Negative correlation ensemble learning for ordinal regression

Ordinal Regression With Pinball Loss

Ordinal regression (OR) aims to solve multiclass classification problems with ordinal classes. Support vector OR (SVOR) is a typical OR algorithm and has been extensively used in OR problems. In this article, based on the characteristics of OR problems, we propose a novel pinball loss function and present an SVOR method with pinball loss (pin-SVOR). Pin-SVOR is fundamentally different from traditional SVOR with hinge loss. Traditional SVOR employs the hinge loss function, and the classifier is determined by only a few data points near the class boundary, called support vectors, which may lead to a noise sensitive and re-sampling unstable classifier. Distinctively, pin-SVOR employs the pinball loss function. It attaches an extra penalty to correctly classified data that lies inside the class, such that all the training data is involved in deciding the classifier. The data near the middle of each class has a small penalty, and that near the class boundary has a large penalty. Thus, the training data tend to lie near the middle of each class instead of on the class boundary, which leads to scatter minimization in the middle of each class and noise insensitivity. The experimental results show that pin-SVOR has better classification performance than state-of-the-art OR methods.

Research Ideas Discovery via Hierarchical Negative Correlation

A new research idea may be inspired by the connections of keywords. Link prediction discovers potential nonexisting links in an existing graph and has been applied in many applications. This article explores a method of discovering new research ideas based on link prediction, which predicts the possible connections of different keywords by analyzing the topological structure of the keyword graph. The patterns of links between keywords may be diversified due to different domains and different habits of authors. Therefore, it is often difficult for a single learner to extract diverse patterns of different research domains. To address this issue, groups of learners are organized with negative correlation to encourage the diversity of sublearners. Moreover, a hierarchical negative correlation mechanism is proposed to extract subgraph features in different order subgraphs, which improves the diversity by explicitly supervising the negative correlation on each layer of sublearners. Experiments are conducted to illustrate the effectiveness of the proposed model to discover new research ideas. Under the premise of ensuring the performance of the model, the proposed method consumes less time and computational cost compared with other ensemble methods.

Global Negative Correlation Learning: A Unified Framework for Global Optimization of Ensemble Models

Ensembles are a widely implemented approach in the machine learning community and their success is traditionally attributed to the diversity within the ensemble. Most of these approaches foster diversity in the ensemble by data sampling or by modifying the structure of the constituent models. Despite this, there is a family of ensemble models in which diversity is explicitly promoted in the error function of the individuals. The negative correlation learning (NCL) ensemble framework is probably the most well-known algorithm within this group of methods. This article analyzes NCL and reveals that the framework actually minimizes the combination of errors of the individuals of the ensemble instead of minimizing the residuals of the final ensemble. We propose a novel ensemble framework, named global negative correlation learning (GNCL), which focuses on the optimization of the global ensemble instead of the individual fitness of its components. An analytical solution for the parameters of base regressors based on the NCL framework and the global error function proposed is also provided under the assumption of fixed basis functions (although the general framework could also be instantiated for neural networks with nonfixed basis functions). The proposed ensemble framework is evaluated by extensive experiments with regression and classification data sets. Comparisons with other state-of-the-art ensemble methods confirm that GNCL yields the best overall performance.

A novel deep ordinal classification approach for aesthetic quality control classification

Nowadays, decision support systems (DSSs) are widely used in several application domains, from industrial to healthcare and medicine fields. Concerning the industrial scenario, we propose a DSS oriented to the aesthetic quality control (AQC) task, which has quickly established itself as one of the most crucial challenges of Industry 4.0. Taking into account the increasing amount of data in this domain, the application of machine learning (ML) and deep learning (DL) techniques offers great opportunities to automatize the overall AQC process. State-of-the-art is mainly oriented to approach this problem with a nominal DL classification method which does not exploit the ordinal structure of the AQC task, thus not penalizing the error among distant AQC classes (which is a relevant aspect for the real use case). The paper introduces a DL ordinal methodology for the AQC classification. Differently from other deep ordinal methods, we combined the standard categorical cross-entropy with the cumulative link model and we imposed the ordinal constraint via the thresholds and slope parameters. Experimental results were performed for solving an AQC task on a novel image dataset originated from a specific company’s demand (i.e., aesthetic assessment of wooden stocks). We demonstrated how the proposed methodology is able to reduce misclassification errors (up to 0.937 quadratic weight kappa loss) among distant classes while overcoming other state-of-the-art deep ordinal models and reducing the bias factor related to the item geometry. The proposed DL approach was integrated as the main core of a DSS supported by Internet of Things (IoT) architecture that can support the human operator by reducing up to 90% the time needed for the qualitative analysis carried out manually in this specific domain.

