Topological Classification of Firn Image Data

When snow persists yearly, previous layers of snowfall along with pockets of air are buried by fresh snow. As this cycle repeats, deeper layers of snow are put under increasing pressure until they solidify into glacial ice. Upper layers of granular snow that have not fully compressed into ice are called firn. The varying pressure causes changes in connectivity which motivates studying firn structure across multiple depths. Connectivity is well defined through homology, and we utilize techniques from persistent homology to map images to a vector space. This vectorized representation is compared with an embedding from a convolutional neural network built using transfer learning. We seek to compare the qualities of these vector representations through techniques from data mining.