Auto-adaptive multi-scale Laplacian Pyramids for modeling non-uniform data

Improving Laplacian Pyramids Regression with Localization in Frequency and Time

“…The stopping scale in the ALP model relays on the mean square error at each level, denoted by err (l) , and results with one global stopping scale, l ⋆ , that is associated with all of the data points. In [7], both the model construction and the extension procedure were modified to provide the freedom for assigning a pointwise stopping scale. A new parameter ν was added to the model.…”

“…The first takes a hybrid approach by combining ALP with the Empirical Mode Decomposition (EMD) [6]. The second reviews and demonstrates the ALP-local model that was recently introduced in [7]. The EMD-ALP hybrid model enhances performance by localizing in frequency and the ALP-local model is constructed based on local, rather than global information in the spatial (or time) domain.…”

“…The ALP scheme that was proposed in [2,5] stops the refinements based on the global L 2 error, thus each data point is decomposed into an equal number of modes. In [7], a modified local stopping scale was introduced. It selects the optimal stopping scale for each point, with respect to the local noise level and the density.…”

datafold: data-driven models for point clouds and time series on manifolds

“…The latter refers to the image and pre-image mapping between the original and latent space (e.g., see analysis in Chiavazzo, Gear, Dsilva, Rabin, & Kevrekidis, 2014). This so-called "out-of-sample" extension interpolates general function values on manifold point clouds and, therefore, has to handle large input data dimensions (Coifman & Lafon, 2006b;Fernández, Rabin, Fishelov, & Dorronsoro, 2020;Rabin & Coifman, 2012). In datafold, out-of-sample extensions are imple-mented efficiently, so that interpolated function values for millions of points can be computed in seconds on a standard desktop computer.…”