Data sets are often modeled as point clouds in $R^D$, for $D$ large. It is\noften assumed that the data has some interesting low-dimensional structure, for\nexample that of a $d$-dimensional manifold $M$, with $d$ much smaller than $D$.\nWhen $M$ is simply a linear subspace, one may exploit this assumption for\nencoding efficiently the data by projecting onto a dictionary of $d$ vectors in\n$R^D$ (for example found by SVD), at a cost $(n+D)d$ for $n$ data points. When\n$M$ is nonlinear, there are no "explicit" constructions of dictionaries that\nachieve a similar efficiency: typically one uses either random dictionaries, or\ndictionaries obtained by black-box optimization. In this paper we construct\ndata-dependent multi-scale dictionaries that aim at efficient encoding and\nmanipulating of the data. Their construction is fast, and so are the algorithms\nthat map data points to dictionary coefficients and vice versa. In addition,\ndata points are guaranteed to have a sparse representation in terms of the\ndictionary. We think of dictionaries as the analogue of wavelets, but for\napproximating point clouds rather than functions.\n