to the restoration of binary text/barcode images and pattern images with multiple distinct pixel values. Experimental results show that soft-rounding enhanced restoration methods achieve significant improvement in both visual quality and quantitative measures (PSNR and SSIM). Furthermore, we show that this regularizer can also benefit the restoration of general natural images.

This paper describes a progress of the previous study on the generalized constraint neural networks (GCNN). The GCNN model aims to utilize any type of priors in an explicate form so that the model can achieve improved performance and better transparency. A specific type of priors, that is, equality function constraints, is investigated in this work. When the existing approaches impose the constrains in a discretized means on the given function, our approach, called GCNN-EF, is able to satisfy the constrain perfectly and completely on the equation. We realize GCNN-EF by a weighted combination of the output of the conventional radial basis function neural network (RBFNN) and the output expressed by the constraints. Numerical studies are conducted on three synthetic data sets in comparing with other existing approaches. Simulation results demonstrate the benefit and efficiency using GCNN-EF.

The study of face alignment has been an area of intense research in computer vision, with its achievements widely used in computer graphics applications. The performance of various face alignment methods is often image-dependent or somewhat random because of their own strategy. This study aims to develop a method that can select an input image with good face alignment results from many results produced by a single method or multiple ones. The task is challenging because different face alignment results need to be evaluated without any ground truth. This study addresses this problem by designing a feasible feature extraction scheme to measure the quality of face alignment results. The feature is then used in various machine learning algorithms to rank different face alignment results. Our experiments show that our method is promising for ranking face alignment results and is able to pick good face alignment results, which can enhance the overall performance of a face alignment method with a random strategy. We demonstrate the usefulness of our ranking-enhanced face alignment algorithm in two practical applications: face cartoon stylization and digital face makeup.

Unsupervised ranking faces one critical challenge in evaluation applications, that is, no ground truth is available. When PageRank and its variants show a good solution in related objects, they are applicable only for ranking from link-structure data. In this work, we focus on unsupervised ranking from multi-attribute data which is also common in evaluation tasks. To overcome the challenge, we propose five essential meta-rules for the design and assessment of unsupervised ranking approaches: scale and translation invariance, strict monotonicity, compatibility of linearity and nonlinearity, smoothness, and explicitness of parameter size. These meta-rules are regarded as high level knowledge for unsupervised ranking tasks. Inspired by the works in [12] and [35], we propose a ranking principal curve (RPC) model, which learns a one-dimensional manifold function to perform unsupervised ranking tasks on multi-attribute observations. Furthermore, the RPC is modeled to be a cubic Bezier curve with control points restricted in the interior of a hypercube, complying with all the five meta-rules to infer a reasonable ranking list. With control points as model parameters, one is able to understand the learned manifold and to interpret and visualize the ranking results. Numerical experiments of the presented RPC model are conducted on two open datasets of different ranking applications. In comparison with the state-of-the-art approaches, the new model is able to show more reasonable ranking lists.

This paper presents a new non-blind image restoration method based on the symmetric generalized Pareto (SGP) prior, which models the heavy-tailed distributions of gradients for natural images. Through experiments we show that the SGP model achieves log likelihood scores comparable to the hyper-Laplacian model when fitted to gradients and other band-pass filter responses. More importantly, when incorporated into a Bayesian MAP framework for non-blind image restoration, the SGP model leads to a closed-form solution for a per-pixel subproblem, which affords computational advantages in comparison with the numerical solutions induced from the hyper-Laplacian model. Experimental results show that our method is comparable to existing methods in restoration quality and processing speed.

In multi-label learning, each sample can be assigned to multiple class labels simultaneously. In this work, we focus on the problem of multi-label learning with missing labels (MLML), where instead of assuming a complete label assignment is provided for each sample, only partial labels are assigned with values, while the rest are missing or not provided. The positive (presence), negative (absence) and missing labels are explicitly distinguished in MLML. We formulate MLML as a transductive learning problem, where the goal is to recover the full label assignment for each sample by enforcing consistency with available label assignments and smoothness of label assignments. Along with an exact solution, we also provide an effective and efficient approximated solution. Our method shows much better performance than several state-of-the-art methods on several benchmark data sets.

Structural identifiability (SI) is a fundamental prerequisite for system modeling and parameter estimation. It concerns theoretical uniqueness of model parameters determined from ideal model structure and error-free input-output observations. In this work, we present an identifying function (IF) approach for examining SI of parameter learning machines with the help of Rank Theorem in Riemann geometry. The resulting theorem works by checking the rank of the derivative matrix (DM) of IF. Further, based on the DM, an analytic method for constructing identifiable independent parametric functions is presented. The relationship of structural nonidentifiability, parameter redundancy and parameter dependence is therefore clarified. Several model examples from the literature are presented to examine their identifiability property.

