A generalized uncorrelated ridge regression with nonnegative labels for unsupervised feature selection

The ridge regression has been widely applied in multiple domains and gains the promising performance. However, due to the unavailability of labels, the ridge regression easily incurs the trivial solution towards unsupervised learning. In this paper, we investigate unsupervised feature selection by virtue of an uncorrelated and nonnegative ridge regression model (UN-RFS). To be specific, a generalized uncorrelated constraint on the projection matrix, and a nonnegative orthogonal constraint on the indicator matrix are imposed upon the proposed regression model. With the proposed method, the most uncorrelated features on the embedded Stiefel manifold is exploited for feature selection and trivial solutions of projection matrix are avoided as well. Besides, equipped with a generalized scatter matrix, the proposed uncorrelated constraint is superior to conventional uncorrelated constraint, since the closed form solution can be achieved directly. In addition, owing to the nonnegative of real labels, the nonnegative orthogonal constraint is employed to suppress the indicator matrix such that the learned labels confront to reality further.