Linear Time Visualization and Search in Big Data using Pixellated Factor Space Mapping

Abstract: It is demonstrated how linear computational time and storage efficient approaches can be adopted when analyzing very large data sets. More importantly, interpretation is aided and furthermore, basic processing is easily supported. Such basic processing can be the use of supplementary, i.e. contextual, elements, or particular associations. Furthermore pixellated grid cell contents can be utilized as a basic form of imposed clustering. For a given resolution level, here related to an associated m-adic ($m$ here is a non-prime integer) or p-adic ($p$ is prime) number system encoding, such pixellated mapping results in partitioning. The association of a range of m-adic and p-adic representations leads naturally to an imposed hierarchical clustering, with partition levels corresponding to the m-adic-based and p-adic-based representations and displays. In these clustering embedding and imposed cluster structures, some analytical visualization and search applications are described