Least-Squares Regression with Unitary Constraints for Network Behaviour Classification

In this paper, we propose a least-squares regression method [2] with unitary constraints with applications to classification and recognition. To do this, we employ a kernel to map the input instances to a feature space on a sphere. In a similar fashion, we view the labels associated with the training data as points which have been mapped onto a Stiefel manifold using random rotations. In this manner, the least-squares problem becomes that of finding the span and kernel parameter matrices that minimise the distance between the embedded labels and the instances on the Stiefel manifold under consideration. We show the effectiveness of our approach as compared to alternatives elsewhere in the literature for classification on synthetic data and network behaviour log data, where we present results on attack identification and network status prediction.