Abstract: A method may include obtaining a first matrix that represents data in a data set and obtaining a number of clusters into which the data is to be grouped. The method may further include constructing a second matrix using the first matrix and the number of clusters. The second matrix may represent a formulation of a first optimization problem in a framework of a second optimization problem. The method may further include solving the second optimization problem using the second matrix to generate a solution of the second optimization problem and mapping the solution of the second optimization problem into a first solution matrix that represents a solution of the first optimization problem. The method may further include grouping the data into multiple data clusters using the first solution matrix. A number of the multiple data clusters may be equal to the number of clusters.

Abstract: A computer-implemented method for analyzing a time-varying graph is provided. The time-varying graph includes nodes representing elements in a network, edges representing transactions between elements, and data associated with the nodes and the edges. The computer-implemented method includes constructing, using a processor, adjacency and feature matrices describing each node and edge of each time-varying graph for stacking into an adjacency tensor and describing the data of each time-varying graph for stacking into a feature tensor, respectively. The adjacency and feature tensors are partitioned into adjacency and feature training tensors and into adjacency and feature validation tensors, respectively. An embedding model and a prediction model are created using the adjacency and feature training tensors. The embedding and prediction models are validated using the adjacency and feature validation tensors to identify an optimized embedding-prediction model pair.

Abstract: A method may include obtaining a first matrix that represents data in a data set and obtaining a number of clusters into which the data is to be grouped. The method may further include constructing a second matrix using the first matrix and the number of clusters. The second matrix may represent a formulation of a first optimization problem in a framework of a second optimization problem. The method may further include solving the second optimization problem using the second matrix to generate a solution of the second optimization problem and mapping the solution of the second optimization problem into a first solution matrix that represents a solution of the first optimization problem. The method may further include grouping the data into multiple data clusters using the first solution matrix. A number of the multiple data clusters may be equal to the number of clusters.

Abstract: A computer-implemented method for analyzing a time-varying graph is provided. The time-varying graph includes nodes representing elements in a network, edges representing transactions between elements, and data associated with the nodes and the edges. The computer-implemented method includes constructing, using a processor, adjacency and feature matrices describing each node and edge of each time-varying graph for stacking into an adjacency tensor and describing the data of each time-varying graph for stacking into a feature tensor, respectively. The adjacency and feature tensors are partitioned into adjacency and feature training tensors and into adjacency and feature validation tensors, respectively. An embedding model and a prediction model are created using the adjacency and feature training tensors. The embedding and prediction models are validated using the adjacency and feature validation tensors to identify an optimized embedding-prediction model pair.