��᠋᠌᠍ ��᠋᠌᠍ Combinatorial Hodge Theory with Applications � � Recall Vectors Graphs Hodge Theory Hodge Decomposition � Example I: Visual Image Patches – Point Cloud Data in Metric Spaces • Ann Lee, Kim Pedersen, David Mumford (2003) studies statistical properties of 3x3 high contrast image patches of natural images (from Van Heteran’s database) • Gunnar Carlsson, Vin de Silva, Tigran Ishkhanov,