Package 'geocmeans'

Description

Function to adjust the spatial weights so that they represent semantic distances between neighbours

Usage

adjustSpatialWeights(data, listw, style, mindist = 1e-11)

Arguments

Value

A listw object (spdep like)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
Wqueen2 <- adjustSpatialWeights(dataset,queen,style="C")

Description

A Landsat 8 image of the bay of Arcachon (France), with a resolution of 30mx30m and 6 bands: blue, green, red, near infrared, shortwave infrared 1 and shortwave infrared 2. The dataset is saved as a Large RasterBrick with the package raster and has the following crs: EPSG:32630. It is provided as a tiff file.

Usage

load_arcachon()

Format

A spaRast with 6 bands

blue

wavelength: 0.45-0.51

green

wavelength: 0.53-0.59

red

wavelength: 0.64-0.67

near infrared

wavelength: 0.85-0.88

shortwave infrared

wavelength: 1.57-1.65

shortwave infrared

wavelength: 2.11-2.29

Source

https://earthexplorer.usgs.gov/

Examples

# loading directly from file
Arcachon <- terra::rast(system.file("extdata/Littoral4_2154.tif", package = "geocmeans"))
names(Arcachon) <- c("blue", "green", "red", "infrared", "SWIR1", "SWIR2")

# loading with the provided function
Arcachon <- load_arcachon()

Description

Return bar plots to compare groups

Usage

barPlots(data, belongmatrix, ncol = 3, what = "mean")

Arguments

Value

a barplot created with ggplot2

Examples

## Not run: 
data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
barPlots(dataset, result$Belongings)

## End(Not run)

Description

Check that the obtained groups are stable by bootstrap

Usage

boot_group_validation(
  object,
  nsim = 1000,
  maxiter = 1000,
  tol = 0.01,
  init = "random",
  verbose = TRUE,
  seed = NULL
)

Arguments

Details

Considering that the classification produced by a FCM like algorithm depends on its initial state, it is important to check if the groups obtained are stable. This function uses a bootstrap method to do so. During a selected number of iterations (at least 1000), a sample of size n (with replacement) is drawn from the original dataset. For each sample, the same classification algorithm is applied and the results are compared with the reference results. For each original group, the most similar group is identified by calculating the Jaccard similarity index between the columns of the two membership matrices. This index is comprised between 0 (exact difference) and 1 (perfect similarity) and a value is calculated for each group at each iteration. One can investigate the values obtained to determine if the groups are stable. Values under 0.5 are a concern and indicate that the group is dissolving. Values between 0.6 and 0.75 indicate a pattern in the data, but a significant uncertainty. Values above 0.8 indicate strong groups. The values of the centres obtained at each iteration are also returned, it is important to ensure that they approximately follow a normal distribution (or are at least unimodal).

Value

A list of two values: group_consistency: a dataframe indicating the consistency across simulations each cluster ; group_centres: a list with a dataframe for each cluster. The values in the dataframes are the centres of the clusters at each simulation.

Examples

## Not run: 
data(LyonIris)

#selecting the columns for the analysis
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14",
                   "Pct_65","Pct_Img","TxChom1564","Pct_brevet","NivVieMed")

#rescaling the columns
Data <- sf::st_drop_geometry(LyonIris[AnalysisFields])
for (Col in names(Data)){
  Data[[Col]] <- as.numeric(scale(Data[[Col]]))
}

Cmean <- CMeans(Data,4,1.5,500,standardize = FALSE, seed = 456,
    tol = 0.00001, verbose = FALSE)

validation <- boot_group_validation(Cmean, nsim = 1000, maxiter = 1000,
    tol = 0.01, init = "random")

## End(Not run)

Description

Check that the obtained groups are stable by bootstrap with multicore support

Usage

boot_group_validation.mc(
  object,
  nsim = 1000,
  maxiter = 1000,
  tol = 0.01,
  init = "random",
  verbose = TRUE,
  seed = NULL
)

Arguments

Details

For more details, see the documentation of the function boot_group_validation

Value

A list of two values: group_consistency: a dataframe indicating the consistency across simulations each cluster ; group_centres: a list with a dataframe for each cluster. The values in the dataframes are the centres of the clusters at each simulation.

Examples

## Not run: 
data(LyonIris)

#selecting the columns for the analysis
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14",
                   "Pct_65","Pct_Img","TxChom1564","Pct_brevet","NivVieMed")

#rescaling the columns
Data <- sf::st_drop_geometry(LyonIris[AnalysisFields])
for (Col in names(Data)){
  Data[[Col]] <- as.numeric(scale(Data[[Col]]))
}

Cmean <- CMeans(Data,4,1.5,500,standardize = FALSE, seed = 456,
    tol = 0.00001, verbose = FALSE)

future::plan(future::multisession(workers=2))

validation <- boot_group_validation.mc(Cmean, nsim = 1000, maxiter = 1000,
    tol = 0.01, init = "random")
## make sure any open connections are closed afterward
if (!inherits(future::plan(), "sequential")) future::plan(future::sequential)

## End(Not run)

Description

Calculate the Local Moran I for a numeric raster

Usage

calc_local_moran_raster(rast, window)