In this paper, we present an asymmetric stagewise least square (ASLS) loss function for imbalanced classification. While keeping all the advantages of the stagewise least square (SLS) loss function, such as, better robustness, computational efficiency and sparseness, the ASLS loss extends the SLS loss by adding another two parameters, namely, ramp coefficient and margin coefficient. Therefore, asymmetric ramps and margins can be formed which makes the ASLS loss be more flexible and appropriate for processing class imbalance problems. A reduced kernel classifier of the ASLS loss is also developed which only uses a small part of the dataset to generate an efficient nonlinear classifier. Experimental results confirm the effectiveness of the ASLS loss in imbalanced classification.

In this work, we define cost-free learning (CFL) formally in comparison with cost-sensitive learning (CSL). The main difference between them is that a CFL approach seeks optimal classification results without requiring any cost information, even in the class imbalance problem. In fact, several CFL approaches exist in the related studies, such as sampling and some criteria-based approaches. However, to our best knowledge, none of the existing CFL and CSL approaches are able to process the abstaining classifications properly when no information is given about errors and rejects. Based on information theory, we propose a novel CFL which seeks to maximize normalized mutual information of the targets and the decision outputs of classifiers. Using the strategy, we can handle binary/multi-class classifications with/without abstaining. Significant features are observed from the new strategy. While the degree of class imbalance is changing, the proposed strategy is able to balance the errors and rejects accordingly and automatically. Another advantage of the strategy is its ability of deriving optimal rejection thresholds for abstaining classifications and the “equivalent” costs in binary classifications. The connection between rejection thresholds and ROC curve is explored. Empirical investigation is made on several benchmark data sets in comparison with other existing approaches. The classification results demonstrate a promising perspective of the strategy in machine learning.

In this paper, both Bayesian and mutual-information classifiers are examined for binary classifications with or without a reject option. The general decision rules are derived for Bayesian classifiers with distinctions on error types and reject types. A formal analysis is conducted to reveal the parameter redundancy of cost terms when abstaining classifications are enforced. The redundancy implies an intrinsic problem of nonconsistency for interpreting cost terms. If no data are given to the cost terms, we demonstrate the weakness of Bayesian classifiers in class-imbalanced classifications. On the contrary, mutual-information classifiers are able to provide an objective solution from the given data, which shows a reasonable balance among error types and reject types. Numerical examples of using two types of classifiers are given for confirming the differences, including the extremely class-imbalanced cases. Finally, we briefly summarize the Bayesian and mutual-information classifiers in terms of their application advantages and disadvantages, respectively.

In this paper, we focus on face clustering in videos. Given the detected faces from real-world videos, we partition all faces into K disjoint clusters. Different from clustering on a collection of facial images, the faces from videos are organized as face tracks and the frame index of each face is also provided. As a result, many pair wise constraints between faces can be easily obtained from the temporal and spatial knowledge of the face tracks. These constraints can be effectively incorporated into a generative clustering model based on the Hidden Markov Random Fields (HMRFs). Within the HMRF model, the pair wise constraints are augmented by label-level and constraint-level local smoothness to guide the clustering process. The parameters for both the unary and the pair wise potential functions are learned by the simulated field algorithm, and the weights of constraints can be easily adjusted. We further introduce an efficient clustering framework specially for face clustering in videos, considering that faces in adjacent frames of the same face track are very similar. The framework is applicable to other clustering algorithms to significantly reduce the computational cost. Experiments on two face data sets from real-world videos demonstrate the significantly improved performance of our algorithm over state-of-the art algorithms.

We describe a novel method that simultaneously clusters and associates short sequences of detected faces (termed as face track lets) in videos. The rationale of our method is that face track let clustering and linking are related problems that can benefit from the solutions of each other. Our method is based on a hidden Markov random field model that represents the joint dependencies of cluster labels and track let linking associations. We provide an efficient algorithm based on constrained clustering and optimal matching for the simultaneous inference of cluster labels and track let associations. We demonstrate significant improvements on the state-of-the-art results in face tracking and clustering performances on several video datasets.

Information Geometry Metric Learning (IGML) is shown to be an effective algorithm for distance metric learning. In this paper, we attempt to alleviate two limitations of IGML: (A) the time complexity of IGML increases rapidly for high dimensional data, (B) IGML has to transform the input low rank kernel into a full-rank one since it is undefined for singular matrices. To this end, two novel algorithms, referred to as Efficient Information Geometry Metric Learning (EIGML) and Scalable Information Geometry Metric Learning (SIGML), are proposed. EIGML scales linearly with the dimensionality, resulting in significantly reduced computational complexity. As for SIGML, it is proven to have a range-space preserving property. Following this property, SIGML is found to be capable of handling both full-rank and low-rank kernels. Additionally, the geometric information from data is further exploited in SIGML. In contrast to most existing metric learning methods, both EIGML and SIGML have closed-form solutions and can be efficiently optimized. Experimental results on various data sets demonstrate that the proposed methods outperform the state-of-the-art metric learning algorithms.

