gen_loc_outl: Contamination with Local Outliers
In SpatialBSS: Blind Source Separation for Multivariate Spatial Data

gen_loc_outl

R Documentation

Contamination with Local Outliers

Description

Generates synthetic local outliers and contaminates a given p-variate random field by swapping observations based on the first principal component score.

Usage

gen_loc_outl(x, coords, alpha = 0.05, 
             neighborhood_type = c("radius", "fixed_n"), 
             radius = NULL, 
             neighborhood_size = NULL, 
             swap_order = c("regular", "reverse", "random"))

Arguments

`x`	a numeric matrix of dimension `c(n, p)` where the `p` columns correspond to the entries of the random field and the `n` rows are the observations.
`coords`	a numeric matrix or data frame with dimension `c(n,2)` containing the coordinates of the observations.
`alpha`	a numeric value between 0 and 1 determining the proportion of the contaminated observations.
`neighborhood_type`	a string determining the type of neighborhood. If `'radius'`, each neighborhood contains all points within the radius determined by the parameter `radius`. If `'fixed_n'`, each neighborhood contains a constant number of closest points, where the constant is determined by the parameter `neighborhood_size`. Default is `'radius'`.
`radius`	a positive numeric value defining the size of the radius when the `neighborhood_type` is `'radius'`. If `NULL` the radius defaults as `0.01*n`.
`neighborhood_size`	a positive integer defining the number of points in each neighborhood when the `neighborhood_type` is `'fixed_n'`. If `NULL` the number of points defaults as `ceiling(0.01*n)`.
`swap_order`	a string to determine which swap order is used. Either `'regular'` (default), `'reverse'` or `'random'`. See details.

Details

gen_loc_outl generates local outliers by swapping the most extreme and the least extreme observations based on the first principal component score under the condition that at most one outliers lies in each neighborhood. For each location s_i, the neighborhood N_i is defined based on the parameter neighborhood_type. When neighborhood_type is 'radius', the neighborhood N_i contains all locations s_j for which the Euclidean norm ||s_i - s_j|| < r, where r is determined by the parameter radius. When neighborhood_type is 'fixed_n', the neighborhood N_i contains m - 1 nearest locations of s_i, where m is determined by the parameter neighborhood_size. For more details see Ernst & Haesbroeck, (2017).

After calculating the neighborhoods, the local outliers are generated following Ernst & Haesbroeck, (2017) and Harris et al. (2014) using the steps:

Sort the observations from highest to lowest by their principle component analysis (PCA) scores of the first component (PC-1).
Set k to be \alpha N/2 rounded to nearest integer and select the set of local outlier points S^{out} by finding k observations with the highest PC-1 values and k observations with the lowest PC-1 values under the condition that for all s_i, s_j \in S_{out} it holds that N_i \neq N_j.
Form sets X_{large}, which contains k observations with the largest PC-1 values of outlier points S_{out} and X^{small}, which contains k observations with the smallest PC-1 values of outlier points S^{out}. Generate the local outliers by swapping X^{small,i} with X^{large, k + 1 - i}, i=1,...,k. The parameter swap_order defines how the sets X^{large} and X^{small} are ordered.

If the parameter swap_order is 'regular', X^{small} and X^{large} are sorted by PC-1 score from smallest to largest. If the parameter swap_order is 'reverse', X^{small} is sorted from largest to smallest and X^{large} from smallest to largest. If the parameter swap_order is 'random', X^{small} and X^{large} are in random order.

Value

gen_loc_outl returns a data.frame containing the contaminated fields as p first columns. The column p + 1 contains a logical indicator whether the observation is an outlier or not.

Note

This function is a modified version of code originally provided by M. Ernst and G. Haesbroeck.

References

Ernst, M., & Haesbroeck, G. (2017). Comparison of local outlier detection techniques in spatial multivariate data. Data Mining and Knowledge Discovery, 31 , 371-399. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s10618-016-0471-0")}

Harris, P., Brunsdon, C., Charlton, M., Juggins, S., & Clarke, A. (2014). Multivariate spatial outlier detection using robust geographically weighted methods. Mathematical Geosciences, 46 , 1-31. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11004-013-9491-0")}

Examples

# simulate coordinates
coords <- runif(1000 * 2) * 20
dim(coords) <- c(1000, 2)
coords_df <- as.data.frame(coords)
names(coords_df) <- c("x", "y")
# simulate random field
if (!requireNamespace('gstat', quietly = TRUE)) {
  message('Please install the package gstat to run the example code.')
} else {
  library(gstat)
  model_1 <- gstat(formula = z ~ 1, locations = ~ x + y, dummy = TRUE, beta = 0, 
                   model = vgm(psill = 0.025, range = 1, model = 'Exp'), nmax = 20)
  model_2 <- gstat(formula = z ~ 1, locations = ~ x + y, dummy = TRUE, beta = 0, 
                   model = vgm(psill = 0.025, range = 1, kappa = 2, model = 'Mat'), 
                   nmax = 20)
  model_3 <- gstat(formula = z ~ 1, locations = ~ x + y, dummy = TRUE, beta = 0, 
                   model = vgm(psill = 0.025, range = 1, model = 'Gau'), nmax = 20)
                   
  field_1 <- predict(model_1, newdata = coords_df, nsim = 1)$sim1
  field_2 <- predict(model_2, newdata = coords_df, nsim = 1)$sim1
  field_3 <- predict(model_3, newdata = coords_df, nsim = 1)$sim1
  field <- cbind(field_1, field_2, field_3)
  
  # Generate 5 % local outliers to data using radius neighborhoods 
  # and regular swap_order.
  field_cont <- gen_loc_outl(field, coords, alpha = 0.05,
                             neighborhood_type = "radius", 
                             radius = 0.5, swap_order = "regular")

  # Generate 10 % local outliers to data using fixed_n neighborhoods 
  # and reverse swap_order.
  field_cont2 <- gen_loc_outl(field, coords, alpha = 0.1, 
                              neighborhood_type = "fixed_n", 
                              neighborhood_size = 10, swap_order = "reverse")
}

SpatialBSS documentation built on July 26, 2023, 5:37 p.m.