Arguments

Value

A SpatRaster or a matrix depending on the input with the local Moran I values

Examples

Arcachon <- terra::rast(system.file("extdata/Littoral4_2154.tif", package = "geocmeans"))
names(Arcachon) <- c("blue", "green", "red", "infrared", "SWIR1", "SWIR2")
rast <- Arcachon[[1]]
w <- matrix(1, nrow = 3, ncol = 3)
calc_local_moran_raster(rast, w)

Description

Calculate the global Moran I for a numeric raster

Usage

calc_moran_raster(rast, window)

Arguments

Value

A float: the global Moran I

Examples

Arcachon <- terra::rast(system.file("extdata/Littoral4_2154.tif", package = "geocmeans"))
names(Arcachon) <- c("blue", "green", "red", "infrared", "SWIR1", "SWIR2")
rast <- Arcachon[[1]]
w <- matrix(1, nrow = 3, ncol = 3)
calc_moran_raster(rast, w)

Description

Calculate the Calinski-Harabasz index of clustering quality.

Usage

calcCalinskiHarabasz(data, belongmatrix, centers)

Arguments

Details

The Calinski-Harabasz index (Da Silva et al. 2020) is the ratio between the clusters separation (between groups sum of squares) and the clusters cohesion (within groups sum of squares). A greater value indicates either more separated clusters or more cohesive clusters.

Value

A float: the Calinski-Harabasz index

References

Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcCalinskiHarabasz(result$Data, result$Belongings, result$Centers)

Description

Calculate the Davies-Bouldin index of clustering quality.

Usage

calcDaviesBouldin(data, belongmatrix, centers)

Arguments

Details

The Davies-Bouldin index (Da Silva et al. 2020) can be seen as the ratio of the within cluster dispersion and the between cluster separation. A lower value indicates a higher cluster compacity or a higher cluster separation. The formula is:

$DB = \frac{1}{k}\sum_{i=1}^k{R_{i}}$

with:

$R_{i} =\max_{i \neq j}\left(\frac{S_{i}+S_{j}}{M_{i, j}}\right)$

$S_{l} =\left[\frac{1}{n_{l}} \sum_{l=1}^{n}\left\|\boldsymbol{x_{l}}-\boldsymbol{c_{i}}\right\|*u_{i}\right]^{\frac{1}{2}}$

$M_{i, j} =\sum\left\|\boldsymbol{c}_{i}-\boldsymbol{c}_{j}\right\|$

So, the value of the index is an average of $R_{i}$ values. For each cluster, they represent its worst comparison with all the other clusters, calculated as the ratio between the compactness of the two clusters and the separation of the two clusters.

Value

A float: the Davies-Bouldin index

References

Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcDaviesBouldin(result$Data, result$Belongings, result$Centers)

Description

Calculate ELSA statistic for a hard partition. This local indicator of spatial autocorrelation can be used to determine where observations belong to different clusters.

Usage

calcELSA(object, nblistw = NULL, window = NULL, matdist = NULL)

Arguments

Details

The ELSA index (Naimi et al. 2019) can be used to measure local autocorrelation for a categorical variable. It varies between 0 and 1, 0 indicating a perfect positive spatial autocorrelation and 1 a perfect heterogeneity. It is based on the Shanon entropy index, and uses a measure of difference between categories. Thus it can reflect that proximity of two similar categories is still a form of positive autocorelation. The authors suggest to calculate the mean of the index at several lag distance to create an entrogram which quantifies global spatial structure and can be represented as a variogram-like graph.

Value

A depending of the input, a vector of ELSA values or a raster with the ELSA values.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
elsa_valus <- calcELSA(result)

Description

Calculate the explained inertia by a classification

Usage

calcexplainedInertia(data, belongmatrix)

Arguments

Value

A float: the percentage of the total inertia explained

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcexplainedInertia(result$Data,result$Belongings)

Description

Calculate Fukuyama and Sugeno index of clustering quality

Usage

calcFukuyamaSugeno(data, belongmatrix, centers, m)

Arguments

Details

The Fukuyama and Sugeno index (Fukuyama 1989) is the difference between the compacity of clusters and the separation of clusters. A smaller value indicates a better clustering. The formula is:

$S(c)=\sum_{k=1}^{n} \sum_{i=1}^{c}\left(U_{i k}\right)^{m}\left(\left\|x_{k}-v_{i}\right\|^{2}-\left\|v_{i}-\bar{x}\right\|^{2}\right) 2$

with n the number of observations, k the number of clusters and $\bar{x}$ the mean of the dataset.

Value

A float: the Fukuyama and Sugeno index

References

Fukuyama Y (1989). “A new method of choosing the number of clusters for the fuzzy c-mean method.” In Proc. 5th Fuzzy Syst. Symp., 1989, 247–250.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcFukuyamaSugeno(result$Data,result$Belongings, result$Centers, 1.5)

Description

Calculate ELSA statistic for a fuzzy partition. This local indicator of spatial autocorrelation can be used to identify areas where close observations tend to belong to different clusters.

Usage

calcFuzzyELSA(object, nblistw = NULL, window = NULL, matdist = NULL)

Arguments

Details

The fuzzy ELSA index is a generalization of the ELSA index (Naimi et al. 2019). It can be used to measure local autocorrelation for a membership matrix. It varies between 0 and 1, 0 indicating a perfect positive spatial autocorrelation and 1 a perfect heterogeneity. It is based on the Shannon entropy index, and uses a measure of dissimilarity between categories.

