2021/07/07 by Helmut Harbrecht, Harbrecht, Helmut, Michael Multerer +1
Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2107.03337
openalex publication_date 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we introduce the concept of samplets by transferring the construction of Tausch-White wavelets to the realm of data. This way we obtain a multilevel representation of discrete data which directly enables data compression, detection of singularities and adaptivity. Applying samplets to represent kernel matrices, as they arise in kernel based learning or Gaussian process regression, we end up with quasi-sparse matrices. By thresholding small entries, these matrices are compressible to O(N log N) relevant entries, where N is the number of data points. This feature allows for the use of fill-in reducing reorderings to obtain a sparse factorization of the compressed matrices. Besides the comprehensive introduction to samplets and their properties, we present extensive numerical studies to benchmark the approach. Our results demonstrate that samplets mark a considerable step in the direction of making large data sets accessible for analysis.