Sample Selection in Support Vector Machines: A Fixed Neighborhood Sphere Approach

When dealing with large data set, support vector machine (SVM) needs lots of time to learn and lots of space to store. For reducing the cost of time and space, it need to select a subset of the training set. The samples locating near the boundary of the data distribution has more information than that locating within the data distribution. For searching the samples locating near the boundary of the data distribution, fixed neighborhood sphere sample selection algorithm is proposed in this paper. Generally, the sample locating within the data distribution has more neighbors in a fixed neighborhood sphere than that locating near the boundary of the data distribution. The samples locating near the boundary of the data distribution can be reserved by counting the number of the neighbors in as fixed neighborhood sphere. The time complexity of naive fixed neighborhood sphere sample selection algorithm is O(n
²
). A fast algorithm to solve the neighbors in a fixed neighborhood sphere in low-dimensional space called grid algorithm is proposed. The time complexity of grid algorithm is only O(n'*n)(n'<;<;n). Experimental results demonstrate that SVM become faster after disposing the samples locating within the data distribution meanwhile its accuracy does not degrade significantly.