Value

either a vector or a raster with the ELSA values.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
elsa_valus <- calcFuzzyELSA(result)

Description

Calculate the Generalized Dunn’s index (v43) of clustering quality.

Usage

calcGD43(data, belongmatrix, centers)

Arguments

Details

The Generalized Dunn’s index (Da Silva et al. 2020) is a ratio of the worst pair-wise separation of clusters and the worst compactness of clusters. A higher value indicates a better clustering. The formula is:

$GD_{r s}=\frac{\min_{i \neq j}\left[\delta_{r}\left(\omega_{i}, \omega_{j}\right)\right]}{\max_{k}\left[\Delta_{s}\left(\omega_{k}\right)\right]}$

The numerator is a measure of the minimal separation between all the clusters i and j given by the formula:

$\delta_{r}\left(\omega_{i}, \omega_{j}\right)=\left\|\boldsymbol{c}_{i}-\boldsymbol{c}_{j}\right\|$

which is basically the Euclidean distance between the centres of clusters $c_{i}$ and $c_{j}$

The denominator is a measure of the maximal dispersion of all clusters, given by the formula:

$\frac{2*\sum_{l=1}^{n}\left\|\boldsymbol{x}_{l}-\boldsymbol{c_{i}}\right\|^{\frac{1}{2}}}{\sum{u_{i}}}$

Value

A float: the Generalized Dunn’s index (43)

References

Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcGD43(result$Data, result$Belongings, result$Centers)

Description

Calculate the Generalized Dunn’s index (v53) of clustering quality.

Usage

calcGD53(data, belongmatrix, centers)

Arguments

Details

The Generalized Dunn’s index (Da Silva et al. 2020) is a ratio of the worst pair-wise separation of clusters and the worst compactness of clusters. A higher value indicates a better clustering. The formula is:

$GD_{r s}=\frac{\min_{i \neq j}\left[\delta_{r}\left(\omega_{i}, \omega_{j}\right)\right]}{\max_{k}\left[\Delta_{s}\left(\omega_{k}\right)\right]}$

The numerator is a measure of the minimal separation between all the clusters i and j given by the formula:

$\delta_{r}\left(\omega_{i}, \omega_{j}\right)=\frac{\sum_{l=1}^{n}\left\|\boldsymbol{x_{l}}-\boldsymbol{c_{i}}\right\|^{\frac{1}{2}} . u_{il}+\sum_{l=1}^{n}\left\|\boldsymbol{x_{l}}-\boldsymbol{c_{j}}\right\|^{\frac{1}{2}} . u_{jl}}{\sum{u_{i}} + \sum{u_{j}}}$

where u is the membership matrix and $u_{i}$ is the column of u describing the membership of the n observations to cluster i. $c_{i}$ is the center of the cluster i.

The denominator is a measure of the maximal dispersion of all clusters, given by the formula:

$\frac{2*\sum_{l=1}^{n}\left\|\boldsymbol{x}_{l}-\boldsymbol{c_{i}}\right\|^{\frac{1}{2}}}{\sum{u_{i}}}$

Value

A float: the Generalized Dunn’s index (53)

References

Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcGD53(result$Data, result$Belongings, result$Centers)

Description

Calculate the Negentropy Increment index of clustering quality.

Usage

calcNegentropyI(data, belongmatrix, centers)

Arguments

Details

The Negentropy Increment index (Da Silva et al. 2020) is based on the assumption that a normally shaped cluster is more desirable. It uses the difference between the average negentropy of all the clusters in the partition, and that of the whole partition. A smaller value indicates a better partition. The formula is:

$NI=\frac{1}{2} \sum_{j=1}^{k} p_{i} \ln \left|{\boldsymbol{\Sigma}}_{j}\right|-\frac{1}{2} \ln \left|\boldsymbol{\Sigma}_{d a t a}\right|-\sum_{j=1}^{k} p_{j} \ln p_{j}$

with a cluster, |.| the determinant of a matrix,

• j a cluster

• |.| the determinant of a matrix

• $\left|{\boldsymbol{\Sigma}}_{j}\right|$ the covariance matrix of the dataset weighted by the membership values to cluster j

• $\left|\boldsymbol{\Sigma}_{d a t a}\right|$ the covariance matrix of the dataset

• $p_{j}$ the sum of the membership values to cluster j divided by the number of observations.

Value

A float: the Negentropy Increment index

References

Da Silva LEB, Melton NM, Wunsch DC (2020). “Incremental cluster validity indices for online learning of hard partitions: Extensions and comparative study.” IEEE Access, 8, 22025–22047.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcNegentropyI(result$Data, result$Belongings, result$Centers)

Description

calculate several clustering quality indexes (some of them come from fclust package)

Usage

calcqualityIndexes(
  data,
  belongmatrix,
  m,
  indices = c("Silhouette.index", "Partition.entropy", "Partition.coeff",
    "XieBeni.index", "FukuyamaSugeno.index", "Explained.inertia")
)

Arguments

Value

A named list with with the values of the required indices

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcqualityIndexes(result$Data,result$Belongings, m=1.5)

Description

Calculate the Silhouette index of clustering quality.

