Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization

The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometric perspective, we derive new separable NMF algorithms that are highly scalable and empirically noise robust, and have several other favorable properties in relation to existing methods. A parallel implementation of our algorithm demonstrates high scalability on shared- and distributed-memory machines.Comment: 15 pages, 6 figure

Segmentation of Unstructured Newspaper Documents

Document layout analysis is one of the important steps in automated document recognition systems. In Document layout analysis, meaningful information is retrieved from document images by identifying, categorizing and labeling the semantics of text blocks from the document images. In this paper, we present simple top-down approach for document page segmentation. We have tested the proposed method on unstructured documents like newspaper which is having complex structures having no fixed structure. Newspaper also has multiple titles and multiple columns. In the proposed method, white gap area which separates titles, columns of text, line of text and words in lines have been identified to separate document into various segments. The proposed algorithm has been successfully implemented and applied over a large number of Indian newspapers and the results have been evaluated by number of blocks detected and taking their correct ordering information into account