# 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 implements 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 for parallel computing.

## Installation

You can install the package from GitHub with:

``````# install.packages("devtools")

## 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] 0.9201221
cmsc(x, x + noise, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] 0.9416416
## dissimilariry
gcsm(y, x + noise, xmin = 0, xmax = 1, ymin = 0, ymax = 1)
#> [1] -0.9201221``````

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,] 0.9405428 0.9107526 0.8956004 0.8758824 0.8983908 0.8752976
#> [2,] 0.9356499 0.9213593 0.9306332 0.9179906 0.9268518 0.9082596
#> [3,] 0.9266229 0.9361720 0.9497504 0.9331137 0.9312823 0.9243788
#> [4,] 0.9044219 0.9205696 0.9334963 0.9157745 0.9144879 0.9159464
#> [5,] 0.9411510 0.9265003 0.9171057 0.9065103 0.9271306 0.9304926
#> [6,] 0.9580466 0.9272437 0.9095319 0.9179363 0.9485734 0.9454656``````

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``````