Subsampling of Correlated Graph Signals

Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based generative model. The question then arises whether measurements can be obtained on a few nodes and whether the correlation structure between the signals can be used to reconstruct the graph signal on the remaining nodes. We show that node subsampling is always possible for graph signals obtained through a generative model. Further, a method to determine the number of nodes to select is proposed based on the tolerable error. A correlation-based fast greedy algorithm is developed for selecting the nodes. Finally, we verify the proposed method on different deterministic and random graphs, and show that near-perfect reconstruction is possible with node subsampling.

PostDoc: Generating Poster from a Long Multimodal Document Using Deep Submodular Optimization

A poster from a long input document can be considered as a one-page easy-to-read multimodal (text and images) summary presented on a nice template with good design elements. Automatic transformation of a long document into a poster is a very less studied but challenging task. It involves content summarization of the input document followed by template generation and harmonization. In this work, we propose a novel deep submodular function which can be trained on ground truth summaries to extract multimodal content from the document and explicitly ensures good coverage, diversity and alignment of text and images. Then, we use an LLM based paraphraser and propose to generate a template with various design aspects conditioned on the input content. We show the merits of our approach through extensive automated and human evaluations.