A comparison of two algorithms for predicting the condition number

Abstract

We present experimental results of comparing the modified K-nearest neighbor (MkNN) algorithm with support vector machine (SVM) in the prediction of condition numbers of sparse matrices. Condition number of a matrix is an important measure in numerical analysis and linear algebra. However, the direct computation of the condition number of a matrix is very expensive in terms of CPU and memory cost, and becomes prohibitive for large size matrices. We use data mining techniques to estimate the condition number of a given sparse matrix. In our previous work, we used support vector machine (SVM) to predict the condition numbers. While SVM is considered a state-of- the-art classification/regression algorithm, kNN is usually used for collaborative filtering tasks. Since prediction can also be interpreted as a classification/regression task, virtually any supervised learning algorithm (such as kNN) can also be applied. Experiments are performed on a publicly available dataset. We conclude that modified kNN (MkNN) performs much better than SVM on this particular dataset.