We study the problem of learning the data samples' distribution as it changes in time. This change, known as concept drift, complicates the task of training a model, as the predictions become less and less accurate. It is known that Support Vector Machines (SVMs) can learn weighted input instances and that they can also be trained online (incremental-decremental learning). Combining these two SVM properties, the open problem is to define an online SVM concept drift model with shifting weighted window. The classic SVM model should be retrained from scratch after each window shift. We introduce the Weighted Incremental-Decremental SVM (WIDSVM), a generalization of the incremental-decremental SVM for shifting windows. WIDSVM is capable of learning from data streams with concept drift, using the weighted shifting window technique. The soft margin constrained optimization problem imposed on the shifting window is reduced to an incremental-decremental SVM. At each window shift, we determine the exact conditions for vector migration during the incremental-decremental process. We perform experiments on artificial and real-world concept drift datasets; they show that the classification accuracy of WIDSVM significantly improves compared to a SVM with no shifting window. The WIDSVM training phase is fast, since it does not retrain from scratch after each window shift.

Data classification in streams where the underlying distribution changes over time is known to be difficult. This problem—known as concept drift detection—involves two aspects: (i) detecting the concept drift and (ii) adapting the classifier. Online training only considers the most recent samples; they form the so-called shifting window. Dynamic adaptation to concept drift is performed by varying the width of the window. Defining an online Support Vector Machine (SVM) classifier able to cope with concept drift by dynamically changing the window size and avoiding retraining from scratch is currently an open problem. We introduce the Adaptive Incremental–Decremental SVM (AIDSVM), a model that adjusts the shifting window width using the Hoeffding statistical test. We evaluate AIDSVM performance on both synthetic and real-world drift datasets. Experiments show a significant accuracy improvement when encountering concept drift, compared with similar drift detection models defined in the literature. The AIDSVM is efficient, since it is not retrained from scratch after the shifting window slides.

Training a support vector machine (SVM) for regression (function approximation) in an incremental/decremental way consists essentially in migrating the input vectors in and out of the support vector set with specific modification of the associated thresholds. We introduce with full details such a method, which allows for defining the exact increments or decrements associated with the thresholds before vector migrations take place. Two delicate issues are especially addressed: the variation of the regularization parameter (for tuning the model performance) and the extreme situations where the support vector set becomes empty. We experimentally compare our method with several regression methods: the multilayer perceptron, two standard SVM implementations, and two models based on adaptive resonance theory.