Twin support vector regression (TSVR) generates two nonparallel hyperplanes by solving a pair of smaller-sized problems instead of a single larger-sized problem in the standard SVR. Due to its efficiency, TSVR is frequently applied in various areas. In this paper, we propose a totally new version of TSVR named Linear Twin Quadratic Surface Support Vector Regression (LTQSSVR), which directly uses two quadratic surfaces in the original space for regression. It is worth noting that our new approach not only avoids the notoriously difficult and time-consuming task for searching a suitable kernel function and its corresponding parameters in the traditional SVR-based method but also achieves a better generalization performance. Besides, in order to make further improvement on the efficiency and robustness of the model, we introduce the 1-norm to measure the error. The linear programming structure of the new model skips the matrix inverse operation and makes it solvable for those huge-sized problems. As we know, the capability of handling large-sized problem is very important in this big data era. In addition, to verify the effectiveness and efficiency of our model, we compare it with some well-known methods. The numerical experiments on 2 artificial data sets and 12 benchmark data sets demonstrate the validity and applicability of our proposed method.

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<p style='text-indent:20px;'>Recently, Synthetic Minority Over-Sampling Technique (SMOTE) has been widely used to handle the imbalanced classification. To address the issues of existing benchmark methods, we propose a novel scheme of SMOTE based on the K-means and Intuitionistic Fuzzy Set theory to assign proper weights to the existing points and generate new synthetic points from them. Besides, we introduce the state-of-the-art kernel-free fuzzy quadratic surface support vector machine (QSSVM) to do the classification. Finally, the numerical experiments on various artificial and real data sets strongly demonstrate the validity and applicability of our proposed method, especially in the presence of mislabeled information.</p>

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