Usage

calcSilhouetteIdx(data, belongings)

Arguments

Details

The index is calculated with the function SIL.F from the package fclust. When the dataset is too large, an approach by subsampling is used to avoid crash.

Value

A float, the fuzzy Silhouette index

Description

Calculate the diversity (or entropy) index.

Usage

calcUncertaintyIndex(belongmatrix)

Arguments

Details

The diversity (or entropy) index (Theil 1972) is calculated for each observation an varies between 0 and 1. When the value is close to 0, the observation belong to only one cluster (as in hard clustering). When the value is close to 1, the observation is undecided and tends to belong to each cluster. Values above 0.9 should be investigated. The formula is:

$H2_{i} = \frac{-\sum[u_{ij}\ln(u_{ij})]}{\ln(k)}$

with i and observation, j a cluster, k the number of clusters and u the membership matrix.

It is a simplified formula because the sum of each row of a membership matrix is 1.

Value

A vector with the values of the diversity (entropy) index

References

Theil H (1972). Statistical decomposition analysis; with applications in the social and administrative sciences. North-Holland.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
calcUncertaintyIndex(result$Belongings)

Description

Function to convert a character vector to a membership matrix (binary matrix). The columns of the matrix are ordered with the order function.

Usage

cat_to_belongings(categories)

catToBelongings(categories)

Arguments

Value

A binary matrix

Description

Create a matrix that can be used as a window when working with rasters. It uses a radius to set to 0 the weights of pixels that are farther than this distance. This is helpful to create circular focals.

Usage

circular_window(radius, res)

Arguments

Details

The original function comes from here: https://scrogster.wordpress.com/2012/10/05/applying-a-circular-moving-window-filter-to-raster-data-in-r/ but we reworked it to make it faster and to ensure that the result is a matrix with odd dimensions.

Value

A binary weight matrix

Examples

# wide of 100 metres for pixels of 2 metres
window <- circular_window(100, 2)
# row standardisation
window_row_std <- window / sum(window)

Description

The classical c-mean algorithm

Usage

CMeans(
  data,
  k,
  m,
  maxiter = 500,
  tol = 0.01,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NULL,
  verbose = TRUE,
  init = "random",
  seed = NULL
)

Arguments

Value

An S3 object of class FCMres with the following slots

• Centers: a dataframe describing the final centers of the groups

• Belongings: the final membership matrix

• Groups: a vector with the names of the most likely group for each observation

• Data: the dataset used to perform the clustering (might be standardized)

• isRaster: TRUE if rasters were used as input data, FALSE otherwise

• k: the number of groups

• m: the fuzyness degree

• alpha: the spatial weighting parameter (if SFCM or SGFCM)

• beta: beta parameter for generalized version of FCM (GFCM or SGFCM)

• algo: the name of the algorithm used

• rasters: a list of rasters with membership values and the most likely group (if rasters were used)

• missing: a boolean vector indicating raster cell with data (TRUE) and with NA (FALSE) (if rasters were used)

• maxiter: the maximum number of iterations used

• tol: the convergence criterio

• lag_method: the lag function used (if SFCM or SGFCM)

• nblistw: the neighbours list used (if vector data were used for SFCM or SGFCM)

• window: the window used (if raster data were used for SFCM or SGFCM)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
result <- CMeans(dataset,k = 5, m = 1.5, standardize = TRUE)

Description

The generalized c-mean algorithm

Usage

GCMeans(
  data,
  k,
  m,
  beta,
  maxiter = 500,
  tol = 0.01,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NULL,
  verbose = TRUE,
  init = "random",
  seed = NULL
)

Arguments

Value

An S3 object of class FCMres with the following slots

• Centers: a dataframe describing the final centers of the groups

• Belongings: the final membership matrix

• Groups: a vector with the names of the most likely group for each observation

• Data: the dataset used to perform the clustering (might be standardized)

• isRaster: TRUE if rasters were used as input data, FALSE otherwise

• k: the number of groups

• m: the fuzyness degree

• alpha: the spatial weighting parameter (if SFCM or SGFCM)

• beta: beta parameter for generalized version of FCM (GFCM or SGFCM)

• algo: the name of the algorithm used

• rasters: a list of rasters with membership values and the most likely group (if rasters were used)

• missing: a boolean vector indicating raster cell with data (TRUE) and with NA (FALSE) (if rasters were used)

• maxiter: the maximum number of iterations used

• tol: the convergence criterio

• lag_method: the lag function used (if SFCM or SGFCM)

• nblistw: the neighbours list used (if vector data were used for SFCM or SGFCM)

• window: the window used (if raster data were used for SFCM or SGFCM)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
result <- GCMeans(dataset,k = 5, m = 1.5, beta = 0.5, standardize = TRUE)

Description

Match the groups obtained from two classifications based on the Jaccard index calculated on the membership matrices.

Usage

groups_matching(object.x, object.y)

Arguments

Details

We can not expect to obtain the groups in the same order in each run of a classification algorithm. This function can be used match the clusters of a first classification with the most similar clusters in a second classification. Thus it might be easier to compare the results of two algorithms or two runs of the same algorithm.

Value

The FCMres object or the membership matrix provided for the parameter object.y with the order of the groups updated.

