
DSL: Discriminative Subgraph Learning via Sparse SelfRepresentation
The goal in network state prediction (NSP) is to classify the global sta...
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Towards Gallai's path decomposition conjecture
A path decomposition of a graph G is a collection of edgedisjoint paths...
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A New Characterization of Path Graphs
Path Graphs are intersection graphs of paths in a tree. Path Graphs are ...
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On density of subgraphs of Cartesian products
In this paper, we extend two classical results about the density of subg...
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Technical Report: GraphStructured Sparse Optimization for Connected Subgraph Detection
Structured sparse optimization is an important and challenging problem f...
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A Regularization Approach for Prediction of Edges and Node Features in Dynamic Graphs
We consider the two problems of predicting links in a dynamic graph sequ...
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Enumerating consistent subgraphs of directed acyclic graphs: an insight into biomedical ontologies
Modern problems of concept annotation associate an object of interest (g...
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Supervised Feature Selection in Graphs with Path Coding Penalties and Network Flows
We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or obtain results that are easier to interpret. Regularization or penalty functions for selecting features in graphs have recently been proposed, but they raise new algorithmic challenges. For example, they typically require solving a combinatorially hard selection problem among all connected subgraphs. In this paper, we propose computationally feasible strategies to select a sparse and wellconnected subset of features sitting on a directed acyclic graph (DAG). We introduce structured sparsity penalties over paths on a DAG called "path coding" penalties. Unlike existing regularization functions that model longrange interactions between features in a graph, path coding penalties are tractable. The penalties and their proximal operators involve path selection problems, which we efficiently solve by leveraging network flow optimization. We experimentally show on synthetic, image, and genomic data that our approach is scalable and leads to more connected subgraphs than other regularization functions for graphs.
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