Supplemental Material for:Finding Dense Subgraphs via Low-Rank Bilinear Optimization

Finding Dense Subgraphs via Low-Rank Bilinear Optimization

Given a graph, the Densest k-Subgraph (DkS) problem asks for the subgraph on k vertices that contains the largest number of edges. In this work, we develop a new algorithm for DkS that searches a lowdimensional space for provably good solutions. Our algorithm comes with novel performance bounds that depend on the graph spectrum. Our graph-dependent bounds are in practice significantly tighter t...

Efficient Optimization for Low-Rank Integrated Bilinear Classifiers

In pattern classification, it is needed to efficiently treat twoway data (feature matrices) while preserving the two-way structure such as spatio-temporal relationships, etc. The classifier for the feature matrix is generally formulated by multiple bilinear forms which result in a matrix. The rank of the matrix, i.e., the number of bilinear forms, should be low from the viewpoint of generalizat...

Bilinear classifiers for visual recognition

We describe an algorithm for learning bilinear SVMs. Bilinear classifiers are a discriminative variant of bilinear models, which capture the dependence of data on multiple factors. Such models are particularly appropriate for visual data that is better represented as a matrix or tensor, rather than a vector. Matrix encodings allow for more natural regularization through rank restriction. For ex...

Discovering Large Dense Subgraphs in Massive Graphs

We present a new algorithm for finding large, dense subgraphs in massive graphs. Our algorithm is based on a recursive application of fingerprinting via shingles, and is extremely efficient, capable of handling graphs with tens of billions of edges on a single machine with modest resources. We apply our algorithm to characterize the large, dense subgraphs of a graph showing connections between ...

Supplemental Material: Unsupervised Feature Extraction Inspired by Latent Low-Rank Representation