Examples

data(LyonIris)

#selecting the columns for the analysis
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14",
                   "Pct_65","Pct_Img","TxChom1564","Pct_brevet","NivVieMed")

#rescaling the columns
Data <- sf::st_drop_geometry(LyonIris[AnalysisFields])
for (Col in names(Data)){
  Data[[Col]] <- as.numeric(scale(Data[[Col]]))
}

Cmean <- CMeans(Data,4,1.5,500,standardize = FALSE, seed = 456, tol = 0.00001, verbose = FALSE)
Cmean2 <- CMeans(Data,4,1.5,500,standardize = FALSE, seed = 789, tol = 0.00001, verbose = FALSE)
ordered_Cmean2 <- groups_matching(Cmean,Cmean2)

Description

Check if an object can be considered as a FCMres object

Usage

## S3 method for class 'FCMres'
is(object, class2 = "FCMres")

Arguments

Value

A boolean, TRUE if x can be considered as a FCMres object, FALSE otherwise group

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
is(result, "FCMres")

Description

A dataset containing social and environmental data for the Iris of Lyon (France)

Usage

LyonIris

Format

A SpatialPolygonsDataFrame with 506 rows and 32 variables:

OBJECTID

a simple OID (integer)

INSEE_COM

the code of each commune (factor)

CODE_IRIS

the code of each unit area : iris (factor)

Lden

the annual daily mean noise exposure values in dB (numeric)

NO2

the annual mean of NO2 concentration in ug/m3 (numeric)

PM25

the annual mean of PM25 concentration in ug/m3 (numeric)

PM10

the annual mean of PM25 concentration in ug/m3 (numeric)

Pct0_14

the percentage of people that are 0 to 14 year old (numeric)

Pct_65

the percentage of people older than 64 (numeric)

Pct_Img

the percentage immigrants (numeric)

TxChom1564

the unemployment rate (numeric)

Pct_brevet

the percentage of people that obtained the college diploma (numeric)

NivVieMed

the median standard of living in euros (numeric)

VegHautPrt

the percentage of the iris surface covered by trees (numeric)

X

the X coordinate of the center of the Iris (numeric)

Y

the Y coordinate of the center of the Iris (numeric)

...

Source

https://data.grandlyon.com/portail/fr/accueil

Description

Build some maps to visualize the results of the clustering

Usage

mapClusters(geodata = NULL, object, undecided = NULL)

Arguments

Value

A named list with :

• ProbaMaps : a list of tmap maps showing for each group the probability of the observations to belong to that group

• ClusterMap : a tmap map showing the most likely group for observation

Examples

## Not run: 
data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
MyMaps <- mapClusters(LyonIris, result$Belongings)

## End(Not run)

Description

Method to plot the results of a FCM.res object

Usage

## S3 method for class 'FCMres'
plot(x, type = "spider", ...)

Arguments

Details

This S3 method is a simple dispatcher for the functions barPlots, violinPlots and spiderPlots. To be able to use all their specific parameters, one can use them directly.

Value

a ggplot2 object, a list, or NULL, depending on the type of plot requested

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")

# rescaling all the variables used in the analysis
for (field in AnalysisFields) {
    LyonIris[[field]] <- scale(LyonIris[[field]])
}

# doing the initial clustering
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SGFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, beta = 0.5, standardize = FALSE)

plot(result, type = "spider")

Description

Function to predict the membership matrix of a new set of observations

Usage

predict_membership(
  object,
  new_data,
  nblistw = NULL,
  window = NULL,
  standardize = TRUE,
  ...
)

Arguments

Value

A numeric matrix with the membership values for each new observation. If rasters were used, return a list of rasters with the membership values.

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")

# rescaling all the variables used in the analysis
for (field in AnalysisFields) {
    LyonIris[[field]] <- scale(LyonIris[[field]])
}

# doing the initial clustering
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SGFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, beta = 0.5, standardize = FALSE)

# using a subset of the original dataframe as "new data"
new_data <- LyonIris[c(1, 27, 36, 44, 73),]
new_dataset <- sf::st_drop_geometry(new_data[AnalysisFields])
new_nb <- spdep::poly2nb(new_data,queen=TRUE)
new_Wqueen <- spdep::nb2listw(new_nb,style="W")

# doing the prediction
predictions <- predict_membership(result, new_dataset, new_Wqueen, standardize = FALSE)

Description

Function to predict the membership matrix of a new set of observations

Usage

## S3 method for class 'FCMres'
predict(
  object,
  new_data,
  nblistw = NULL,
  window = NULL,
  standardize = TRUE,
  ...
)

Arguments

Value

A numeric matrix with the membership values for each new observation

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")

# rescaling all the variables used in the analysis
for (field in AnalysisFields) {
    LyonIris[[field]] <- scale(LyonIris[[field]])
}

# doing the initial clustering
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SGFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, beta = 0.5, standardize = FALSE)

# using a subset of the original dataframe as "new data"
new_data <- LyonIris[c(1, 27, 36, 44, 73),]
new_dataset <- sf::st_drop_geometry(new_data[AnalysisFields])
new_nb <- spdep::poly2nb(new_data,queen=TRUE)
new_Wqueen <- spdep::nb2listw(new_nb,style="W")

# doing the prediction
predictions <- predict(result, new_dataset, new_Wqueen, standardize = FALSE)

Description

print a FCMres object

Usage

## S3 method for class 'FCMres'
print(x, ...)

Arguments

Value

A boolean, TRUE if x can be considered as a FCMres object, FALSE otherwise group

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
result <- CMeans(dataset, k = 5, m = 1.5, standardize = TRUE)
print(result, "FCMres")

Description

Function to select the parameters for a clustering algorithm.

