Void-and-Cluster Sampling of Large Scattered Data and Trajectories

Abstract

We propose a data reduction technique for scattered data based on statistical sampling. Our void-and-cluster sampling technique finds a representative subset that is optimally distributed in the spatial domain with respect to the blue noise property. In addition, it can adapt to a given density function, which we use to sample regions of high complexity in the multivariate value domain more densely. Moreover, our sampling technique implicitly defines an ordering on the samples that enables progressive data loading and a continuous level-of-detail representation. We extend our technique to sample time-dependent trajectories, for example pathlines in a time interval, using an efficient and iterative approach. Furthermore, we introduce a local and continuous error measure to quantify how well a set of samples represents the original dataset. We apply this error measure during sampling to guide the number of samples that are taken. Finally, we use this error measure and other quantities to evaluate the quality, performance, and scalability of our algorithm.Data reduction is thus a necessary means to reduce storage requirements for both simulation, measurement devices, and for subsequent data analysis.We specifically consider the reduction of large, spatio-temporal scattered data, i.e. unstructured points in space-time with an associated value domain. In particular, we investigate the use of statistical sampling to reduce large data sets to a representative subset. Sampling scales well to higher dimensional data and is well-suited for scattered data. Although simple random sampling gives decent results, recent work improves upon this using stratified [21, 28] and informationguided sampling [3,27]. These results emphasize the significance of 1 arXiv:1907.05073v1 [cs.GR]

Blue Noise Plots

“…By exploiting task-dependent cost functions, they are able to obtain satisfying scatter plot designs, which compete with those crafted by humans. Yuan et al[YXX * 20] and Rapp et al [RPD20] also address the problem of overdraw in scatter plots where they select a subset of data points from a large data set such that the resulting patterns follows the density, yet has blue noise. Our work does not select subsets, but shows all data points, and introduce an additional, non-encoding dimension so that dots can become blue noise in the first place.…”

Uniform-in-Phase-Space Data Selection with Iterative Normalizing Flows

“…The main hurdle to overcome is the estimation of the PDF of the dataset in phase-space, which is ultimately used to compute the acceptance probability. Different solutions have been proposed, including kernel methods [30] and binning [12]. Although the binning strategy is scalable with respect to the number of data points, the quality of the estimation may be dependent on the number of bins used [31].…”

“…For the visualization of scatter plots, a perceptual loss was proposed to assess whether the scatter plot of downselected data was consistent with the original dataset [29]. Methods similar to the one proposed here have been proposed in the past [12,30], but either do not scale with the number of dimensions (D) or instances (N). Rapp et al [30] proposed a method to display a multidimensional scatter plot by transforming the distribution into an arbitrary one.…”

“…Methods similar to the one proposed here have been proposed in the past [12,30], but either do not scale with the number of dimensions (D) or instances (N). Rapp et al [30] proposed a method to display a multidimensional scatter plot by transforming the distribution into an arbitrary one. However, this method may not scale well with the dimensionality of the data, as it requires a neighbor search for the density estimation.…”

A Survey of Seed Placement and Streamline Selection Techniques

“…In situ processing is typically performed with a limited computational budget and in a distributed memory environment. Initial studies in this space have used SPSS techniques to represent and store steady state vector field data in the form of streamlines [HTZ*19] and unsteady state vector field data in the form of pathlines [ACG*14, BJ15, COJ15, SBC18, SCB19, RPD19]. These methods use SPSS techniques to perform an intelligent sampling and reduction of large vector fields such that they can be accurately reconstructed and explored post hoc.…”