¹Department of Computer Science and Technology, Xiamen University of Technology, Xiamen 361024, China
²Key lab of Spatial Data Mining and Information Sharing, Ministry of Education, Fuzhou University, Fuzhou 350002, China
³Department of Automation,Xiamen University, Xiamen 361005, China

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Abstract—In this paper, the expansion of feature points of the linear scale space is transformed into the classification of multi-scale data set within the same scale, which belongs to the classification of scale invariant non-equilibrium .The paper presents a sample approach based on kernel learning to solve classification on imbalance dataset by Support Vector Machine (SVM). The method first preprocesses the data by oversampling the minority class in kernel space, and then the pre-images of the synthetic samples are found based on a distance relation between kernel space and input space. Finally, these pre-images are appended to the original dataset to train a SVM. As a result, the inconsistency which is brought about by processing samples in different spaces is overcome. On the other hand, the sampling strategies of the method not only can decrease imbalanced rate of training dataset, but also can enlarge convex hull of the minority class. Consequently, the problem of the boundary skew can be amended more effectively. Experiments on real dataset indicate that the generalization performance of the result classifier is improved and the algorithm can work well on expanding the feature points stably for a certain scale.

Index Terms—Kernel learning, Convex hull, Kernel space, Pre-image, Scale space.

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Cite: Shunzhi Zhu, Kaibiao Lin, Zhiqiang Zeng, Lizhao Liu, Wenxing Hong, "A Sampling Method Based on Gauss Kernel Learning and the Expanding Research," Journal of Computers vol. 7, no. 2, pp. 547-554, 2012.