(a) We first present a novel way to reduce the solution space of non-negative matrix factorization (NMF). We project the data matrix into the space of a sparse non-negative dictionary. Such a projection transforms the data into one that covers most of the positive orthant defined by the atoms of the dictionary. A simplicial cone containing the transformed data that occupies most of the positive orthant has little room to grow, thus reduces the solutions space. This allows guarantee of being close to an optimal solution with fewer random initializations. (b) We then switch gears and present a method to segment a hyperspectral image with only partial annotation. To make use of the partial annotation and the correlations between bands, we pose this as a semi-supervised learning problem. We first reduce the feature space using semi-supervised NMF. We then fit an ultrametric distance measure that support triple constraints derived from the partial annotation for semi-supervised hierarchical clustering. We further decide where to cut the dendogram using validation data, which clusters to assign to each class. The resulting segmentation and classification outperforms other methods tested. (c) We next show a practical application of sparse NMF in stain separation and density application in histological images, and its utility in tissue segmentation.
Amit Sethi is an Assistant Professor in EEE at Indian Institute of Technology Guwahati, and a visiting Instructor in Pathology at University of Illinois as Chicago. His current interests are computational pathology, deep learning, and non-negative matrix factorization. He also works in video classification, and has previously worked in structure from motion and human visual perception. Before joining IIT Guwahati, he worked as a management consultant in ZS Associates' Chicago office, where he worked with big data in the healthcare sector. He obtained his PhD in ECE from University of Illinois at Urbana-Champaign, and BTech in EE from IIT Delhi.