SONNET: A self-guided ordinal regression neural network for segmentation and classification of nuclei in large-scale multi-tissue histology images

Automated nuclei segmentation and classification are the keys to analyze and understand the cellular characteristics and functionality, supporting computer-aided digital pathology in disease diagnosis. However, the task still remains challenging due to the intrinsic variations in size, intensity, and morphology of different types of nuclei. Herein, we propose a self-guided ordinal regression neural network for simultaneous nuclear segmentation and classification that can exploit the intrinsic characteristics of nuclei and focus on highly uncertain areas during training. The proposed network formulates nuclei segmentation as an ordinal regression learning by introducing a distance decreasing discretization strategy, which stratifies nuclei in a way that inner regions forming a regular shape of nuclei are separated from outer regions forming an irregular shape. It also adopts a self-guided training strategy to adaptively adjust the weights associated with nuclear pixels, depending on the difficulty of the pixels that is assessed by the network itself. To evaluate the performance of the proposed network, we employ large-scale multi-tissue datasets with 276349 exhaustively annotated nuclei. We show that the proposed network achieves the state-of-the-art performance in both nuclei segmentation and classification in comparison to several methods that are recently developed for segmentation and/or classification.

A Deep Learning Approach to Competing Risks Representation in Peer-to-Peer Lending

Online peer-to-peer (P2P) lending is expected to benefit both investors and borrowers due to their low transaction cost and the elimination of expensive intermediaries. From the lenders' perspective, maximizing their return on investment is an ultimate goal during their decision-making procedure. In this paper, we explore and address a fundamental problem underlying such a goal: how to represent the two competing risks, charge-off and prepayment, in funded loans. We propose to model both potential risks simultaneously, which remains largely unexplored until now. We first develop a hierarchical grading framework to integrate two risks of loans both qualitatively and quantitatively. Afterward, we introduce an end-to-end deep learning approach to solve this problem by breaking it down into multiple binary classification subproblems that are amenable to both feature representation and risks learning. Particularly, we leverage deep neural networks to jointly solve these subtasks, which leads to the in-depth exploration of the interaction involved in these tasks. To the best of our knowledge, this is the first attempt to characterize competing risks for loans in P2P lending via deep neural networks. The comprehensive experiments on real-world loan data show that our methodology is able to achieve an appealing investment performance by modeling the competition within and between risks explicitly and properly. The feature analysis based on saliency maps provides useful insights into payment dynamics of loans for potential investors intuitively.

Dimensionality Reduction in Multiple Ordinal Regression

Supervised dimensionality reduction (DR) plays an important role in learning systems with high-dimensional data. It projects the data into a low-dimensional subspace and keeps the projected data distinguishable in different classes. In addition to preserving the discriminant information for binary or multiple classes, some real-world applications also require keeping the preference degrees of assigning the data to multiple aspects, e.g., to keep the different intensities for co-occurring facial expressions or the product ratings in different aspects. To address this issue, we propose a novel supervised DR method for DR in multiple ordinal regression (DRMOR), whose projected subspace preserves all the ordinal information in multiple aspects or labels. We formulate this problem as a joint optimization framework to simultaneously perform DR and ordinal regression. In contrast to most existing DR methods, which are conducted independently of the subsequent classification or ordinal regression, the proposed framework fully benefits from both of the procedures. We experimentally demonstrate that the proposed DRMOR method (DRMOR-M) well preserves the ordinal information from all the aspects or labels in the learned subspace. Moreover, DRMOR-M exhibits advantages compared with representative DR or ordinal regression algorithms on three standard data sets.

