Potential depth#
- potential(x, data, pretransform='1Mom', kernel='EDKernel', mah_parMcd=0.75, kernel_bandwidth=0)[source]#
- Description
Calculate the potential of the points w.r.t. a multivariate data set. The potential is the kernel-estimated density multiplied by the prior probability of a class. Different from the data depths, a density estimate measures at a given point how much mass is located around it.
- Arguments
- x
Matrix of objects (numerical vector as one object) whose depth is to be calculated; each row contains a d-variate point. Should have the same dimension as data.
- data
Matrix of data where each row contains a d-variate point, w.r.t. which the depth is to be calculated.
- pretransform
- The method of data scaling.
'1Mom'or'NMom'for scaling using data moments.'1MCD'or'NMCD'for scaling using robust data moments (Minimum Covariance Determinant (MCD). - kernel
'EDKernel'for the kernel of type 1/(1+kernel.bandwidth*EuclidianDistance2(x,y)),'GKernel'[default and recommended] for the simple Gaussian kernel,'EKernel'exponential kernel: exp(-kernel.bandwidth*EuclidianDistance(x, y)),'VarGKernel'variable Gaussian kernel, where kernel.bandwidth is proportional to the depth.zonoid of a point.- kernel.bandwidth
the single bandwidth parameter of the kernel. If
0- the Scott’s rule of thumb is used.- mah.parMcd
is the value of the argument alpha for the function covMcd is used when
pretransform='MCD'.
- References
Pokotylo, O. and Mosler, K. (2019). Classification with the pot–pot plot. Statistical Papers, 60, 903-931.
- Examples
>>> import numpy as np >>> from depth.multivariate import * >>> mat1=[[1, 0, 0],[0, 2, 0],[0, 0, 1]] >>> mat2=[[1, 0, 0],[0, 1, 0],[0, 0, 1]] >>> x = np.random.multivariate_normal([1,1,1], mat2, 10) >>> data = np.random.multivariate_normal([0,0,0], mat1, 20) >>> potential(x, data) [7.51492797 8.34322926 5.42761506 6.25418171 4.25774485 8.09733146 6.65788017 5.11324521 5.74407939 9.26030661] >>> potential(x, data, kernel_bandwidth=0.1) [13.56510469 13.95553893 11.23251702 12.42491604 10.17527509 13.70947682 12.67352469 11.2080649 11.73402562 14.93067103] >>> potential(x, data, pretransform = "NMCD", mah_parMcd=0.6, kernel_bandwidth=0.1) [11.0603282 11.49509828 8.99303793 8.63168006 7.86456928 11.03588551 10.45468945 8.84989798 9.56799496 12.29832608]