We consider the problem of labeling a partially labeled graph. This setting may arise in a number of situations from survey sampling to information retrieval to pattern recognition in manifold settings. It is also of potential practical importance, when the data is abundant, but labeling is expensive or requires human assistance. Our approach develops a framework for regularization on such grap...

This paper presents a novel symmetric graph regularization framework for pairwise constraint propagation. We first decompose the challenging problem of pairwise constraint propagation into a series of two-class label propagation subproblems and then deal with these subproblems by quadratic optimization with symmetric graph regularization. More importantly, we clearly show that pairwise constrai...

In semi-supervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with “spikes” at labeled points in R for d ≥ 2. These optimization problems all use the graph Laplacian regularizer as a common penalty term. In this paper...

In this work, we propose a supervised dictionary learning algorithm, that attempts to preserve the local geometry in both dimensions of the data. A graph-based regularization explicitly takes into account the local manifold structure of the data, and a second graph regularization gives similar treatment to the feature domain and helps in learning a more robust dictionary. Both graphs can be con...

We propose a novel multi-task learning method that minimizes the effect of negative transfer by allowing asymmetric transfer between the tasks based on task relatedness as well as the amount of individual task losses, which we refer to as Asymmetric Multi-task Learning (AMTL). To tackle this problem, we couple multiple tasks via a sparse, directed regularization graph, that enforces each task p...

Data with intrinsic feature relationships are becoming abundant in many applications including bioinformatics and sensor network analysis. In this paper we consider a classification problem where there is a fixed and known binary relation defined on the features of a set of multivariate random variables. We formalize such a problem as an aligned graph classification problem. By incorporating th...

We consider the problem of learning the structure of a Markov Random Field (MRF) when a node-specific degree distribution is provided. The problem setting is inspired by protein contact map (i.e., graph) prediction in which the contact number (i.e., degree) of an individual residue (i.e., node) can be predicted without knowing the contact graph. We formulate this problem using maximum pseudo-li...

This theoretical paper aims to provide a probabilistic framework for graph signal processing. By modeling signals on graphs as Gaussian Markov Random Fields, we present numerous important aspects of graph signal processing, including graph construction, graph transform, graph downsampling, graph prediction, and graph-based regularization, from a probabilistic point of view. As examples, we disc...