this talk is about representation learning with a nontrivial geometry of variables. a convolutional neural network can be viewed as a statistical machine to detect and count features in an image progressively through a multi-scale system. the constructed features are insensitive to nuance variations in the input, while sufficiently discriminative to predict labels. we introduce the haar scattering transform as a model of such a system for unsupervised learning. employing haar wavelets makes it applicable to data lying on graphs that are not necessarily pixel grids. when the underlying graph is unknown, an adaptive version of the algorithm infers the geometry of variables by optimizing the construction of the haar basis so as to minimize data variation. given time, i will also mention an undergoing project of flow cytometry data analysis, where histogram-like features are used for comparing empirical distributions. after ``binning'' samples on a mesh in space, the problem can be closely related to feature learning when a variable geometry is present.