Massive, high-dimensional data sets, for which traditional methods are inadequate, pose challenges in processing, interpretation and analyses. These challenges have led to increased innovations in scale and complexity of data where a fusion of various approaches is required. The purpose of this workshop is to bring together research directions using geometric, topological and graphical model methods with applications to subjects such as bioinformatics, genetics and neurosciences, to name a few. The kernel of this workshop stems from some of the working groups coming from the 2013-14 SAMSI LDHD program. invited speakers will present their methodological advancements with a heavy emphasis on applications.