Usage

select_parameters(
  algo,
  data,
  k,
  m,
  alpha = NA,
  beta = NA,
  nblistw = NULL,
  lag_method = "mean",
  window = NULL,
  spconsist = TRUE,
  classidx = TRUE,
  nrep = 30,
  indices = NULL,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NA,
  maxiter = 500,
  tol = 0.01,
  seed = NULL,
  init = "random",
  verbose = TRUE
)

selectParameters(
  algo,
  data,
  k,
  m,
  alpha = NA,
  beta = NA,
  nblistw = NULL,
  lag_method = "mean",
  window = NULL,
  spconsist = TRUE,
  classidx = TRUE,
  nrep = 30,
  indices = NULL,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NA,
  maxiter = 500,
  tol = 0.01,
  seed = NULL,
  init = "random",
  verbose = TRUE
)

Arguments

Value

A dataframe with indicators assessing the quality of classifications

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
#set spconsist to TRUE to calculate the spatial consistency indicator
#FALSE here to reduce the time during package check
values <- select_parameters(algo = "SFCM", dataset, k = 5, m = seq(2,3,0.1),
    alpha = seq(0,2,0.1), nblistw = Wqueen, spconsist=FALSE)


data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
#set spconsist to TRUE to calculate the spatial consistency indicator
#FALSE here to reduce the time during package check
values <- selectParameters(algo = "SFCM", dataset, k = 5, m = seq(2,3,0.1),
    alpha = seq(0,2,0.1), nblistw = Wqueen, spconsist=FALSE)

Description

Function to select the parameters for a clustering algorithm. This version of the function allows to use a plan defined with the package future to reduce calculation time.

Usage

select_parameters.mc(
  algo,
  data,
  k,
  m,
  alpha = NA,
  beta = NA,
  nblistw = NULL,
  lag_method = "mean",
  window = NULL,
  spconsist = TRUE,
  classidx = TRUE,
  nrep = 30,
  indices = NULL,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NA,
  maxiter = 500,
  tol = 0.01,
  chunk_size = 5,
  seed = NULL,
  init = "random",
  verbose = TRUE
)

selectParameters.mc(
  algo,
  data,
  k,
  m,
  alpha = NA,
  beta = NA,
  nblistw = NULL,
  lag_method = "mean",
  window = NULL,
  spconsist = TRUE,
  classidx = TRUE,
  nrep = 30,
  indices = NULL,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NA,
  maxiter = 500,
  tol = 0.01,
  chunk_size = 5,
  seed = NULL,
  init = "random",
  verbose = TRUE
)

Arguments

Value

A dataframe with indicators assessing the quality of classifications

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
future::plan(future::multisession(workers=2))
#set spconsist to TRUE to calculate the spatial consistency indicator
#FALSE here to reduce the time during package check
values <- select_parameters.mc("SFCM", dataset, k = 5, m = seq(1,2.5,0.1),
    alpha = seq(0,2,0.1), nblistw = Wqueen, spconsist=FALSE)
## make sure any open connections are closed afterward
if (!inherits(future::plan(), "sequential")) future::plan(future::sequential)


data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
future::plan(future::multisession(workers=2))
#set spconsist to TRUE to calculate the spatial consistency indicator
#FALSE here to reduce the time during package check
values <- select_parameters.mc("SFCM", dataset, k = 5, m = seq(1,2.5,0.1),
    alpha = seq(0,2,0.1), nblistw = Wqueen, spconsist=FALSE)

Description

spatial version of the c-mean algorithm (SFCMeans, FCM_S1)

Usage

SFCMeans(
  data,
  nblistw = NULL,
  k,
  m,
  alpha,
  lag_method = "mean",
  window = NULL,
  noise_cluster = FALSE,
  delta = NULL,
  maxiter = 500,
  tol = 0.01,
  standardize = TRUE,
  robust = FALSE,
  verbose = TRUE,
  init = "random",
  seed = NULL
)

Arguments

Details

The implementation is based on the following article : doi:10.1016/j.patcog.2006.07.011.

the membership matrix (u) is calculated as follow

$u_{ik} = \frac{(||x_{k} - v{_i}||^2 + \alpha||\bar{x_{k}} - v{_i}||^2)^{(-1/(m-1))}}{\sum_{j=1}^c(||x_{k} - v{_j}||^2 + \alpha||\bar{x_{k}} - v{_j}||^2)^{(-1/(m-1))}}$

the centers of the groups are updated with the following formula

$v_{i} = \frac{\sum_{k=1}^N u_{ik}^m(x_{k} + \alpha\bar{x_{k}})}{(1 + \alpha)\sum_{k=1}^N u_{ik}^m}$

with

• vi the center of the group vi

• xk the data point k

• xk_bar the spatially lagged data point k

Value

An S3 object of class FCMres with the following slots

• Centers: a dataframe describing the final centers of the groups

• Belongings: the final membership matrix

• Groups: a vector with the names of the most likely group for each observation

• Data: the dataset used to perform the clustering (might be standardized)