Multiple-Instance Ordinal Regression

Ordinal regression (OR) is a paradigm in supervised learning, which aims at learning a prediction model for ordered classes. The existing studies mainly focus on single-instance OR, and the multi-instance OR problem has not been explicitly addressed. In many real-world applications, considering the OR problem from a multiple-instance aspect can yield better classification performance than from a single-instance aspect. For example, in image retrieval, an image may contain multiple and possibly heterogeneous objects. The user is usually interested in only a small part of the objects. If we represent the whole image as a global feature vector, the useful information from the targeted objects that the user is of interest may be overridden by the noisy information from irrelevant objects. However, this problem fits in the multiple-instance setting well. Each image is considered as a bag, and each object region is treated as an instance. The image is considered as of the user interest if it contains at least one targeted object region. In this paper, we address the multi-instance OR where the OR classifier is learned on multiple-instance data, instead of single-instance data. To solve this problem, we present a novel multiple-instance ordinal regression (MIOR) method. In MIOR, a set of parallel hyperplanes is used to separate the classes, and the label ordering information is incorporated into learning the classifier by imputing the parallel hyperplanes with an order. Moreover, considering that a bag may contain instances not belonging to its class, for each bag, the instance which is nearest to the middle of the corresponding class is selected to learn the classifier. Compared with the existing single-instance OR work, MIOR is able to learn a more accurate OR classifier on multiple-instance data where only the bag label is available and the instance label is unknown. Extensive experiments show that MIOR outperforms the existing single-instance OR methods.

Methodological Research for Modular Neural Networks Based on “an Expert With Other Capabilities”

This article contains a new subnet training method for modular neural networks, proposed with the inspiration of the principle of “an expert with other capabilities”. The key point of this method is that a subnet learns the neighbor data sets while fulfilling its main task: learning the objective data set. Additionally, a relative distance measure is proposed to replace the absolute distance measure used in the classical subnet learning method and its advantage in the general case is theoretically discussed. Both methodology and empirical study of this new method are presented. Two types of experiments respectively related with the approximation problem and the prediction problem in nonlinear dynamic systems are designed to verify the effectiveness of the proposed method. Compared with the classical subnet learning method, the average testing error of the proposed method is dramatically decreased and more stable. The superiority of the relative distance measure is also corroborated.

Multiobjective Deep Belief Networks Ensemble for Remaining Useful Life Estimation in Prognostics

In numerous industrial applications where safety, efficiency, and reliability are among primary concerns, condition-based maintenance (CBM) is often the most effective and reliable maintenance policy. Prognostics, as one of the key enablers of CBM, involves the core task of estimating the remaining useful life (RUL) of the system. Neural networks-based approaches have produced promising results on RUL estimation, although their performances are influenced by handcrafted features and manually specified parameters. In this paper, we propose a multiobjective deep belief networks ensemble (MODBNE) method. MODBNE employs a multiobjective evolutionary algorithm integrated with the traditional DBN training technique to evolve multiple DBNs simultaneously subject to accuracy and diversity as two conflicting objectives. The eventually evolved DBNs are combined to establish an ensemble model used for RUL estimation, where combination weights are optimized via a single-objective differential evolution algorithm using a task-oriented objective function. We evaluate the proposed method on several prognostic benchmarking data sets and also compare it with some existing approaches. Experimental results demonstrate the superiority of our proposed method.

Multiple Ordinal Regression by Maximizing the Sum of Margins

Human preferences are usually measured using ordinal variables. A system whose goal is to estimate the preferences of humans and their underlying decision mechanisms requires to learn the ordering of any given sample set. We consider the solution of this ordinal regression problem using a support vector machine algorithm. Specifically, the goal is to learn a set of classifiers with common direction vectors and different biases correctly separating the ordered classes. Current algorithms are either required to solve a quadratic optimization problem, which is computationally expensive, or based on maximizing the minimum margin (i.e., a fixed-margin strategy) between a set of hyperplanes, which biases the solution to the closest margin. Another drawback of these strategies is that they are limited to order the classes using a single ranking variable (e.g., perceived length). In this paper, we define a multiple ordinal regression algorithm based on maximizing the sum of the margins between every consecutive class with respect to one or more rankings (e.g., perceived length and weight). We provide derivations of an efficient, easy-to-implement iterative solution using a sequential minimal optimization procedure. We demonstrate the accuracy of our solutions in several data sets. In addition, we provide a key application of our algorithms in estimating human subjects' ordinal classification of attribute associations to object categories. We show that these ordinal associations perform better than the binary one typically employed in the literature.

