# GCSM

The goal of GCSM is to implement the generic composite similarity measure (GCSM), described in “A generic composite measure of similarity between geospatial variables” by Liu et al. (2020) doi:10.1016/j.ecoinf.2020.101169. This package also provides implementations of SSIM and CMSC. Functions are given to compute composite similarity between vectors (e.g, `gcsm`), on spatial windows (e.g., `gcsm_sw`) or temporal windows (e.g., `gcsm_tw`). They are implemented in C++ with RcppArmadillo. OpenMP is used to facilitate parallel computing.

## Installation

You can install the released version of GCSM from CRAN with:

``install.packages("GCSM")``

Or install the development version from GitHub with:

``````# install.packages("devtools")
devtools::install_github("liuyadong/GCSM")``````

## Examples

Composite similarity between vectors:

``````library(GCSM)

x = runif(9)
gcsm(x, x)
#> [1] 1
cmsc(x, x)
#> [1] 1

# mean shift
gcsm(x, x - 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.8
cmsc(x, x - 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.96
gcsm(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.8
cmsc(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.96
## dissimilarity
y = 1 - x # y is the perfect antianalog of x
gcsm(y, x)
#> [1] -1
gcsm(y, x - 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] -0.8
gcsm(y, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] -0.8

# random noise
noise = rnorm(9, mean = 0, sd = 0.1)
gcsm(x, x + noise, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.7719099
cmsc(x, x + noise, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.9427791
## dissimilariry
gcsm(y, x + noise, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] -0.7719099``````

Composite similarity on spatial windows:

``````x = matrix(runif(36), nrow = 6, ncol = 6)
gcsm_sw(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1, ksize = 3)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]  0.8  0.8  0.8  0.8  0.8  0.8
#> [2,]  0.8  0.8  0.8  0.8  0.8  0.8
#> [3,]  0.8  0.8  0.8  0.8  0.8  0.8
#> [4,]  0.8  0.8  0.8  0.8  0.8  0.8
#> [5,]  0.8  0.8  0.8  0.8  0.8  0.8
#> [6,]  0.8  0.8  0.8  0.8  0.8  0.8
cmsc_sw(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1, ksize = 3)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.96 0.96 0.96 0.96 0.96 0.96
#> [2,] 0.96 0.96 0.96 0.96 0.96 0.96
#> [3,] 0.96 0.96 0.96 0.96 0.96 0.96
#> [4,] 0.96 0.96 0.96 0.96 0.96 0.96
#> [5,] 0.96 0.96 0.96 0.96 0.96 0.96
#> [6,] 0.96 0.96 0.96 0.96 0.96 0.96
ssim_sw(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1, ksize = 3)
#>           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
#> [1,] 0.9411454 0.9214168 0.9169390 0.9461954 0.9712785 0.9777024
#> [2,] 0.9625560 0.9545538 0.9517716 0.9632256 0.9717116 0.9736731
#> [3,] 0.9703725 0.9675556 0.9610270 0.9679905 0.9633441 0.9609509
#> [4,] 0.9688934 0.9684905 0.9655600 0.9679028 0.9587779 0.9518538
#> [5,] 0.9538236 0.9484908 0.9404195 0.9511968 0.9568499 0.9606823
#> [6,] 0.9476272 0.9330108 0.9286503 0.9456641 0.9650384 0.9701094``````

Composite similarity on temporal windows:

``````x = array(runif(81), dim = c(3, 3, 9))
gcsm_tw(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#>      [,1] [,2] [,3]
#> [1,]  0.8  0.8  0.8
#> [2,]  0.8  0.8  0.8
#> [3,]  0.8  0.8  0.8
cmsc_tw(x, x + 0.2, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#>      [,1] [,2] [,3]
#> [1,] 0.96 0.96 0.96
#> [2,] 0.96 0.96 0.96
#> [3,] 0.96 0.96 0.96``````