• isRaster: TRUE if rasters were used as input data, FALSE otherwise

• k: the number of groups

• m: the fuzyness degree

• alpha: the spatial weighting parameter (if SFCM or SGFCM)

• beta: beta parameter for generalized version of FCM (GFCM or SGFCM)

• algo: the name of the algorithm used

• rasters: a list of rasters with membership values and the most likely group (if rasters were used)

• missing: a boolean vector indicating raster cell with data (TRUE) and with NA (FALSE) (if rasters were used)

• maxiter: the maximum number of iterations used

• tol: the convergence criterio

• lag_method: the lag function used (if SFCM or SGFCM)

• nblistw: the neighbours list used (if vector data were used for SFCM or SGFCM)

• window: the window used (if raster data were used for SFCM or SGFCM)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)

Description

spatial version of the generalized c-mean algorithm (SGFCMeans)

Usage

SGFCMeans(
  data,
  nblistw = NULL,
  k,
  m,
  alpha,
  beta,
  lag_method = "mean",
  window = NULL,
  maxiter = 500,
  tol = 0.01,
  standardize = TRUE,
  robust = FALSE,
  noise_cluster = FALSE,
  delta = NULL,
  verbose = TRUE,
  init = "random",
  seed = NULL
)

Arguments

Details

The implementation is based on the following article : doi:10.1016/j.dsp.2012.09.016.

the membership matrix (u) is calculated as follow

$u_{ik} = \frac{(||x_{k} - v{_i}||^2 -b_k + \alpha||\bar{x_{k}} - v{_i}||^2)^{(-1/(m-1))}}{\sum_{j=1}^c(||x_{k} - v{_j}||^2 -b_k + \alpha||\bar{x_{k}} - v{_j}||^2)^{(-1/(m-1))}}$

the centers of the groups are updated with the following formula

$v_{i} = \frac{\sum_{k=1}^N u_{ik}^m(x_{k} + \alpha\bar{x_{k}})}{(1 + \alpha)\sum_{k=1}^N u_{ik}^m}$

with

• vi the center of the group vi

• xk the data point k

• xk_bar the spatially lagged data point k

  $b_k = \beta \times min(||x_{k} - v||)$

Value

An S3 object of class FCMres with the following slots

• Centers: a dataframe describing the final centers of the groups

• Belongings: the final membership matrix

• Groups: a vector with the names of the most likely group for each observation

• Data: the dataset used to perform the clustering (might be standardized)

• isRaster: TRUE if rasters were used as input data, FALSE otherwise

• k: the number of groups

• m: the fuzyness degree

• alpha: the spatial weighting parameter (if SFCM or SGFCM)

• beta: beta parameter for generalized version of FCM (GFCM or SGFCM)

• algo: the name of the algorithm used

• rasters: a list of rasters with membership values and the most likely group (if rasters were used)

• missing: a boolean vector indicating raster cell with data (TRUE) and with NA (FALSE) (if rasters were used)

• maxiter: the maximum number of iterations used

• tol: the convergence criterio

• lag_method: the lag function used (if SFCM or SGFCM)

• nblistw: the neighbours list used (if vector data were used for SFCM or SGFCM)

• window: the window used (if raster data were used for SFCM or SGFCM)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SGFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, beta = 0.5, standardize = TRUE)

Description

Start a local Shiny App to explore the results of a classification

Usage

sp_clust_explorer(
  object = NULL,
  spatial = NULL,
  membership = NULL,
  dataset = NULL,
  port = 8100,
  ...
)

Arguments

Examples

## Not run: 
data(LyonIris)

#selecting the columns for the analysis
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14",
                   "Pct_65","Pct_Img","TxChom1564","Pct_brevet","NivVieMed")

#rescaling the columns
Data <- sf::st_drop_geometry(LyonIris[AnalysisFields])
for (Col in names(Data)){
  Data[[Col]] <- as.numeric(scale(Data[[Col]]))
}

Cmean <- CMeans(Data,4,1.5,500,standardize = FALSE, seed = 456, tol = 0.00001, verbose = FALSE)

sp_clust_explorer(Cmean, LyonIris)

## End(Not run)

Description

Utility function to facilitate the spatial diagnostic of a classification

Calculate the following indicators: Moran I index (spdep::moranI) for each column of the membership matrix, Join count test (spdep::joincount.multi) for the most likely groups of each datapoint, Spatial consistency index (see function spConsistency) and the Elsa statistic (see function calcElsa). Note that if the FCMres object given was constructed with rasters, the joincount statistic is not calculated and no p-values are provided for the Moran I indices.

