Recent studies have shown that imbalance ratio is not the only cause of the performance loss of a classifier in imbalanced data classification. In fact, other data factors, such as small disjuncts, noises and overlapping, also play the roles in tandem with imbalance ratio, which makes the problem difficult. Thus far, the empirical studies have demonstrated the relationship between the imbalance ratio and other data factors only. To the best of our knowledge, there is no any measurement about the extent of influence of class imbalance on the classification performance of imbalanced data. Further, it is also unknown for a dataset which data factor is actually the main barrier for classification. In this paper, we focus on Bayes optimal classifier and study the influence of class imbalance from a theoretical perspective. Accordingly, we propose an instance measure called Individual Bayes Imbalance Impact Index ( @math ) and a data measure called Bayes Imbalance Impact Index ( @math ). @math and @math reflect the extent of influence purely by the factor of imbalance in terms of each minority class sample and the whole dataset, respectively. Therefore, @math can be used as an instance complexity measure of imbalance and @math is a criterion to show the degree of how imbalance deteriorates the classification. As a result, we can therefore use @math to judge whether it is worth using imbalance recovery methods like sampling or cost-sensitive methods to recover the performance loss of a classifier. The experiments show that @math is highly consistent with the increase of prediction score made by the imbalance recovery methods and @math is highly consistent with the improvement of F1 score made by the imbalance recovery methods on both synthetic and real benchmark datasets.
The second data factor is noise. Noisy samples are usually defined as the ones from one class located deep into the other class @cite_17 . The existence of noise samples in the minority class will make blind oversampling methods like SMOTE generate more noises, so that applying oversampling on the noisy the minority class may even degrade the performance @cite_2 . Therefore, data cleaning methods are usually adopted to tackle the noises such as Tomek link @cite_9 and ENN @cite_13 . Another straightforward method to find noise is to collect the samples which are wrongly classified by @math NN classifier @cite_0 . Van Hulse and Khoshgoftaar experimented on data with artificial noises @cite_34 , where the class noise is injected to real datasets by randomly relabelling the samples before training. The results show that the minority class is severely effected by noises with all compared classifiers.
@cite_9 @cite_0 @cite_2 @cite_34 @cite_13 @cite_17
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Data mining and knowledge discovery aim at producing useful and reliable models from the data. Unfortunately some databases contain noisy data which perturb the generalization of the models. An important source of noise consists of mislabelled training instances. We offer a new approach which deals with improving classification accuracies by using a preliminary filtering procedure. An example is suspect when in its neighbourhood defined by a geometrical graph the proportion of examples of the same class is not significantly greater than in the database itself. Such suspect examples in the training data can be removed or relabelled. The filtered training set is then provided as input to learning algorithms. Our experiments on ten benchmarks of UCI Machine Learning Repository using 1-NN as the final algorithm show that removal gives better results than relabelling. Removing allows maintaining the generalization error rate when we introduce from 0 to 20 of noise on the class, especially when classes are well separable. The filtering method proposed is finally compared to the relaxation relabelling schema. There are several aspects that might influence the performance achieved by existing learning systems. It has been reported that one of these aspects is related to class imbalance in which examples in training data belonging to one class heavily outnumber the examples in the other class. In this situation, which is found in real world data describing an infrequent but important event, the learning system may have difficulties to learn the concept related to the minority class. In this work we perform a broad experimental evaluation involving ten methods, three of them proposed by the authors, to deal with the class imbalance problem in thirteen UCI data sets. Our experiments provide evidence that class imbalance does not systematically hinder the performance of learning systems. In fact, the problem seems to be related to learning with too few minority class examples in the presence of other complicating factors, such as class overlapping. Two of our proposed methods deal with these conditions directly, allying a known over-sampling method with data cleaning methods in order to produce better-defined class clusters. Our comparative experiments show that, in general, over-sampling methods provide more accurate results than under-sampling methods considering the area under the ROC curve (AUC). This result seems to contradict results previously published in the literature. Two of our proposed methods, Smote + Tomek and Smote + ENN, presented very good results for data sets with a small number of positive examples. Moreover, Random over-sampling, a very simple over-sampling method, is very competitive to more complex over-sampling methods. Since the over-sampling methods provided very good performance results, we also measured the syntactic complexity of the decision trees induced from over-sampled data. Our results show that these trees are usually more complex then the ones induced from original data. Random over-sampling usually produced the smallest increase in the mean number of induced rules and Smote + ENN the smallest increase in the mean number of conditions per rule, when compared among the investigated over-sampling methods. Imbalanced learning problems contain an unequal distribution of data samples among different classes and pose a challenge to any classifier as it becomes hard to learn the minority class samples. Synthetic oversampling methods address this problem by generating the synthetic minority class samples to balance the distribution between the samples of the majority and minority classes. This paper identifies that most of the existing oversampling methods may generate the wrong synthetic minority samples in some scenarios and make learning tasks harder. To this end, a new method, called Majority Weighted Minority Oversampling TEchnique (MWMOTE), is presented for efficiently handling imbalanced learning problems. MWMOTE first identifies the hard-to-learn informative minority class samples and assigns them weights according to their euclidean distance from the nearest majority class samples. It then generates the synthetic samples from the weighted informative minority class samples using a clustering approach. This is done in such a way that all the generated samples lie inside some minority class cluster. MWMOTE has been evaluated extensively on four artificial and 20 real-world data sets. The simulation results show that our method is better than or comparable with some other existing methods in terms of various assessment metrics, such as geometric mean (G-mean) and area under the receiver operating curve (ROC), usually known as area under curve (AUC). Classification using class-imbalanced data is biased in favor of the majority class. The bias is even larger for high-dimensional data, where the number of variables greatly exceeds the number of samples. The problem can be attenuated by undersampling or oversampling, which produce class-balanced data. Generally undersampling is helpful, while random oversampling is not. Synthetic Minority Oversampling TEchnique (SMOTE) is a very popular oversampling method that was proposed to improve random oversampling but its behavior on high-dimensional data has not been thoroughly investigated. In this paper we investigate the properties of SMOTE from a theoretical and empirical point of view, using simulated and real high-dimensional data. While in most cases SMOTE seems beneficial with low-dimensional data, it does not attenuate the bias towards the classification in the majority class for most classifiers when data are high-dimensional, and it is less effective than random undersampling. SMOTE is beneficial for k-NN classifiers for high-dimensional data if the number of variables is reduced performing some type of variable selection; we explain why, otherwise, the k-NN classification is biased towards the minority class. Furthermore, we show that on high-dimensional data SMOTE does not change the class-specific mean values while it decreases the data variability and it introduces correlation between samples. We explain how our findings impact the class-prediction for high-dimensional data. In practice, in the high-dimensional setting only k-NN classifiers based on the Euclidean distance seem to benefit substantially from the use of SMOTE, provided that variable selection is performed before using SMOTE; the benefit is larger if more neighbors are used. SMOTE for k-NN without variable selection should not be used, because it strongly biases the classification towards the minority class.