The present study introduces a method for improving the classification performance of imbalanced multiclass data streams from wireless body worn sensors. Data imbalance is an inherent problem in activity recognition caused by the irregular time distribution of activities, which are sequential and dependent on previous movements. We use conditional random fields (CRF), a graphical model for structured classification, to take advantage of dependencies between activities in a sequence. However, CRFs do not consider the negative effects of class imbalance during training. We propose a class-wise dynamically weighted CRF (dWCRF) where weights are automatically determined during training by maximizing the expected overall F-score. Our results based on three case studies from a healthcare application using a batteryless body worn sensor, demonstrate that our method, in general, improves overall and minority class F-score when compared to other CRF based classifiers and achieves similar or better overall and class-wise performance when compared to SVM based classifiers under conditions of limited training data. We also confirm the performance of our approach using an additional battery powered body worn sensor dataset, achieving similar results in cases of high class imbalance.
This section reviews previous methods developed for improving the classification of imbalanced data, such as data re-sampling @cite_4 @cite_32 @cite_7 @cite_37 , adjusting decision thresholds @cite_22 or the inclusion of cost parameters or weights into the classification algorithm @cite_27 @cite_21 @cite_3 @cite_34 @cite_11 @cite_25 @cite_15 @cite_30 . The approach presented in this article is based on the latter.
@cite_30 @cite_37 @cite_4 @cite_22 @cite_7 @cite_21 @cite_32 @cite_3 @cite_27 @cite_15 @cite_34 @cite_25 @cite_11
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Many established classifiers fail to identify the minority class when it is much smaller than the majority class. To tackle this problem, researchers often first rebalance the class sizes in the training dataset, through oversampling the minority class or undersampling the majority class, and then use the rebalanced data to train the classifiers. This leads to interesting empirical patterns. In particular, using the rebalanced training data can often improve the area under the receiver operating characteristic curve (AUC) for the original, unbalanced test data. The AUC is a widely-used quantitative measure of classification performance, but the property that it increases with rebalancing has, as yet, no theoretical explanation. In this note, using Gaussian-based linear discriminant analysis (LDA) as the classifier, we demonstrate that, at least for LDA, there is an intrinsic, positive relationship between the rebalancing of class sizes and the improvement of AUC. We show that the largest improvement of AUC is achieved, asymptotically, when the two classes are fully rebalanced to be of equal sizes. 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. The problem of learning from imbalanced data sets, while not the same problem as learning when misclassication costs are unequal and unknown, can be handled in a similar manner. That is, in both contexts, we can use techniques from roc analysis to help with classier design. We present results from two studies in which we dealt with skewed data sets and unequal, but unknown costs of error. We also compare for one domain these results to those obtained by over-sampling and under-sampling the data set. The operations of sampling, moving the decision threshold, and adjusting the cost matrix produced sets of classiers that fell on the same roc curve. In this paper, a novel inverse random under sampling (IRUS) method is proposed for the class imbalance problem. The main idea is to severely under sample the majority class thus creating a large number of distinct training sets. For each training set we then find a decision boundary which separates the minority class from the majority class. By combining the multiple designs through fusion, we construct a composite boundary between the majority class and the minority class. The proposed methodology is applied on 22 UCI data sets and experimental results indicate a significant increase in performance when compared with many existing class-imbalance learning methods. We also present promising results for multi-label classification, a challenging research problem in many modern applications such as music, text and image categorization. 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. In the standard support vector machines for classification, training sets with uneven class sizes results in classification biases towards the class with the large training size. That is to say, the larger the training sample size for one class is, the smaller its corresponding classification error rate is, while the smaller the sample size, the larger the classification error rate. The main causes lie in that the penalty of misclassification for each training sample is considered equally. Weighted support vector machines for classification are proposed in this paper where penalty of misclassification for each training sample is different. By setting the equal penalty for the training samples belonging to same class, and setting the ratio of penalties for different classes to the inverse ratio of the training class sizes, the obtained weighted support vector machines compensate for the undesirable effects caused by the uneven training class size, and the classification accuracy for the class with small training size is improved. Experimental simulations on breast cancer diagnosis show the effectiveness of the proposed methods. a b s t r a c t Linear Proximal Support Vector Machines (LPSVMs), like decision trees, classic SVM, etc. are originally not equipped to handle drifting data streams that exhibit high and varying degrees of class imbalance. For online classification of data streams with imbalanced class distribution, we propose a dynamic class imbalance learning (DCIL) approach to incremental LPSVM (IncLPSVM) modeling. In doing so, we simplify a computationally non-renewable weighted LPSVM to several core matrices multiplying two simple weight coefficients. When data addition and or retirement occurs, the proposed DCIL-IncLPSVM 1 accommodates newly presented class imbalance by a simple matrix and coefficient updating, meanwhile ensures no discriminative information lost throughout the learning process. Experiments on benchmark datasets indicate that the proposed DCIL-IncLPSVM outperforms classic IncSVM and IncLPSVM in terms of F -measure and G-mean metrics. Moreover, our application to online face membership authentication shows that the proposed DCIL-IncLPSVM remains effective in the presence of highly dynamic class imbalance, which usually poses serious problems to previous approaches. Abstract Cost-sensitive learning has received increased attention in recent years. However, in existing studies, most of the works are devoted to make decision trees cost-sensitive and very few works discuss cost-sensitive Bayesian network classifiers. In this paper, an instance weighting method is incorporated into various Bayesian network classifiers. The probability estimation of Bayesian network classifiers is modified by the instance weighting method, which makes Bayesian network classifiers cost-sensitive. The experimental results on 36 UCI data sets show that when cost ratio is large, the cost-sensitive Bayesian network classifiers perform well in terms of the total misclassification costs and the number of high cost errors. When cost ratio is small, the advantage of cost-sensitive Bayesian network classifiers is not so obvious in terms of the total misclassification costs, but still obvious in terms of the number of high cost errors, compared to the original cost-insensitive Bayesian network classifiers.