A foundational problem in semi-supervised learning is the construction of a graph underlying the data. We propose to use a method which optimally combines a number of differently constructed graphs. For each of these graphs we associate a basic graph kernel. We then compute an optimal combined kernel. This kernel solves an extended regularization problem which requires a joint minimization over...

Minimal surface regularization has been used in several applications ranging from stereo to image segmentation, sometimes hidden as a graph-cut discrete formulation, or as a strictly convex approximation to TV minimization. In this paper we consider a modified version of minimal surface regularization coupled with a robust data fitting term for interpolation purposes, where the corresponding ev...

Given a directed graph in which some of the nodes are labeled, we investigate the question of how to exploit the link structure of the graph to infer the labels of the remaining unlabeled nodes. To that extent we propose a regularization framework for functions defined over nodes of a directed graph that forces the classification function to change slowly on densely linked subgraphs. A powerful...

In this paper, we propose a general formulation of discrete functional regularization on weighted graphs. This framework can be used to on any multi-dimensional data living on graphs of arbitrary topologies. But, in this work, we focus on the microscopic image segmentation and classification with a semi and unsupervised schemes. Moreover, to provide a fast image segmentation we propose a graph ...

We present a flexible formulation of semisupervised learning for structured models, which seamlessly incorporates graphbased and more general supervision by extending the posterior regularization (PR) framework. Our extension allows for any regularizer that is a convex, differentiable function of the appropriate marginals. We show that surprisingly, non-linearity of such regularization does not...

Many previous graph-based methods perform dimensionality reduction on a pre-defined graph. However, due to the noise and redundant information in the original data, the pre-defined graph has no clear structure and may not be appropriate for the subsequent task. To overcome the drawbacks, in this paper, we propose a novel approach called linear manifold regularization with adaptive graph (LMRAG)...

We consider parametric Feynman integrals and their dimensional regularization from the point of view of differential forms on hypersurface complements and the approach to mixed Hodge structures via oscillatory integrals. We consider restrictions of linear subspaces that slice the singular locus, to handle the presence of non-isolated singularities. In order to account for all possible choices o...

In this paper, we propose to represent and classify complicated objects. In order to represent the objects, we propose a multi-graph-view model which uses graphs constructed from multiple graph-views to represent an object. In addition, a bag based multi-graph model is further used to relax labeling by only requiring one label for a bag of graphs, which represent one object. In order to learn c...

Minimization of regularized losses is a principled approach to weak supervision well-established in deep learning, in general. However, it is largely overlooked in semantic segmentation currently dominated by methods mimicking full supervision via “fake” fully-labeled training masks (proposals) generated from available partial input. To obtain such full masks the typical methods explicitly use ...

Image segmentation techniques typically require proper weighting of competing data fidelity and regularization terms. Conventionally, the associated parameters are set through tedious trial and error procedures and kept constant over the image. However, spatially varying structural characteristics, such as object curvature, combined with varying noise and imaging artifacts, significantly compli...