This paper proposes a novel nonnegative sparse representation approach, called two-stage sparse representation (TSR), for robust face recognition on a large-scale database. Based on the divide and conquer strategy, TSR decomposes the procedure of robust face recognition into outlier detection stage and recognition stage. In the first stage, we propose a general multisubspace framework to learn a robust metric in which noise and outliers in image pixels are detected. Potential loss functions, including L1 , L2,1, and correntropy are studied. In the second stage, based on the learned metric and collaborative representation, we propose an efficient nonnegative sparse representation algorithm to find an approximation solution of sparse representation. According to the L1 ball theory in sparse representation, the approximated solution is unique and can be optimized efficiently. Then a filtering strategy is developed to avoid the computation of the sparse representation on the whole large-scale dataset. Moreover, theoretical analysis also gives the necessary condition for nonnegative least squares technique to find a sparse solution. Extensive experiments on several public databases have demonstrated that the proposed TSR approach, in general, achieves better classification accuracy than the state-of-the-art sparse representation methods. More importantly, a significant reduction of computational costs is reached in comparison with sparse representation classifier; this enables the TSR to be more suitable for robust face recognition on a large-scale dataset.

In this paper, a novel approach, namely Globality and Locality Preserving Projections (GLPP), is proposed in the study of dimensionality reduction. The method is designed to combine the ideas behind Locality Preserving (LP), Discriminating Power (DP) and Maximally Collapsing Metric Learning (MCML), resulting in a unified model. Several distinguished features are obtained from the integration design. First, the method is able to take into account both global and local information of the data set. We introduce a new formula for calculating the conditional probabilities, which can remove the locality distortions from MCML. Second, discrimination information is applied so that a projection matrix is formed which can collapse all data points of the same class closer together, while pushing points of different classes further away. Third, the proposed method guarantees a supervised convex algorithm, which is a critical feature in data processing. Furthermore on this concern, GLPP is mapped to a Graphics Processor Unit (GPU) architecture in the implementation to be appropriate for large scale data sets. Several numerical studies are conducted on a variety of data sets. The numerical results confirm that GLPP consistently outperforms most up-to-date methods, allowing high classification accuracy, good visualization and sharply decreased consuming time.

Feature selection is fundamental to knowledge discovery from massive amount of high-dimensional data. In an effort to establish theoretical justification for feature selection algorithms, this paper presents a theoretically optimal criterion, namely, the discriminative optimal criterion (DoC) for feature selection. Compared with the existing representative optimal criterion (RoC, [CHECK END OF SENTENCE]) which retains maximum information for modeling the relationship between input and output variables, DoC is pragmatically advantageous because it attempts to directly maximize the classification accuracy and naturally reflects the Bayes error in the objective. To make DoC computationally tractable for practical tasks, we propose an algorithmic framework, which selects a subset of features by minimizing the Bayes error rate estimated by a nonparametric estimator. A set of existing algorithms as well as new ones can be derived naturally from this framework. As an example, we show that the Relief algorithm [CHECK END OF SENTENCE] greedily attempts to minimize the Bayes error estimated by the k-Nearest-Neighbor (kNN) method. This new interpretation insightfully reveals the secret behind the family of margin-based feature selection algorithms [CHECK END OF SENTENCE], [CHECK END OF SENTENCE] and also offers a principled way to establish new alternatives for performance improvement. In particular, by exploiting the proposed framework, we establish the Parzen-Relief (P-Relief) algorithm based on Parzen window estimator, and the MAP-Relief (M-Relief) which integrates label distribution into the max-margin objective to effectively handle imbalanced and multiclass data. Experiments on various benchmark data sets demonstrate the effectiveness of the proposed algorithms.

Mean-Shift (MS) is a powerful nonparametric clustering method. Although good accuracy can be achieved, its computational cost is particularly expensive even on moderate data sets. In this paper, for the purpose of algorithmic speedup, we develop an agglomerative MS clustering method along with its performance analysis. Our method, namely Agglo-MS, is built upon an iterative query set compression mechanism which is motivated by the quadratic bounding optimization nature of MS algorithm. The whole framework can be efficiently implemented in linear running time complexity. We then extend Agglo-MS into an incremental version which performs comparably to its batch counterpart. The efficiency and accuracy of Agglo-MS are demonstrated by extensive comparing experiments on synthetic and real data sets.

