Graph-based approaches for semi-supervised learning have received increasing amount of interest in recent years. Despite their good performance, many pure graph based algorithms do not have explicit functions and can not predict the label of unseen data. Graph regularization is a recently proposed framework which incorporates the intrinsic geometrical structure as a regularization term. It can ...

As more and more complex data sources become available, the analysis of graph and manifold data has become an essential part of various sciences. In this thesis, learning functions through samples on a manifold is investigated. Toward this goal, several problems are studied. First, regularization in Sobolev spaces on manifolds are studied, which can be used to find a smooth function on the data...

The problem of fitting a union of subspaces to a collection of data points drawn from multiple subspaces is considered in this paper. In the traditional low rank representation model, the dictionary used to represent the data points is chosen as the data points themselves and thus the dictionary is corrupted with noise. This problem is solved in the low rank subspace clustering model which deco...

In this paper we propose a novel approach to define task-driven regularization constraints in deformable image registration using learned deformation priors. Our method consists of representing deformation through a set of control points and an interpolation strategy. Then, using a training set of images and the corresponding deformations we seek for a weakly connected graph on the control poin...

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...

Manifold regularization (MR) provides a powerful framework for semi-supervised classification (SSC) using both the labeled and unlabeled data. It first constructs a single Laplacian graph over the whole dataset for representing the manifold structure, and then enforces the smoothness constraint over such graph by a Laplacian regularizer in learning. However, the smoothness over such a single La...

A graph containing some edges with probability measures and other uncertain is referred to as an random graph. Numerous real-world problems in social networks transportation can be boiled down optimization graphs. Actually, information graphs always asymmetric. Regularization a common problem theory, the regularity index fundamentally measurable indicator of Therefore, this paper investigates w...

We introduce and study a mathematical framework for broad class of regularization functionals ill-posed inverse problems: Regularization Graphs. graphs allow to construct using as building blocks linear operators convex functionals, assembled by means that can be seen generalizations classical infimal convolution operators. This exhaustively covers existing approaches it is flexible enough craf...

The well-known regularity lemma of E. Szemerédi for graphs (i.e. 2-uniform hypergraphs) claims that for any graph there exists a vertex partition with the property of quasi-randomness. We give a simple construction of such a partition. It is done just by taking a constant-bounded number of random vertex samplings only one time (thus, iteration-free). Since it is independent from the definition ...