R package TDA (Topological Data Analysis)

Authors: Brittany Fasy, Jisu Kim, Fabrizio Lecci, Clement Maria, Vincent Rouvreau

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Description: TDA provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information about the underlying space, such as the distance function, the distance to a measure, the kNN density estimator, the kernel density estimator, and the kernel distance. The salient topological features of the sublevel sets (or superlevel sets) of these functions can be quantified with persistent homology. We provide an R interface for the efficient algorithms of the C++ libraries GUDHI, Dionysus and PHAT, including a function for the persistent homology of the Rips filtration, and one for the persistent homology of sublevel sets (or superlevel sets) of arbitrary functions evaluated over a grid of points. The significance of the features in the resulting persistence diagrams can be analyzed with functions that implement recently developed statistical methods. The R package TDA also includes the implementation of an algorithm for density clustering, which allows us to identify the spatial organization of the probability mass associated to a density function and visualize it by means of a dendrogram, the cluster tree.

R package longfused

Authors: Samrachana Adhikari, Fabrizio Lecci, Ryan Tibshirani

Maintainer: Fabrizio Lecci

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Description: we studied regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). The R package longfused provides an efficient algorithm for computing such estimates, based on proximal gradient descent and entirely coded in C++. For more info see the related paper.