This paper describes an interactive system, called "Idiot Pencil", that enables users to design pencil drawings directly from 3D polygonal models. The potential users of the system are professional designers or non-professional users. The system will automatically generates feature strokes, and provides fast and easy-to-use tools for hatching stroke design. Users only need to specify hatching carriers according to their experiences or intentions. The hatching tools can perceive hatching regions and arrange hatching strokes automatically. In this way, the system allocates most of manual, yet tedious works to the computer while retaining aesthetic control for users. Compared with the existing manual pencil drawing method, the system can speed up the user's drawing and reduce their drawing skill requirements. Several examples of drawings are given by the Idiot Pencil system. The compelling features are obtained from viewpoints of both handcrafted effect and high efficiency when using the computer-aided drawing system.

An informative and discriminative graph plays an important role in the graph-based semi-supervised learning methods. This paper introduces a nonnegative sparse algorithm and its approximated algorithm based on the l0-l1equivalence theory to compute the nonnegative sparse weights of a graph. Hence, the sparse probability graph (SPG) is termed for representing the proposed method. The nonnegative sparse weights in the graph naturally serve as clustering indicators, benefiting for semi-supervised learning. More important, our approximation algorithm speeds up the computation of the nonnegative sparse coding, which is still a bottle-neck for any previous attempts of sparse non-negative graph learning. And it is much more efficient than using l1-norm sparsity technique for learning large scale sparse graph. Finally, for discriminative semi-supervised learning, an adaptive label propagation algorithm is also proposed to iteratively predict the labels of data on the SPG. Promising experimental results show that the nonnegative sparse coding is efficient and effective for discriminative semi-supervised learning.

This work presents a novel clustering algorithm, named Adaptive Information Theoretic Clustering (AITC). Specific adaptations concerned in AITC are densities and neighbors. Based on the utilization of the within/between information potential, the proposed algorithm is easily computable and carries an intuitive interpretation. We also propose two ways in implementations, the direct and indirect ones, which can not only provide a lower degree of complexity compared with conventional hierarchical clusterings, but also facilitate the adjustment of parameters. Experiments to evaluate the performance of AITC are presented on both synthetic and real datasets with different types of distributions. Better results are gained by the proposed algorithm in comparison with other widely used clustering algorithms.

This letter proposes a new multiple linear regression model using regularized correntropy for robust pattern recognition. First, we motivate the use of correntropy to improve the robustness of the classical mean square error (MSE) criterion that is sensitive to outliers. Then an l1regularization scheme is imposed on the correntropy to learn robust and sparse representations. Based on the half-quadratic optimization technique, we propose a novel algorithm to solve the nonlinear optimization problem. Second, we develop a new correntropy-based classifier based on the learned regularization scheme for robust object recognition. Extensive experiments over several applications confirm that the correntropy-based l1regularization can improve recognition accuracy and receiver operator characteristic curves under noise corruption and occlusion.

In this paper, we present a sparse correntropy framework for computing robust sparse representations of face images for recognition. Compared with the state-of-the-art l(1)norm-based sparse representation classifier (SRC), which assumes that noise also has a sparse representation, our sparse algorithm is developed based on the maximum correntropy criterion, which is much more insensitive to outliers. In order to develop a more tractable and practical approach, we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half-quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration. Our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state-of-the-art methods. In particular, it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic (ROC) curves, while the computational cost is much lower than the SRC algorithms.

Principal component analysis (PCA) minimizes the mean square error (MSE) and is sensitive to outliers. In this paper, we present a new rotational-invariant PCA based on maximum correntropy criterion (MCC). A half-quadratic optimization algorithm is adopted to compute the correntropy objective. At each iteration, the complex optimization problem is reduced to a quadratic problem that can be efficiently solved by a standard optimization method. The proposed method exhibits the following benefits: 1) it is robust to outliers through the mechanism of MCC which can be more theoretically solid than a heuristic rule based on MSE; 2) it requires no assumption about the zero-mean of data for processing and can estimate data mean during optimization; and 3) its optimal solution consists of principal eigenvectors of a robust covariance matrix corresponding to the largest eigenvalues. In addition, kernel techniques are further introduced in the proposed method to deal with nonlinearly distributed data. Numerical results demonstrate that the proposed method can outperform robust rotational-invariant PCAs based on L(1) norm when outliers occur.

