Title: Geometry and Topology of DataAbstract: Data sets are often equipped with distances between data points, and thereby constitute a discrete metric space. We develop general notions of curvature that capture local and global properties of such spaces and relate them to topological concepts such as hyperconvexity. This also leads to a new interpretation of TDA.
AbstractWe propose a new unsupervised learning method for clustering a large number of time series based on a latent factor structure. Each cluster is characterized by its own cluster-specific factors in addition to some common factors which impact on all the time series concerned. Our setting also offers the flexibility that some time series may not belong to any clusters. The consistency with...