Usage

spatialDiag(
  object,
  nblistw = NULL,
  window = NULL,
  undecided = NULL,
  matdist = NULL,
  nrep = 50
)

Arguments

Value

A named list with :

• MoranValues : the moran I values for each column of the membership matrix (spdep::MoranI)

• JoinCounts : the result of the join count test calculated with the most likely group for each datapoint (spdep::joincount.multi)

• SpConsist : the mean value of the spatial consistency index (the lower, the better, see ?spConsistency for details)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
spatialDiag(result, undecided=0.45, nrep=30)

Description

Calculate a spatial consistency index

Usage

spConsistency(
  object,
  nblistw = NULL,
  window = NULL,
  nrep = 999,
  adj = FALSE,
  mindist = 1e-11
)

Arguments

Details

This index is experimental, it aims to measure how much a clustering solution is spatially consistent. A classification is spatially inconsistent if neighbouring observation do not belong to the same group. See detail for a description of its calculation

The total spatial inconsistency (*Scr*) is calculated as follow

$isp = \sum_{i}\sum_{j}\sum_{k} (u_{ik} - u_{jk})^{2} * W_{ij}$

With U the membership matrix, i an observation, k the neighbours of i and W the spatial weight matrix This represents the total spatial inconsistency of the solution (true inconsistency) We propose to compare this total with simulated values obtained by permutations (simulated inconsistency). The values obtained by permutation are an approximation of the spatial inconsistency obtained in a random context Ratios between the true inconsistency and simulated inconsistencies are calculated A value of 0 depict a situation where all observations are identical to their neighbours A value of 1 depict a situation where all observations are as much different as their neighbours that what randomness can produce A classification solution able to reduce this index has a better spatial consistency

Value

A named list with

• Mean : the mean of the spatial consistency index

• prt05 : the 5th percentile of the spatial consistency index

• prt95 : the 95th percentile of the spatial consistency index

• samples : all the value of the spatial consistency index

• sum_diff : the total sum of squarred difference between observations and their neighbours

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
# NOTE : more replications are needed for proper inference
spConsistency(result$Belongings, nblistw = Wqueen, nrep=25)

Description

Display spider charts to quickly compare values between groups

Usage

spiderPlots(data, belongmatrix, chartcolors = NULL)

Arguments

Details

For each group, the weighted mean of each variable in data is calculated based on the probability of belonging to this group of each observation. On the chart the exterior ring represents the maximum value obtained for all the groups and the interior ring the minimum. The groups are located between these two limits in a linear way.

Value

NULL, the plots are displayed directly by the function (see fmsb::radarchart)

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
spiderPlots(dataset,result$Belongings)

Description

Create functions to standardize and unstandardize data

Usage

standardizer(x)

Arguments

Value

If x was a vector, the function returns a list containing two functions : scale and unscale. The first one is an equivalent of the classical function scale(x, center = TRUE, scale = TRUE). The second can be used to reverse the scaling and get back original units. If x was a data.frame, the same pair of functions is returned inside of a list for each numeric column.

Examples

data(LyonIris)
LyonScales <- standardizer(sf::st_drop_geometry(LyonIris))

Description

Calculate some descriptive statistics of each group

Usage

summarizeClusters(data, belongmatrix, weighted = TRUE, dec = 3, silent = TRUE)

Arguments

Value

A list of length k (the number of group). Each element of the list is a dataframe with summary statistics for the variables of data for each group

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
summarizeClusters(dataset, result$Belongings)

Description

Calculate some descriptive statistics of each group of a FCMres object

Usage

## S3 method for class 'FCMres'
summary(object, data = NULL, weighted = TRUE, dec = 3, silent = TRUE, ...)

Arguments

Value

A list of length k (the number of group). Each element of the list is a dataframe with summary statistics for the variables of data for each group

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
summary(result)

Description

Return a map to visualize membership matrix

Usage

uncertaintyMap(
  geodata,
  belongmatrix,
  njit = 150,
  radius = NULL,
  colors = NULL,
  pt_size = 0.05
)

Arguments

Details

This function maps the membership matrix by plotting random points in polygons, along lines or around points representing the original observations. Each cluster is associated with a color and each random point has a probability to be of that color equal to the membership value of the feature it belongs itself. Thus, it is possible to visualize regions with uncertainty and to identify the strongest clusters.

Value

a map created with tmap

Examples

## Not run: 
data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
  "TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
uncertaintyMap(LyonIris, result$Belongings)

## End(Not run)

Description

Identify the observation for which the classification is uncertain

Usage

undecidedUnits(belongmatrix, tol = 0.1, out = "character")

Arguments

Value

A vector indicating the most likely group for each observation or "Undecided" if the maximum probability for the observation does not reach the value of the tol parameter

Examples

data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometry(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
undecidedUnits(result$Belongings, tol = 0.45)

Description

Return violin plots to compare the distribution of each variable for each group.

Usage

violinPlots(data, groups)

Arguments

Value

A list of plots created with ggplot2

Examples

## Not run: 
data(LyonIris)
AnalysisFields <-c("Lden","NO2","PM25","VegHautPrt","Pct0_14","Pct_65","Pct_Img",
"TxChom1564","Pct_brevet","NivVieMed")
dataset <- sf::st_drop_geometrie(LyonIris[AnalysisFields])
queen <- spdep::poly2nb(LyonIris,queen=TRUE)
Wqueen <- spdep::nb2listw(queen,style="W")
result <- SFCMeans(dataset, Wqueen,k = 5, m = 1.5, alpha = 1.5, standardize = TRUE)
violinPlots(dataset, result$Groups)

## End(Not run)