This paper is reports an extension of our previous investigations on adding transparency to neural networks. We focus on a class of linear priors (LPs), such as symmetry, ranking list, boundary, monotonicity, etc., which represent either linear-equality or linear-inequality priors. A generalized constraint neural network-LPs (GCNN-LPs) model is studied. Unlike other existing modeling approaches, the GCNN-LP model exhibits its advantages. First, any LP is embedded by an explicitly structural mode, which may add a higher degree of transparency than using a pure algorithm mode. Second, a direct elimination and least squares approach is adopted to study the model, which produces better performances in both accuracy and computational cost over the Lagrange multiplier techniques in experiments. Specific attention is paid to both "hard (strictly satisfied)" and "soft (weakly satisfied)" constraints for regression problems. Numerical investigations are made on synthetic examples as well as on the real-world datasets. Simulation results demonstrate the effectiveness of the proposed modeling approach in comparison with other existing approaches.

This paper proposes a novel robust sparse representation method, called the two-stage sparse representation (TSR), for robust recognition on a large-scale database. Based on the divide and conquer strategy, TSR divides the procedure of robust recognition into outlier detection stage and recognition stage. In the first stage, a weighted linear regression is used to learn a metric in which noise and outliers in image pixels are detected. In the second stage, based on the learnt metric, the large-scale dataset is firstly filtered into a small set according to the nearest neighbor criterion. Then a sparse representation is computed by the non-negative least squares technique. The sparse solution is unique and can be optimized efficiently. The extensive numerical experiments on several public databases demonstrate that the proposed TSR approach generally obtains better classification accuracy than the state of the art Sparse Representation Classification (SRC). At the same time, by using the TSR, a significant reduction of computational cost is reached by over fifty times in comparison with the SRC, which enables the TSR to be deployed more suitably for large-scale dataset.

Most well-known discriminative clustering models, such as spectral clustering (SC) and maximum margin clustering (MMC), are non-Bayesian. Moreover, they merely considered to embed domain-dependent prior knowledge into data-specific kernels, while other forms of prior knowledge were seldom considered in these models. In this paper, we propose a Bayesian maximum margin clustering model (BMMC) based on the low-density separation assumption, which unifies the merits of both Bayesian and discriminative approaches. In addition to stating prior distribution on functions explicitly as traditional Gaussian processes, special prior knowledge can be embedded into BMMC implicitly via the Universum set easily. Furthermore, it is much easier to solve a BMMC than an MMC since the integer variables in the optimization are eliminated. Experimental results show that the BMMC achieves comparable or even better performance than state-of-the-art clustering methods and solving BMMC is more efficiently.

In this work, a new algorithm, which can incorporate the ranking information as prior knowledge into the regression model, is presented. Comparing with the method that treats the ranking information as hard constraints, We handle ranking reasonably by maximization of Normalized Discount Cumulative Gain (NDCG) as information retrieval (IR) evaluation measure, which is used to evaluate the performance of ranking model. In addition, an upper bound of one minus NDCG is given by weighted pairwise loss, and a connection between weighted pairwise loss and NDCG is also revealed. In this paper, RBF regression model and the pairwise shifted hinge loss and logistic loss are proposed under the suggested approach. One benefit of the proposed approach is that the weighted pairwise loss is more reasonable than the unweighted loss and all the weights are set based on the NDCG. Finally, one synthetic example shows that the method incorporated the ranking as hard constraints into regression model may cause the deteriorated results, but the good performance is shown by the proposed method. Numerical results from three existing benchmark regression problems further confirm the beneficial aspects on the proposed approach.

In this paper, we present a robust feature extraction framework based on information-theoretic learning. Its formulated objective aims at simultaneously maximizing the Renyi's quadratic information potential of features and the Renyi's cross information potential between features and class labels. This objective function reaps the advantages in robustness from both redescending M-estimator and manifold regularization, and can be efficiently optimized via half-quadratic optimization in an iterative manner. In addition, the popular algorithms LPP, SRDA and LapRLS for feature extraction are all justified to be the special cases within this framework. Extensive comparison experiments on several real-world data sets, with contaminated features or labels, well validate the encouraging gain in algorithmic robustness from this proposed framework.

We propose Dirichlet-Bernoulli Alignment (DBA), a generative model for corpora in which each pattern (e.g., a document) contains a set of instances (e.g., paragraphs in the document) and belongs to multiple classes. By casting predefined classes as latent Dirichlet variables (i.e., instance level labels), and modeling the multi-label of each pattern as Bernoulli variables conditioned on the weighted empirical average of topic assignments, DBA automatically aligns the latent topics discovered from data to human-defined classes. DBA is useful for both pattern classification and instance disambiguation, which are tested on text classification and named entity disambiguation for web search queries respectively.

