Kernel Weights
Kernel Weights applies kernel function to determine the distance decay in the derived continuous weights kernel. The kernel weights are defined as a function K(z) of the ratio between the distance dij from i to j, and the bandwidth hi, with z=dij/hi. The kernel functions include {triangular , uniform, quadratic , epanechnikov, quartic, gaussian}.
- Uniform, K(z)=1/2 for |z|<1,
- Triangular, K(z)=(1−|z|) for |z|<1,
- Quadratic or Epanechnikov, K(z)=(3/4)(1−z^2) for |z|<1,
- Quartic, K(z)=(15/16)(1−z^2)^2 for |z|<1|z|<1, and
- Gaussian. K(z) = (2π)^{1/2}exp(-z^2/2)
For more information, please read: https://geodacenter.github.io/workbook/4c_distance_functions/lab4c.html#kernel-weights
There are two types of fixed bandwidths for kernel weights. One is the max-min distance used earlier (the largest of the nearest-neighbor distances): kernel_weights(). The other is the maximum distance for a given specification of k-nearest neighbors: kernel_knn_weights().
function getKernelWeights(
String mapUid,
Number distBand,
String kernel,
Number power,
Boolean isInverse,
Boolean isArc,
Boolean isMile,
Boolean useKernelDiagonals)
Arguments
Input Arguments | Type | Description |
mapUid | String | the unique map id |
distBand | Number | the distance band/threshold that makes sure each observation has at least one neighbor |
kernel | String | a varchar value of kernel method, which has to be one of {'triangular', 'uniform', 'epanechnikov', 'quartic', 'gaussian'} |
useKernelDiagonals | Boolean | if apply kernel on the diagonal of weights matrix. Default: FALSE. |
power | Number | the power/exponent corresponds to the number of times the base (dist_band) is used as a factor. Default: 1. |
isInverse | Boolean | if apply inverse on distance value. Default: False. |
isArc | Boolean | if compute arc distance between two observations. Default: FALSE. |
isMile | Boolean | if convert distance unit from mile to kilometer(KM). Default: TRUE. |
Return
Value | Description |
WeightsResult | the weights structure for each observation in binary format. |
With knn set to a given value, the maximum distance between the selected k-nearest neighbors' pairs is used as a "fixed" bandwidth. However, a drawback of fixed bandwidth kernel weights is that the number of non-zero weights can vary considerably, especially when the density of the point locations is not uniform throughout space. The argument
adaptive_bandwidth is provided to allow adaptive bandwidth in knn kernel weights: instead of a fixed distance bandwidth, the distance to the k-th nearest neighbor is used in the kernel function for each observation. API
function getKernelKnnWeights(
String map_uid,
integer k,
String kernel,
Boolean adaptive_bandwidth,
Number power,
Boolean is_inverse,
Boolean is_arc,
Boolean is_mile,
Boolean use_kernel_diagonals)
Arguments
Input Arguments | Type | Description |
map_uid | String | the unique map id |
k | Number | the k nearest neighbors |
kernel | String | a varchar value of kernel method, which has to be one of {'triangular', 'uniform', 'epanechnikov', 'quartic', 'gaussian'} |
adaptive_bandwidth | Boolean | if use adaptive bandwidth (distance to k-th nearest neighbor for each observation), or use max knn distance of all observations. Default: FALSE. |
use_kernel_diagonals | Boolean | if apply kernel on the diagonal of weights matrix. Default: FALSE. |
power | Number | the power/exponent corresponds to the number of times the base (dist_band) is used as a factor. Default: 1. |
is_inverse | Boolean | if apply inverse on distance value. Default: False. |
is_arc | Boolean | if compute arc distance between two observations. Default: FALSE. |
is_mile | Boolean | if convert distance unit from mile to kilometer(KM). Default: TRUE. |
Return
Value | Description |
WeightResult | the weights structure for each observation. |
Try it yourself in the playground (jsgeoda + deck.gl):