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Label distribution learning (LDL) is a new machine learning paradigm that addresses label ambiguity by emphasizing the relevance of each label to a particular instance. In supervised learning, many LDL algorithms have been proposed, which often require a large amount of well-annotated training data to achieve good performance. However, annotating a label distribution is more complicated and expensive than annotating a single label or multiple labels with logical values of 0 and 1. Thus, we propose a projection graph embedding algorithm for semi-supervised label distribution learning (PGE-SLDL). Specifically, we seek a potential space by orthogonal neighborhood preserving projections, named capture space. This capture space is used to select more valuable features and construct a graph that contains more accurate data structure information. We utilize the sample correlation information contained between graph nodes to recover the unknown label distribution. In addition, compared with fixed graphs in traditional semi-supervised learning, we carry out projection and graph construction simultaneously to obtain a self-updating projection graph, which is more helpful to learn label distribution. The experimental results validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• We define the interval-set decision tables and a similarity relation based on similarity degree in interval-set decision tables. • We extend the concepts of accuracy and roughness in Pawlak rough set model for interval-set decision tables. • We propose an interval-decision entropy to measure the uncertainty of the interval-set decision tables, which is caused by the approximations and the size of similarity classes. • We propose a definition of reduct based on the interval-decision entropy and design an addition-based heuristic attribute reduction algorithm in interval-set decision tables. Uncertainty measurement is considered as a vital quantitative way for analyzing and mining potential characteristic features in different types of decision tables. However, considering the equivalent relation is not suitable for evaluating the relationships of objects, few studies focused on the interval-set decision tables. In this paper, we address the uncertainty measurement problem in interval-set decision tables. Firstly, a similarity relation is induced by the similarity degree. Based on the similarity relation, a notion of granular structure is defined and the corresponding properties are investigated in interval-set decision tables. Secondly, we extend the accuracy and the roughness, called the interval approximation accuracy and the interval approximation roughness, to measure the uncertainty under the granular structures. By the analysis of the two extended measures, they can effectively evaluate the uncertainty caused by the approximations in the rough set model. Considering that the size of similarity classes can also affect the uncertainty, an alternative uncertainty measure based on the conditional information entropy, called the interval-decision entropy, is proposed. Moreover, a definition of reduct based on our proposed measure is provided and a heuristic attribute reduction algorithm is designed. Finally, numerical experiments demonstrate that the proposed uncertainty measures are effective and suitable for interval-set decision tables. [ABSTRACT FROM AUTHOR]

The notion of uncertainty measure is one of the most important topics in rough set theory and has been studied in different kinds of information tables. However, few studies have focused on the interval set information table, which is regarded as one of the generalized models of single-valued information tables. This paper aims at studying the uncertainty measurements for interval set information tables. Firstly, an interval δ -similarity relation is induced based on the similarity degree. The similarity relation induces the granules, which form a covering in interval set information tables. Secondly, four types of granularity measures are defined to measure the granularity of a covering. Thirdly, the concepts of accuracy and roughness in rough set theory are respectively extended to δ -accuracy and δ -roughness for interval set information tables. Furthermore, four new combinations ofuncertainty measures by considering proposed granularity measures and δ -accuracy and δ -roughness are defined and analyzed. Theoretical analyses and experimental results illustrate that the proposed measures are effective and accurate for interval set information tables. [ABSTRACT FROM AUTHOR]

Irony detection in social networks has drawn much attention in recent years. In this work, we propose a three-way decisions based feature fusion method for Chinese irony detection in microblog. First, we build a set of discriminating features for Chinese irony detection by considering the characteristics of both Chinese language and social networks, including lexical feature, homophonic pun, consecutive punctuation, length of microblog, passive verbs, and affective imbalance. Second, to tackle the problem of extreme imbalance between different kinds of features, we propose a two-stage classification method for Chinese irony detection by considering feature fusion. In the first stage, a three-way decisions based classifier is trained to predict the ironic tendency based on the lexical feature only. This procedure can reduce the thousands-of-dimensions based lexical feature into a one-dimensional feature. In the second stage, the constructed new feature is merged with other five features into a new feature vector for learning. Experimental results show that our proposed two-stage classification method can get a significant improvement than one-stage classification method. [ABSTRACT FROM AUTHOR]

Abstract The decision-theoretic rough set (DTRS) can be regarded as a type of cost-sensitive learning method that incorporates cost functions. Three-way decisions for an object are made in the DTRS model to obtain the minimum Bayesian decision cost, including acceptance, rejection and deferment decisions. However, because the cost matrix in traditional cost-sensitive learning problems does not include the cost for deferment decisions, DTRS cannot be directly used to solve traditional cost-sensitive learning problems. In this paper, we present a multiclass three-way decision-theoretic rough set model that can be directly applied to traditional cost-sensitive learning problems. This model can calculate the corresponding cost for deferment decisions based on the traditional cost matrix. In addition, we propose a multiphase cost-sensitive learning method based on the multiclass three-way decision-theoretic rough set model. The deferment and rejection samples are reduced and eliminated through multiphase iterative learning. Compared with the existing multiclass cost-sensitive learning methods, our proposed method can achieve higher classification accuracy and lower misclassification cost. [ABSTRACT FROM AUTHOR]

