Density-based weighting multi-surface least squares classification with its applications

Abstract

Traditionally, multi-plane support vector machines (SVM), including twin support vector machine (TWSVM) and least squares twin support vector machine (LSTSVM), consider all of points and view them as equally important points. In real cases, most of the samples of a dataset are highly correlated. These samples generally lie in the high-density regions and may be important for performances of classifiers. This motivates the rush toward new classifiers that can sufficiently take advantage of the points in the high-density regions. Illuminated by several new geometrically motivated algorithms, we propose density-based weighting multi-surface least squares classification (DWLSC) method, which is designed for classification. Considering the special features of multi-plane SVMs, DWLSC can measure the importance of points sharing the same labels by density weighting method and sufficiently make the full use of margin point information between pairs of points from different classes. It also includes naturally an extension of the non-linear case. In addition to keeping the respective advantages of both TWSVM and LSTSVM, our method improves the separation of the points sharing different classes and is shown to be better than other multi-plane classifiers in favor of reduction in space complexity, especially when confronted with the non-linear case. In addition, experimental evidence suggests that our method is effective in performing classification tasks.