We introduce a method called multi-scale local shape analysis for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine learning algorithms operating on the dataset. Using synthetic and real dataset examples, we demonstrate significant performance improvement of classification algorithms constructed for these datasets with correspondingly augmented features.

We show that every linearly recursive query can be expressed as a transitive closure possibly preceded and followed by operations already available in relational algebra. This reduction is possible even if there are repeated variables in the recursive literals and if some of the arguments in the recursive literals are constants. Such an equivalence has significant theoretical and practical ramifications. One the one hand it influences the design of expressive notations to capture recursion as an augmentation of relational query languages. On the other hand implementation of deductive databases is impacted in that the design does not have to provide the generality that linear recursion would demand. It suffices to study the single problem of transitive closure and to provide an efficient implementation for it.