ABSTRACT
This chapter discusses data analytics as the discovery of symmetries in data. It addresses contemporary big data needs, especially because symmetries can be at different resolution scales. The chapter includes the following: to locate symmetry and group theory at the crossroads of data mining and data analytics too. It describes ultrametric topology as an expression of hierarchy. The chapter shows an important goal that how it lays bare many diverse symmetries in the observed phenomenon represented by the data. The main distinguishing feature of p-adic numbers is the treelike hierarchical structure. The chapter explains how the p-adic or ultrametric framework provides significant focus and commonality of viewpoint. A very fundamental principle in much of statistics, signal processing and data analysis is that of sparsity, but, by "codifying the inter-dependency structure" in the data new perspectives are opened up above and beyond sparsity.