Mean-Shift (MS) is a powerful non-parametric clustering method. Although good accuracy can be achieved, its computational cost is particularly expensive even on moderate data sets. In this paper, for the purpose of algorithm speedup, we develop an agglomerative MS clustering method called Agglo-MS, along with its mode-seeking ability and convergence property analysis. Our method is built upon an iterative query set compression mechanism which is motivated by the quadratic bounding optimization nature of MS. The whole framework can be efficiently implemented in linear running time complexity. Furthermore, we show that the pairwise constraint information can be naturally integrated into our framework to derive a semi-supervised non-parametric clustering method. Extensive experiments on toy and real-world data sets validate the speedup advantage and numerical accuracy of our method, as well as the superiority of its semi-supervised version.

This brief presents a two-phase construction approach for pruning both input and hidden units of multilayer perceptrons (MLPs) based on mutual information (MI). First, all features of input vectors are ranked according to their relevance to target outputs through a forward strategy. The salient input units of an MLP are thus determined according to the order of the ranking result and by considering their contributions to the network's performance. Then, the irrelevant features of input vectors can be identified and eliminated. Second, the redundant hidden units are removed from the trained MLP one after another according to a novel relevance measure. Compared with its related work, the proposed strategy exhibits better performance. Moreover, experimental results show that the proposed method is comparable or even superior to support vector machine (SVM) and support vector regression (SVR). Finally, the advantages of the MI-based method are investigated in comparison with the sensitivity analysis (SA)-based method.

In this work, we propose a preliminary study on objective approaches in evaluating the synthesized 3D plants from the given image data. Two measures, in a general name of "resemblance index (RI)", are defined and investigated based on the normalized mutual information (RINI), and coincident-bit-counting criterion (RICBC), respectively. We propose a strategy of hierarchical evaluations on different attributes of objects. In this study, we only consider the geometrical and crown distribution attributes. The numerical investigations confirm the approach to be useful for a fast evaluation of 3D reconstructed plants/trees from image data. Discussions are given about the two measures based on the numerical examples.

Level set methods have been extensively used to track the dynamical interfaces between different materials for physically based simulation, geometry modeling, oceanic modeling and other scientific and engineering applications. Due to the inherent Eulerian characteristics, interface evolution based on level set usually suffers from numerical diffusion, sharp feature missing and mass loss. Although some effective methods such as Particle Level Set (PLS) and Marker Level Set (MLS) have been proposed to tackle these difficulties, the complicated correction process and the high computational cost pose severe limitations for real-time applications. In this paper we provide an efficient parallel implementation of the Marker Level Set method on latest graphics hardware. Each step of the MLS method is fully mapped on GPU with an innovative combination of different computation techniques. Relying on GPU's parallelism and flexible programmability, the method provides real-time performance for large size 2D examples and moderate 3D examples, which is significantly faster than previous CPU-based methods.

A novel support vector machine (SVM) with weighted features is proposed. To assign appropriate weights for each feature, a mutual information (MI) based approach is presented. Although the calculation of feature weights may add an extra computational cost, the proposed method generally exhibits better generalization performance over the traditional SVM. The numerical studies on one synthetic and five existing benchmark classification problems confirm the benefits in using the proposed method.

This paper presents a stagewise least square (SLS) loss function for classification. It uses a least square form within each stage to approximate a bounded monotonic nonconvex loss function in a stagewise manner. Several benefits are obtained from using the SLS loss function, such as: (i) higher generalization accuracy and better scalability than classical least square loss; (ii) improved performance and robustness than convex loss (e.g., hinge loss of SVM); (iii) computational advantages compared with nonconvex loss (e.g. ramp loss in ψ-learning); (iv) ability to resist myopia of Empirical Risk Minimization and to boost the margin without boosting the complexity of the classifier. In addition, it naturally results in a kernel machine which is as sparse as SVM, yet much faster and simpler to train. A fast online learning algorithm with an integrated sparsification procedure is also provided. Experimental results on several benchmarks confirm the advantages of the proposed approach.

We address the problem of updating road maps in dense urban areas by extracting the main road network from a very high resolution (VHR) satellite image. Our model of the region occupied by the road network in the image is innovative. It incorporates three different types of prior geometric knowledge: generic boundary smoothness constraints, equivalent to a standard active contour prior; knowledge of the geometric properties of road networks (i.e. that they occupy regions composed of long, low-curvature segments joined at junctions), equivalent to a higher-order active contour prior; and knowledge of the road network at an earlier date derived from GIS data, similar to other ‘shape priors’ in the literature. In addition, we represent the road network region as a ‘phase field’, which offers a number of important advantages over other region modelling frameworks. All three types of prior knowledge prove important for overcoming the complexity of geometric ‘noise’ in VHR images. Promising results and a comparison with several other techniques demonstrate the effectiveness of our approach.

This paper presents a new prototype of web-based query by humming(QbH) system, which is designed specifically for music retrieval on Web applications. Besides the humming input interface, the system also provides an alternative interface of note strike. Schemes for signal processing and music indexing, such as inverted index and contour snippet are discussed in detail. In addition, a preliminary test was also provided, showing that the performance is acceptable for Web search service.

