- Paper reference: Chen, Yen-Chi, Christopher R. Genovese, and Larry Wasserman. "Statistical Inference using the Morse-Smale Complex." arXiv preprint arXiv:1506.08826 (2015).
MSHD.R: The main script for the method.example.R: An example (used in the paper) for applying MSHD.
MSHD = function(grids, grids.values, pLevel=0.01, knn=3*ncol(grids)) UseMethod("MSHD")
MSHD.default = function(grids, grids.values, pLevel=0.01, knn=3*ncol(grids))
- Visualization for a high dimensional function
- Inputs:
- grids: The grid points where the high dimensional function is evaluated.
- grids.values: The values for the high dimensional function at the corresponding grid point.
- pLevel: The persistent level used in
$MSR$ package. - knn: The number of nearest neighbor used in
$MSR$ package.
- Output:
- An S4 object of class "MSHD". A list consisting:
- grids: The input grid points.
- grids.values: The input grid values.
- label.cell: The cell label for each grid point.
- cell.info: A matrix containing information for each cell. Each row corresponds to a cell.
- beta: The regression coefficients for linear approximation for the high dimensional function.
- An S4 object of class "MSHD". A list consisting:
cell.plot = function(x, lv.pos = NULL, lv.neg = NULL, grid.width = NULL, r_circle = 1, col.cell = "limegreen", col.cell.filled = "limegreen", col.edge = "brown", col.pie = c("dodgerblue", "red"), lwd.cell = 4, lwd.edge = 10, use.legend=T)
- Visualizing a high dimensional function using Morse-Smale cells.
- Inputs:
- x: An MSHD object.
- lv.pos: The threshold for claiming a grid point is significantly high.
- lv.neg: The threshold for claiming a grid point is significantly low.
- grid.width: The grid width that will be used to compute the number of grid points that two cells share.
- r_circle: The visualization radius for each cell.
- col.cell: Color for the cell (boundaries of the circle).
- col.cell.filled: The filled-in color for the cell.
- col.edge: Color for the edge.
- col.pie: Color for significantly positive and negative region.
- lwd.cell: Width of the circle for the cell.
- lwd.edge: Width for the edges.
- cex.cell.txt:
txtof the text label for each cell. - pos.cell.txt:
posof the text label for each cell. - offset.cell.txt:
offsetof the text label for each cell. - use.legend: To display the legend or not.
- Output:
- A plot for visualization using cells and a list consisting:
- cell.vis: The visualization coordinates for each cell.
- cell.edgepoints: Number of edge points for a pair of cell.
- cell.size: The size (number of grid points) for each cell, including total size, significantly positive grid points, and significantly negative grid points.
- A plot for visualization using cells and a list consisting:
MSEtest = function(data1, data2, grids, h=NULL, pLevel=0.01, knn=3*ncol(grids))
- Morse-Smale Two Sample Test using Energy Statistics and KDE.
- Inputs:
- data1: The first group of data
- data2: The second group of data
- grids: The grid points where the density will be evaluated
- h: The smoothing parameter.
- pLevel: The persistent level used in
MSRpackage. - knn: The number of nearest neighbor used in
MSRpackage.
- Output:
- An S4 object of class "MSHD". A list consisting:
- cell1.data: The sample from 1st group for constructing Morse-Smale cells.
- cell2.data: The sample from 2nd group for constructing Morse-Smale cells.
- test1.data: The sample from 1st group for conducting energy test.
- test2.data: The sample from 2nd group for conducting energy test.
- grids: The grid points.
- grids.density: A matrix containing the density evaluated at the grid points. First column is the density from cell1 data; second column is from cell2 data; and the last column is the density difference.
- labels: A list consisting of cell labels for grids, cell1, cell2, test1, and test2.
- p.values: The p.values for each cell. The value is \emph{NA} if there is only one point from either test1 or test2 for this cell.
- bandwidth: The smoothing bandwidth used to estimate density.
- An S4 object of class "MSHD". A list consisting: