Neighbors’ distribution property and sample reduction for support vector machines

• A novel method is proposed to detect boundary regions of data set.
• The samples locating in boundary regions take place of overlap regions to represent training set during pre-processing of SVMs.
• The proposed method can avoid assuming that there are overlap regions between different classes.

For data pre-processing of SVMs, many scholars tried to find those samples, which would become support vectors. Generally, support vectors locate in the overlap regions, which are between different classes. But overlap region does not always exist. In this paper, a new method is proposed to find the boundary regions of each class instead of overlap regions. This method could deal with the dataset without overlap regions. Summing the cosine of the sample-neighbor angle, the sum ranges from 0 to k. When the sample locates in the boundary region of data distribution, the sum would be close to k; when the sample locates in the interior of the data distribution, the sum would be close to 0. Using cosine sum, the samples locating in the interior of each class can be disposed before SVMs training. Experimental results show that the proposed method can solve the problem, which the methods based on finding overlap regions cannot deal with.

Sample-neighbor angle of x0 is defined as x0−x¯k and x0 − xi (x¯k is mass center, x¯k=(1/k)∑i=1kxi;   xi∈kNN(x0)).Figure optionsDownload as PowerPoint slide