A Maximum Margin Approach for Semisupervised Ordinal Regression Clustering

Ordinal regression (OR) is generally defined as the task where the input samples are ranked on an ordinal scale. OR has found a wide variety of applications, and a great deal of work has been done on it. However, most of the existing work focuses on supervised/semisupervised OR classification, and the semisupervised OR clustering problems have not been explicitly addressed. In real-world OR applications, labeling a large number of training samples is usually time-consuming and costly, and instead, a set of unlabeled samples can be utilized to set up the OR model. Moreover, although the sample labels are unavailable, we can sometimes get the relative ranking information of the unlabeled samples. This sample ranking information can be utilized to refine the OR model. Hence, how to build an OR model on the unlabeled samples and incorporate the sample ranking information into the process of improving the clustering accuracy remains a key challenge for OR applications. In this paper, we consider the semisupervised OR clustering problems with sample-ranking constraints, which give the relative ranking information of the unlabeled samples, and put forward a maximum margin approach for semisupervised OR clustering ( [Formula: see text]SORC). On one hand, [Formula: see text]SORC seeks a set of parallel hyperplanes to partition the unlabeled samples into clusters. On the other hand, a loss function is put forward to incorporate the sample ranking information into the clustering process. As a result, the optimization function of [Formula: see text]SORC is formulated to maximize the margins of the closest neighboring clusters and meanwhile minimize the loss associated with the sample-ranking constraints. Extensive experiments on OR data sets show that the proposed [Formula: see text]SORC method outperforms the traditional semisupervised clustering methods considered.

Ordinal regression by a generalized force-based model

This paper introduces a new instance-based algorithm for multiclass classification problems where the classes have a natural order. The proposed algorithm extends the state-of-the-art gravitational models by generalizing the scaling behavior of the class-pattern interaction force. Like the other gravitational models, the proposed algorithm classifies new patterns by comparing the magnitude of the force that each class exerts on a given pattern. To address ordinal problems, the algorithm assumes that, given a pattern, the forces associated to each class follow a unimodal distribution. For this reason, a weight matrix that allows to modify the metric in the attributes space and a vector of parameters that allows to modify the force law for each class have been introduced in the model definition. Furthermore, a probabilistic formulation of the error function allows the estimation of the model parameters using global and local optimization procedures toward minimization of the errors and penalization of the non unimodal outputs. One of the strengths of the model is its competitive grade of interpretability which is a requisite in most of real applications. The proposed algorithm is compared to other well-known ordinal regression algorithms on discretized regression datasets and real ordinal regression datasets. Experimental results demonstrate that the proposed algorithm can achieve competitive generalization performance and it is validated using nonparametric statistical tests.

Ordinal neural networks without iterative tuning

Ordinal regression (OR) is an important branch of supervised learning in between the multiclass classification and regression. In this paper, the traditional classification scheme of neural network is adapted to learn ordinal ranks. The model proposed imposes monotonicity constraints on the weights connecting the hidden layer with the output layer. To do so, the weights are transcribed using padding variables. This reformulation leads to the so-called inequality constrained least squares (ICLS) problem. Its numerical solution can be obtained by several iterative methods, for example, trust region or line search algorithms. In this proposal, the optimum is determined analytically according to the closed-form solution of the ICLS problem estimated from the Karush-Kuhn-Tucker conditions. Furthermore, following the guidelines of the extreme learning machine framework, the weights connecting the input and the hidden layers are randomly generated, so the final model estimates all its parameters without iterative tuning. The model proposed achieves competitive performance compared with the state-of-the-art neural networks methods for OR.

Cost-sensitive AdaBoost algorithm for ordinal regression based on extreme learning machine

In this paper, the well known stagewise additive modeling using a multiclass exponential (SAMME) boosting algorithm is extended to address problems where there exists a natural order in the targets using a cost-sensitive approach. The proposed ensemble model uses an extreme learning machine (ELM) model as a base classifier (with the Gaussian kernel and the additional regularization parameter). The closed form of the derived weighted least squares problem is provided, and it is employed to estimate analytically the parameters connecting the hidden layer to the output layer at each iteration of the boosting algorithm. Compared to the state-of-the-art boosting algorithms, in particular those using ELM as base classifier, the suggested technique does not require the generation of a new training dataset at each iteration. The adoption of the weighted least squares formulation of the problem has been presented as an unbiased and alternative approach to the already existing ELM boosting techniques. Moreover, the addition of a cost model for weighting the patterns, according to the order of the targets, enables the classifier to tackle ordinal regression problems further. The proposed method has been validated by an experimental study by comparing it with already existing ensemble methods and ELM techniques for ordinal regression, showing competitive results.