Multi-label learning deals with training examples each represented by a single instance while associated with multiple class labels. Due to the exponential number of possible label sets to be considered by the predictive model, it is commonly assumed that label correlations should be well exploited to design an effective multi-label learning approach. On the other hand, class-imbalance stands as an intrinsic property of multi-label data which significantly affects the generalization performance of the multi-label predictive model. For each class label, the number of training examples with positive labeling assignment is generally much less than those with negative labeling assignment. To deal with the class-imbalance issue for multi-label learning, a simple yet effective class-imbalance aware learning strategy called cross-coupling aggregation (COCOA) is proposed in this article. Specifically, COCOA works by leveraging the exploitation of label correlations as well as the exploration of class-imbalance simultaneously. For each class label, a number of multiclass imbalance learners are induced by randomly coupling with other labels, whose predictions on the unseen instance are aggregated to determine the corresponding labeling relevancy. Extensive experiments on 18 benchmark datasets clearly validate the effectiveness of COCOA against state-of-the-art multi-label learning approaches especially in terms of imbalance-specific evaluation metrics.

As a practical problem in open and dynamic environments, class-incremental learning has attracted much attention from many fields. Learning with augmented class (LAC) problem formulates one of the core difficulties of class-incremental learning: instances of augmented class need to be predicted with the restriction that only examples from seen classes are observed in training phase. LACU framework advances the study of LAC problem by exploiting unlabeled data, while it does not take into account an important practical problem widely-existing in real-world applications of LAC - imbalanced class distributions among seen classes, which will further increase the learning difficulties of LAC problem. We propose a novel approach Label Confidence Propagation (LCP) to tackle the problem of imbalanced augmented class learning with unlabeled data. LCP enlarges the labeled training data set by estimating class labels for unlabeled data, to meet the challenge of lacking supervision information of augmented classes via identifying some of their instances, and to alleviate the damage of class-imbalance via identifying more instances for each seen class. LCP firstly initializes label confidence, i.e., the posterior probability distributions of all classes (including augmented classes) for unlabeled data, then iteratively propagates label confidence to identify a valid label for each unlabeled instance to enlarge the labeled training data set. Finally, LCP predicts for unseen instances by linear neighborhood reconstruction to be robust to potential noise. Results on abundant experiments show that LCP is significantly superior to many state-of-the-art methods, and robust to high imbalance ratio and high open level. LCP can sufficiently unleash its strength especially when there are abundant unlabeled data available.

Partial label learning deals with the problem where each training example is represented by a feature vector while associated with a set of candidate labels, among which only one label is valid. To learn from such ambiguous labeling information, the key is to try to disambiguate the candidate label sets of partial label training examples. Existing disambiguation strategies work by either identifying the ground-truth label iteratively or treating each candidate label equally. Nonetheless, the disambiguation process is generally conducted by focusing on manipulating the label space, and thus ignores making full use of potentially useful information from the feature space. In this paper, a novel two-stage approach is proposed to learning from partial label examples based on feature-aware disambiguation. In the first stage, the manifold structure of feature space is utilized to generate normalized labeling confidences over candidate label set. In the second stage, the predictive model is learned by performing regularized multi-output regression over the generated labeling confidences. Extensive experiments on artificial as well as real-world partial label data sets clearly validate the superiority of the proposed feature-aware disambiguation approach.

Class-imbalance is very common in real-world applications. Previous studies focused on binary-class imbalance problem, whereas multi-class imbalance problem is more general and more challenging. Under-sampling is an effective and efficient method for binary-class imbalanced data. But when it is used for multi-class imbalanced data, many more majority class examples are ignored because there are often multiple majority classes, and the minority class often has few data. To utilize the information contained in the majority class examples ignored by under-sampling, this paper proposes a method ChunkCombine. For each majority class, it performs under-sampling multiple times to obtained non-overlapping data chunks, such that they contain the most information that a data sample of the same size can contain. Each data chunk has the same size as the minority class to achieve balance. Then every possible combination of the minority class and each data chunk from every majority class forms a balanced training set. ChunkCombine uses ensemble techniques to learn from the different training sets derived from all the possible combinations. Experimental results show it is better than many other popular methods for multi-class imbalanced data when average accuracy, G-mean and MAUC are used as evaluation measures. Besides, we discuss different evaluation measures and suggest that, a multi-class F-measure Mean F-Measure (MFM) is unsuitable for multi-class imbalanced data in many situations because it is not consistent with the standard F-measure in binary-class case and it is close to accuracy.

Class-imbalance is very common in real data mining tasks. Previous studies focused on binary-class imbalance problem, whereas multi-class imbalance problem is more challenging. Error correcting output codes (ECOC) technique can be applied to class-imbalance problem, however, the standard ECOC aims at maximizing accuracy, ignoring the fact that, when class-imbalance is really a problem, the minority classes are more important than the majority classes. To enable ECOC to tackle multi-class imbalance, it is desired to have an appropriate code matrix, an effective learning strategy and a decoding strategy emphasizing the minority classes. In this paper, based on the aforementioned consideration, we propose the imECOC method which works on dichotomies to handle both the between-class imbalance and within-class imbalance. As the dichotomy classifiers contribute differently to the final prediction, imECOC assigns weights to dichotomies and uses weighted distance for decoding, where the optimal dichotomy weights are obtained by minimizing a weighted loss in favor of the minority classes. Experimental results on fourteen data sets show that, imECOC performs significantly better than many state-of-the-art multi-class imbalance learning methods, no matter whether multi-class F1, G-mean or AUC are used as evaluation measures.

