Semi-supervised learning gets estimated marginal distribution X P with a large number of unlabeled examples and then constrains the conditional probability ) | ( x y p with a few labeled examples. In this paper, we focus on a regularization approach for semi-supervised classification. The label information graph is first defined to keep the pairwise label relationship and can be incorporated wi...

We propose a discrete regularization framework on weighted graphs of arbitrary topology, which unifies image and mesh filtering. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses the discrete p-Laplace operator, and an approximation one. This formulation leads to a family of simple nonlinear f...

Nonnegative Matrix Tri-factorization (NMTF) and its graph regularized extensions have been widely used for co-clustering task to group data points and features simultaneously. However existing methods are sensitive to noises and outliers which is because of the squared loss function is used to measure the quality of data reconstruction and graph regularization. In this paper, we extend GNMTF by...

Graph cut minimization formulates the image segmentation as a linear combination of problem constraints. The salient constraints of the computer vision problems are data and smoothness which are combined through a regularization parameter. The main task of the regularization parameter is to determine the weight of the smoothness constraint on the graph energy. However, the difference in functio...

We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to train fully-connected network jointly with the graph neural via parameter sharing and interpolation-based regularization. Further, provide theoretical analysis of how GraphMix improves generalization bounds underlying network, without making any assumptions ab...

Visualization of high-dimensional data, such as text documents, is useful to map out the similarities among various data points. In the high-dimensional space, documents are commonly represented as bags of words, with dimensionality equal to the vocabulary size. Classical approaches to document visualization directly reduce this into visualizable two or three dimensions. Recent approaches consi...

one of the main steps within the geoid computation methodology without applying the stokes formula is downward continuation of the harmonic residual observables from the surface of the earth down to the surface of the reference ellipsoid. this downward continuation is done via the abel-poisson integral and its derivatives. this integral in which the unknowns, i.e. harmonic residual potential va...

A new method for diffusion tensor (DT) image regularization is presented that relies on heat diffusion on discrete structures. We represent a DT image using a weighted undirected graph, where the weights of the edges are determined from the geometry of the white matter fiber pathways. Diffusion across this weighted graph is captured by the heat equation, and the solution, i.e. the heat kernel, ...

The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hölder functions. As an intermediate s...

We propose a discrete regularization framework on weighted graphs of arbitrary topology, which leads to a family of nonlinear filters, such as the bilateral filter or the TV digital filter. This framework, which minimizes a loss function plus a regularization term, is parameterized by a weight function defined as a similarity measure. It is applicable to several problems in image processing, da...