We consider the problem of outlier rejection in single subspace learning. Classical approaches work with a direct representation of the subspace, and are thus efficient when the subspace dimension is small. Our approach works with a dual representation of the subspace and hence aims to find its orthogonal complement; as such it is particularly suitable for high-dimensional subspaces. We pose th...

Linear convergence rates of descent methods for unconstrained minimization are usually proven under the assumption that the objective function is strongly convex. Recently it was shown that the weaker assumption of restricted strong convexity suffices for linear convergence of the ordinary gradient descent method. A decisive difference to strong convexity is that the set of minimizers of a rest...

The concave-convex procedure (CCCP) is a majorization-minimization algorithm that solves d.c. (difference of convex functions) programs as a sequence of convex programs. In machine learning, CCCP is extensively used in many learning algorithms like sparse support vector machines (SVMs), transductive SVMs, sparse principal component analysis, etc. Though widely used in many applications, the con...

In Shallit’s problem (SIAM Review, 1994), it was proposed to justify a two-term asymptotics of the minimum rational function $$n$$ variables defined as sum special form whose number terms is order $$n^2$$ $$n\to\infty$$ . Of particular interest second term this (“Shallit’s constant”). The solution published in SIAM Review presented an iteration algorithm for calculating constant, which conta...