Existing cost-sensitive learning methods require that the unequal misclassification costs should be given as precise values. In many real-world applications, however, it is generally difficult to have a precise cost value since the user maybe only knows that one type of mistake is much more severe than another type, yet it is infeasible to give a precise description. In such situations, it is more meaningful to work with a cost interval instead of a precise cost value. In this paper we report the first study along this direction. We propose the CISVM method, a support vector machine, to work with cost interval information. Experiments show that when there are only cost intervals available, CISVM is significantly superior to standard cost-sensitive SVMs using any of the minimal cost, mean cost and maximal cost to learn. Moreover, considering that in some cases other information about costs can be obtained in addition to cost intervals, such as the distribution of costs, we propose a general approach CODIS for using the distribution information to help improve performance. Experiments show that this approach can reduce 60% more risks than the standard cost-sensitive SVM which assumes the expected cost is the true value.

Rescaling is possibly the most popular approach to cost‐sensitive learning. This approach works by rebalancing the classes according to their costs, and it can be realized in different ways, for example, re‐weighting or resampling the training examples in proportion to their costs, moving the decision boundaries of classifiers faraway from high‐cost classes in proportion to costs, etc. This approach is very effective in dealing with two‐class problems, yet some studies showed that it is often not so helpful on multi‐class problems. In this article, we try to explore why the rescaling approach is often helpless on multi‐class problems. Our analysis discloses that the rescaling approach works well when the costs are consistent, while directly applying it to multi‐class problems with inconsistent costs may not be a good choice. Based on this recognition, we advocate that before applying the rescaling approach, the consistency of the costs must be examined at first. If the costs are consistent, the rescaling approach can be conducted directly; otherwise it is better to apply rescaling after decomposing the multi‐class problem into a series of two‐class problems. An empirical study involving 20 multi‐class data sets and seven types of cost‐sensitive learners validates our proposal. Moreover, we show that the proposal is also helpful for class‐imbalance learning.

Undersampling is a popular method in dealing with class-imbalance problems, which uses only a subset of the majority class and thus is very efficient. The main deficiency is that many majority class examples are ignored. We propose two algorithms to overcome this deficiency. EasyEnsemble samples several subsets from the majority class, trains a learner using each of them, and combines the outputs of those learners. BalanceCascade trains the learners sequentially, where in each step, the majority class examples that are correctly classified by the current trained learners are removed from further consideration. Experimental results show that both methods have higher Area Under the ROC Curve, F-measure, and G-mean values than many existing class-imbalance learning methods. Moreover, they have approximately the same training time as that of undersampling when the same number of weak classifiers is used, which is significantly faster than other methods.

Under-sampling is a class-imbalance learning method which uses only a subset of major class examples and thus is very efficient. The main deficiency is that many major class examples are ignored. We propose two algorithms to overcome the deficiency. EasyEnsemble samples several subsets from the major class, trains a learner using each of them, and combines the outputs of those learners. BalanceCascade is similar to EasyEnsemble except that it removes correctly classified major class examples of trained learners from further consideration. Experiments show that both of the proposed algorithms have better AUC scores than many existing class-imbalance learning methods. Moreover, they have approximately the same training time as that of under-sampling, which trains significantly faster than other methods.

In real-world applications the number of examples in one class may overwhelm the other class, but the primary interest is usually on the minor class. Cost-sensitive learning has been deeded as a good solution to these class-imbalanced tasks, yet it is not clear how does the class-imbalance affect cost-sensitive classifiers. This paper presents an empirical study using 38 data sets, which discloses that class-imbalance often affects the performance of cost-sensitive classifiers: When the misclassification costs are not seriously unequal, cost-sensitive classifiers generally favor natural class distribution although it might be imbalanced; while when misclassification costs are seriously unequal, a balanced class distribution is more favorable.

This paper studies empirically the effect of sampling and threshold-moving in training cost-sensitive neural networks. Both oversampling and undersampling are considered. These techniques modify the distribution of the training data such that the costs of the examples are conveyed explicitly by the appearances of the examples. Threshold-moving tries to move the output threshold toward inexpensive classes such that examples with higher costs become harder to be misclassified. Moreover, hard-ensemble and soft-ensemble, i.e., the combination of above techniques via hard or soft voting schemes, are also tested. Twenty-one UCl data sets with three types of cost matrices and a real-world cost-sensitive data set are used in the empirical study. The results suggest that cost-sensitive learning with multiclass tasks is more difficult than with two-class tasks, and a higher degree of class imbalance may increase the difficulty. It also reveals that almost all the techniques are effective on two-class tasks, while most are ineffective and even may cause negative effect on multiclass tasks. Overall, threshold-moving and soft-ensemble are relatively good choices in training cost-sensitive neural networks. The empirical study also suggests that some methods that have been believed to be effective in addressing the class imbalance problem may, in fact, only be effective on learning with imbalanced two-class data sets.