Density Ranking

Analyzing data using density ranking.

• Paper reference:
  • Chen, Yen-Chi, and Adrian Dobra. "Measuring Human Activity Spaces With Density Ranking Based on GPS Data." arXiv preprint arXiv:1708.05017 (2017).
  • Chen, Yen-Chi. "Generalized Cluster Trees and Singular Measures." arXiv preprint arXiv:1611.02762 (2016).
• Maintianer: yenchic@uw.edu
• DR.R: the main script for running the program.
• DR_demo.R: an example for applying DR method to a dataset.

To try this script, please execute the programs in DR_demo.R. Note that you need to download the dataset from https://archive.ics.uci.edu/ml/datasets/GPS+Trajectories before implementing DR_demo.R.

DR.R

Here is a description for the main function.

DR

DR = function(data, h, kernel="Gaussian", xlim=NULL, ylim=NULL, CL_lev = NULL, n_res=201, n_tg=100, ...)

• Density ranking analysis for 2D datasets (GPS).
• Inputs:
  • data: Input 2D data matrix.
  • h: Smoothing parameter.
  • kernel: kernel function, choosing from "Gaussian", "uniform", and "quartic". Default is Gaussian kernel.
  • xlim: The range of first variable.
  • ylim: The range of second variable.
  • CL_lev: The levels for contours lines. If not specify, it will automatically choose 0.05, 0.10, ..., 0.95 as the levels.
  • n_res: The resolution of grids. 201 means a 201 by 201 matrix over the range of xlim and ylim.
  • n_tg: The levels for evaluating the mass-volume curve, Betti number, and persistence curves.
• Outputs:
  • The density ranking analysis result; a list consisting of
    • h: The smoothing bandwidth.
    • x_grid: The grid point for the first variable.
    • y_grid: The grid point for the second variable.
    • gr_alpha: The density ranking value at each grid point.
    • data_alpha: The density ranking value at each data point.
    • CL_lev: The contour levels.
    • CL: A list of contour lines corresponding to CL_lev.
    • persistent: The persistent diagram of density ranking.
    • clevel: The levels where the mass-volume, Betti number, and persistence curves are evaluated.
    • Mcurve: The value of the mass-volume curve evaluated at clevel.
    • Bcurve: The value of the Betti number curve evaluated at clevel.
    • Pcurve: The value of the persistence curve evaluated at clevel.