We propose a Bayesian framework for generalized associative functional networks (GAFN) and provide variational Bayes (VB) learning algorithm to approximate the posterior distributions over parameters of GAFN. The learning procedure for GAFN involves equality constraints on parameters, thus conventional approaches, like probabilistic graphical model or Lagrange multiplier method, will be inconvenient or expensive for solving the GAFN model in a direct way. We provide a linear transformation algorithm for the learning of parameters of GAFN. By means of the linear transformation, the evaluation of Lagrange multipliers is avoided and an iterative VB approximate procedure is restricted to a subspace of the original weight space. The VB framework naturally prevents overfltting and statistical inference can be made conveniently for weights of GAFN by the approximate posterior distributions over weights. The Bayesian GAFN is applied to autoregressive time series and the experimental results are comparable to other existing methods.

Natural mountains and valleys are gradually eroded by rainfall and river flows. Physically-based modeling of this complex phenomenon is a major concern in producing realistic synthesized terrains. However, despite some recent improvements, existing algorithms are still computationally expensive, leading to a time-consuming process fairly impractical for terrain designers and 3D artists. In this paper, we present a new method to model the hydraulic erosion phenomenon which runs at interactive rates on today's computers. The method is based on the velocity field of the running water, which is created with an efficient shallow-water fluid model. The velocity field is used to calculate the erosion and deposition process, and the sediment transportation process. The method has been carefully designed to be implemented totally on GPU, and thus takes full advantage of the parallelism of current graphics hardware. Results from experiments demonstrate that the proposed method is effective and efficient. It can create realistic erosion effects by rainfall and river flows, and produce fast simulation results for terrains with large sizes.

Nonnegative Matrix Factorization (NMF) has been proven to be effective in text mining. However, since NMF is a well-known unsupervised components analysis technique, the existing NMF method can not deal with prior constraints, which are beneficial to clustering or classification tasks. In this paper, we address the text clustering problem via a novel strategy, called Pairwise Constraintsguided Non-negative Matrix Factorization (PCNMF for short). Differing from the traditional NMF method, the proposed method can capture the available abundance prior constraints in original space, which result in more effective for clustering or information retrieval. Therefore, PCNMF enforces the discriminative capability in the reduced space. Utilizing the appropriate transformation, PCNMF represents as a new optimization problem, which can be efficiently solved by an iterative approach. The cluster membership of each document can be easily determined as the standard NMF. Empirical studies based on Benchmark document corpus demonstrate appealing results.

This paper explores an optimal robust design problem for a feedback system with one-input fuzzy PID controllers and simplification of the design problem. We tend to achieve robust stability and performance of one-input fuzzy PID control systems. Robustness is addressed in terms of stability margin and multiplicative perturbations. The design method is proposed in the framework of an optimal solver with a stability constraint using conicity conditions for the worst point of the perturbed plant. The stability of the fuzzy system is treated using conicity criteria derived from the small gain theorem but is less conservative. A simple genetic algorithm (SGA) approach is used as an optimal solver. We evaluate the one-input fuzzy PID controllers with inverted pendulum tracking. Two one-input fuzzy PID controllers are designed. In numerical simulations, the results show that the fuzzy PID obtained from the proposed method can achieve robust performance for the perturbed plant, while the fuzzy PID only considers performance without stability constraints causing system instability when parameters of the plant are perturbed in certain ranges.

A function-based evaluation approach is proposed for a systematic study of fuzzy proportional-integral-derivative (PID)-like controllers. This approach is applied for deriving process-independent design guidelines from addressing two issues: simplicity and nonlinearity. To examine the simplicity of fuzzy PID controllers, we conclude that direct-action controllers exhibit simpler design properties than gain-scheduling controllers. Then, we evaluate the inference structures of direct-action controllers in five criteria: control-action composition, input coupling, gain dependency, gain-role change, and rule/parameter growth. Three types of fuzzy PID controllers, using one-, two- and three-input inference structures, are analyzed. The results, according to the criteria, demonstrate some shortcomings in Mamdani's two-input controllers. For keeping the simplicity feature like a linear PID controller, a one-input fuzzy PID controller with "one-to-three" mapping inference engine is recommended. We discuss three evaluation approaches in a nonlinear approximation study: function-estimation-based, generalization-capability-based and nonlinearity-variation-based approximations. The study focuses on the last approach. A nonlinearity evaluation is then performed for several one-input fuzzy PID controllers based on two measures: nonlinearity variation index and linearity approximation index. Using these quantitative indices, one can make a reasonable selection of fuzzy reasoning mechanisms and membership functions without requiring any process information. From the study we observed that the Zadeh-Mamdani's "max-min-gravity" scheme produces the highest score in terms of nonlinearity variations, which is superior to other schemes, such as Mizumoto's "product-sum-gravity" and "Takagi-Sugeno-Kang" schemes.

