Potential Support Vector Machine Based On Sampling

Potential SVM proposed by Hochreiter in 2006 is a new technique for the analysis of dyadic data, which describe the correlations between the samples of the two datasets by each element of the matrix. Potential Support Vector Machine (PSVM) has overcome the problem of the sensitivity of the dataset, and it can also handle the kernel matrices which are neither positive definite nor square. PSVM often learns large-scale datasets in the actual application, which take up so large memory that the training speed is very slow. Therefore, it is very meaningful to accelerate the training speed of PSVM for large-scale data.For PSVM learning of large-scale datasets, the learning process of PSVM takes up so large memory that the training speed is very slow. To accelerate the training speed of the PSVM for large-scale datasets, a new method is proposed, which introduces PSVM based on sampling. The Improved algorithm is divided into two strategies, one is support vector tracking strategy based on sampling, and the other is deletion of samples strategy based on sampling. Support vector tracking strategy removes most non-support vectors, and keep support vectors playing a decisive role in the process of classification, then compresses the support vectors to the sampling set. When the number of support vectors is large relative to the number of the entire sample set, all the support vectors can not be fully compressed into the sampling set, so this strategy is especially suitable for the case of less number of support vectors. Deletion of samples strategy removes most non-support vectors, keeps the samples that are on and near the boundary in the sample set after the deletion, which may be the support vectors. This strategy is especially suitable for large-scale datasets and the large number of support vectors. Simulation experiments and theoretical analysis indicate that the two strategies have accelerated the training time of the PSVM classifier.