Abstract Attribute reduction plays an important role in rough set theory. Many attribute reduction methods have been proposed based on different definitions of attribute reduct, while an attribute reduct can be regarded as a minimal attribute subset that satisfies specific criteria. Most reducts are defined on the basis of a single criterion, which can only affect one specific characteristic of the data or one preference of users. However, the single criterion-based attribute reduct may not meet the requirement of complex problems. To address this problem, based on three-way decision-theoretic rough set model, this paper defines a multi-objective attribute reduct. Three types of criteria for defining attribute reduct including the positive region, decision cost and mutual information are considered and combined to a multi-objective optimization problem. Based on the proposed multi-objective attribute reduct, we also introduce a multi-objective optimization-based attribute reduction method and an ensemble learning-based attribute reduction method. Experimental results on several datasets show that the proposed attribute reduction methods can obtain a robust and better classification performance. [ABSTRACT FROM AUTHOR]

Abstract: In classical rough set models, attribute reduction generally keeps the positive or non-negative regions unchanged, as these regions do not decrease with the addition of attributes. However, the monotonicity property in decision-theoretic rough set models does not hold. This is partly due to the fact that all regions are determined according to the Bayesian decision procedure. Consequently, it is difficult to evaluate and interpret region-preservation attribute reduction in decision-theoretic rough set models. This paper provides a new definition of attribute reduct for decision-theoretic rough set models. The new attribute reduction is formulated as an optimization problem. The objective is to minimize the cost of decisions. Theoretical analysis shows the meaning of the optimization problem. Both the problem definition and the objective function have good interpretation. A heuristic approach, a genetic approach and a simulated annealing approach to the new problem are proposed. Experimental results on several data sets indicate the efficiency of these approaches. [Copyright &y& Elsevier]

• We propose an interpretable bilateral learning framework for 4K resolution low light image enhancement, which can process 4K (3840 × 2160) resolution images at 100 fps. • We propose a novel frequency loss function to reconstruct the details of UHD images. • We propose a polynomial channel enhancement method to enhance three channels of UHD images. • We establish a large and high-quality UHD image dataset for UHD low-light image enhancement. Convolutional neural networks (CNNs) have achieved unparalleled success in the single Low-light Image Enhancement (LIE) task. Existing CNN-based LIE models over-focus on pixel-level reconstruction effects, hence ignoring the theoretical guidance for sustainable optimization, which hinders their application to Ultra-High Definition (UHD) images. To address the above problems, we propose a new interpretable network, which capable of performing LIE on UHD images in real time on a single GPU. The proposed network consists of two CNNs: the first part is to use the first-order unfolding Taylor's formula to build an interpretable network, and combine two UNets in the form of first-order Taylor's polynomials. Then we use this constructed network to extract the feature maps of the low-resolution input image, and finally process the feature maps to form a multi-dimensional tensor termed a bilateral grid that acts on the original image to yield an enhanced result. The second part is the image enhancement using the bilateral grid. In addition, we propose a polynomial channel enhancement method to enhance UHD images. Experimental results show that the proposed method significantly outperforms state-of-the-art methods for UHD LIE on a single GPU with 24G RAM (100 fps). [ABSTRACT FROM AUTHOR]

Three-way concept analysis provides a novel model for three-way decisions, and also extends the classical formal concept analysis, which has attracted many attentions in recent years. In order to construct three-way concept lattices, original formal context and its complement context need to be considered simultaneously. In this paper, a new method of constructing attribute-induced three-way (AE) and object-induced three-way (OE) concept lattices is proposed. Firstly, we introduce an AE-oriented composite operator and an OE-oriented composite operator that combine a pair of formal concepts coming from the concept lattices of original formal context and its complement context. Secondly, we define the candidate AE concepts and redundant AE concepts based on the AE-oriented composite operator, and define the candidate OE concepts and redundant OE concepts based on the OE-oriented composite operator, respectively. Finally, we propose an AE lattice construction algorithm and an OE lattice construction algorithm. Theoretical analysis and experimental results demonstrate that the proposed method is simple and effective, and it is a useful supplement to current three-way concept lattice construction methods. [ABSTRACT FROM AUTHOR]

Label distribution learning (LDL) as a soft-labeling paradigm is allowed to learn single or multi-labeled information distribution. Overwhelmingly, in the open world, the distribution of labels is usually disturbed by the noise (such as the man-made induction bias, shake of hardware devices), which in turn affects the decision of downstream tasks. To address this problem, we propose a novel LDL approach by using the three-way decisions theory to clear the amplified noise in this paper. First, we evaluate the confidence of each training sample and use a three-way decisions-based method to identify the trustworthy samples and the noisy samples. Second, we apply the sample correlation between the trustworthy samples and the noisy samples to correct the noisy labels. Finally, we re-weight every sample based on the learned confidences to train the robust LDL model. Experiments show that our approach has better performance in handling noisy data compared to existing algorithms. [ABSTRACT FROM AUTHOR]

As an extension of Pawlak rough set model, decision-theoretic rough set model (DTRS) adopts the Bayesian decision theory to compute the required thresholds in probabilistic rough set models. It gives a new semantic interpretation of the positive, boundary and negative regions by using three-way decisions. DTRS has been widely discussed and applied in data mining and decision making. However, one limitation of DTRS is its lack of ability to deal with numerical data directly. In order to overcome this disadvantage and extend the theory of DTRS, this paper proposes a neighborhood based decision-theoretic rough set model (NDTRS) under the framework of DTRS. Basic concepts of NDTRS are introduced. A positive region related attribute reduct and a minimum cost attribute reduct in the proposed model are defined and analyzed. Experimental results show that our methods can get a short reduct. Furthermore, a new neighborhood classifier based on three-way decisions is constructed and compared with other classifiers. Comparison experiments show that the proposed classifier can get a high accuracy and a low misclassification cost. [ABSTRACT FROM AUTHOR]