AbstractDeep convolutional networks have proved to be extremely powerful in image analysis. However.they tend to be biased toward local features such as texture and often fail to capture the globalstructure of image and volume data. Persistent homology (PH), a tool from the emerging field oftopological data analysis, has been successfully used to detect global characteristics of data thatare ov...
IntroductionCurrently the problem of transferring results of algebraic topology to discrete objects and, in particular, to various categories of digraphs and graphs, is widely investigated. The main technical tools are given by the homotopy theory and various homology theories. We present the basic methods of algebraic topology in graph theory and describe relations between continious and discr...
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