Given a matrix (of Data) we describe methodologies to build two multiscale (inference) Geometries/Harmonic Analysis one on the rows , the other on the columns . The geometries are designed to simplify the representation of the data base . We will provide a number of examples including; matrices of operators , psychological questionnaires, vector valued images, scientific articles, etc. In all these cases tensor Haar orthogonal bases play a crucial role in organizing the data base viewed as a function of two variables (row, column) in the case of potential operators we relate to Calderon Zugmund decompositions , while for other data this is a "data agnostic analytic learning tool" For the example of the matrix of eigenfunctions of a discretized Laplace operator ( say, on a compact manifold) we obtain both the Geometry of the domain of the Laplace operator as well as a dual multiscale Geometry of the eigenvectors...