Fuzzy PID tuning requires two stages of tuning; low level tuning followed by high level tuning. At the higher level, a nonlinear tuning is performed to determine the nonlinear characteristics of the fuzzy output. At the lower level, a linear tuning is performed to determine the linear characteristics of the fuzzy output for achieving overall performance of fuzzy control. First, different fuzzy systems are defined and then simplified for two-point control. Non-linearity tuning diagrams are constructed for fuzzy systems in order to perform high level tuning. The linear tuning parameters are deduced from the conventional PID tuning knowledge. Using the tuning diagrams, high level tuning heuristics are developed. Finally, different applications are demonstrated to show the validity of the proposed tuning method.

The paper discusses cell detection and tracking in a microscope scene for a cell-operation robot. An approach integrating a morphological operator and Bayesian estimation technique is used for cell detection and tracking. One of the problems in the implementation is difficulty in obtaining accurate information of cells. We introduce classification criteria which rely on both shape and texture information of the cell to get fine results, and we present geometric constraints incorporating a nonlinear diffusion process to reduce the drift of points during the tracking procedure. A preliminary test is conducted on the system. Experimental results show the effectiveness of the proposed methods.

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation.

The majority of the research work on fuzzy PID controllers focuses on the conventional two-input PI or PD type controller proposed by Mamdani (1974). However, fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. This paper investigates different fuzzy PID controller structures, including the Mamdani-type controller. By expressing the fuzzy rules in different forms, each PLD structure is distinctly identified. For purpose of analysis, a linear-like fuzzy controller is defined. A simple analytical procedure is developed to deduce the closed form solution for a three-input fuzzy inference. This solution is used to identify the fuzzy PID action of each structure type in the dissociated form. The solution for single-input-single-output nonlinear fuzzy inferences illustrates the effect of nonlinearity tuning. The design of a fuzzy PID controller is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear gains, including scale factors of fuzzy variables. By assigning a minimum number of rules to each type, the linear and nonlinear gains are deduced and explicitly presented. The tuning characteristics of different fuzzy PID structures are evaluated with respect to their functional behaviors. The rule decoupled and one-input rule structures proposed in this paper provide greater flexibility and better functional properties than the conventional fuzzy PHD structures.

In this work, we address an issue of nonlinearity variation evaluation for fuzzy PID controllers. This evaluation, or analysis, is important and basic in the light of nonlinear control design. The paper tries to investigate fuzzy controllers in regard to their nonlinearity variations when a finite number of tuning parameters are used. We suggest a nonlinearity variation index (NVI) for assessing the nonlinear design of the one-input fuzzy PID controllers developed by the authors. This index provides a quantitative measure to examine the nonlinearity freedom, or limitation, of the fuzzy systems. Using the NVI as a process-independent measure, designers are able to improve the design in the selections of the fuzzy rules, membership functions and inference schemes. Two differently-designed controllers are studied for the demonstration of how to use the NVI for an in-depth analysis of the nonlinear systems.

The fuzzy PID controller based on three-input inference is analyzed. Defining linear fuzzy regions in a linguistic error state space, a general linear-like fuzzy logic controller output is obtained. The solutions for twoand one-input fuzzy outputs are obtained as special cases of the three-input solution. The outputs of each controller are decomposed into linear and nonlinear terms with simple expressions. The multiphase solution that exists in the fuzzy output solution is expressed with least number of nonlinear terms. The linear output is used to identify the apparent linear PID gains of each controller type. The behavior of the apparent gains is similar to linear gain terms in a conventional PID controller. Thus three types of fuzzy controllers are tuned for obtaining overall performance.

This work presents the enhancement and application of a fuzzy classification technique for automated grading of fish products. Common features inherent in grading-type data and their specific requirements in processing for classification are identified. A fuzzy classifier with a four-level hierarchy is developed based on the "generalized K-nearest neighbor rules". Both conventional and fuzzy classifiers are examined using a realistic set of herring roe data (collected from the fish processing industry) to compare the classification performance in terms of accuracy and computational cost. The classification results show that the generalized fuzzy classifier provides the best accuracy at 89%. The grading system can be tuned through two parameters-the threshold of fuzziness and the cost weighting of error types-to achieve higher classification accuracy. An optimization scheme is also incorporated into the system for automatic determination of these parameter values with respect to a specific optimization function that is based on process renditions, including the product price and labor cost. Since the primary common features are accommodated in the classification algorithm, the method presented here provides a general capability for both grading and sorting-type problems in food processing.