Kernel methods with asymmetric and robust loss function

The least squares support vector machine (LSSVM) has achieved great success in various fields, but it still has certain limitations. Firstly, it treats all points equally and does not take into account the impact of different sample locations. Secondly, it is vulnerable to outliers and noise. Moreover, when class-imbalanced data are encountered, the decision boundary is biased toward the minority class. To address above problems, this paper introduces a bounded linear-exponential (BLINEX) loss function into LSSVM (LSKB), where the asymmetry and boundedness of the BLINEX loss function allow LSKB to assign distinct weights to each sample and be insensitive to noise and outliers. Further, this paper extends LSKB to a cost sensitive (CSLSKB) form to make it adapt to the class-imbalanced data. A fast optimization algorithm based on NESVM is developed to solve non-convex LSKB and CSLSKB (NEBLL). Numerous experiments demonstrate their effectiveness in dealing with class-balanced as well as class-imbalanced problems.