Modern data analysis involves large sets of structured data, where the structure carries critical information about the nature of the data. These relationships between entities, such as features or data samples, are usually described by a graph structure. While many real-world data are intrinsically graph-structured, e.g. social and traffic networks, there is still a large number of applications, where the graph topology is not readily available. For instance, gene regulations in biological applications or neuronal connections in the brain are not known. In these applications, the graphs need to be learned since they reveal the relational structure and may assist in a variety of learning tasks. Graph learning (GL) deals with the inference of a topological structure among entities from a set of observations on these entities, i.e., graph signals. Most of the existing work on graph learning focuses on learning a single graph structure, assuming that the relations between the observed data samples are homogeneous. However, in many real-world applications, there are different forms of interactions between data samples, such as single-cell RNA sequencing (scRNA-seq) across multiple cell types. This talk will present a new framework for multiview graph learning in two settings: i) multiple views of the same data and ii) heterogeneous data with unknown cluster information. In the first case, a joint learning approach where both individual graphs and a consensus graph are learned will be developed. In the second case, a unified framework that merges classical spectral clustering with graph signal smoothness will be developed for joint clustering and multiview graph learning. 
This is joint work with Abdullah Karaaslanli, Satabdi Saha and Taps Maiti.