BACKGROUND The prognosis of cancer recurrence is an important research area in bioinformatics and is challenging due to the small sample sizes compared to the vast number of genes. There have been several attempts to predict cancer recurrence. Most studies employed a supervised approach, which uses only a few labeled samples. Semi-supervised learning can be a great alternative to solve this pro...

Semi-supervised learning has witnessed increasing interest in the past decade. One common assumption behind semi-supervised learning is that the data labels should be sufficiently smooth with respect to the intrinsic data manifold. Recent research has shown that the features also lie on a manifold. Moreover, there is a duality between data points and features, that is, data points can be classi...

This paper presents a numerical comparison of two regularizations of the Euler equations, namely, the vortex blob regularization and regularization by physical viscosity. The initial condition is a flat vortex sheet whose vorticity has been smoothed by convolution. The sheet rolls up into a vortex pair. We compute the frequency of oscillations in the core vorticity and scale it using results fo...

An iterative method is introduced for solving noisy, ill-conditioned inverse problems. Analysis of the semi-convergence behavior identifies three error components iteration error, noise error, and initial guess error. A derived expression explains how the three errors are related to each other relative to the number of iterations. The Standard Tikhonov regularization method is just the first it...

The subject of this paper is an application of the multigrid method to the inverse problem in the Electrical Impedance Tomography. The multigrid algorithm of a new type has been developed for solving this problem, involving near-boundary semi-coarsening cycles within full-coarsening cycles. The results of the developed algorithm were compared with another previously developed multigrid algorith...

Our aim in this paper is to study generalizations of the Allen-Cahn equation based on a modification of the Ginzburg-Landau free energy proposed in [25]. In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence ...

We study anisotropic surface diffusion of curves with a small corner energy regularization. The regularization allows the use of nonconvex free energy densities and turns the evolution law into a 6th order geometric equation. Using a semi-implicit time discretization, we present a variational formulation of this equation for parametric curves, leading to a discretization based on linear finite ...

Most conventional semi-supervised learning methods attempt to directly include unlabeled data into training objectives. This paper presents an alternative approach that learns feature affinity information from unlabeled data, which is incorporated into the training objective as regularization of a maximum entropy model. The regularization favors models for which correlated features have similar...

In this study, we present an error analysis for Tikhonov regularization in a semi-stochastic setting. The analysis is carried out in such a way that it can be applied to any kind of inverse problem in atmospheric remote sensing. A method for selecting the optimal regularization parameter relying on the minimization of an estimator of the bound of the error between the first iterate and the exac...

Tree based ensemble methods can be seen as a way to learn a kernel from a sample of input-output pairs. This paper proposes a regularization framework to incorporate non-standard information not used in the kernel learning algorithm, so as to take advantage of incomplete information about output values and/or of some prior information about the problem at hand. To this end a generic convex opti...