Normalized Dissimilarity Score

Demonstration function to computes the psi dissimilarity score (Birks and Gordon 1985). Psi is computed as \(\psi = (2a / b) - 1\), where \(a\) is the sum of distances between the relevant samples of two time series, and \(b\) is the cumulative sum of distances between consecutive samples in the two time series.

If a is computed with dynamic time warping, and diagonals are used in the computation of the least cost path, then one is added to the result of the equation above.

Usage

psi_equation(a = NULL, b = NULL, diagonal = TRUE)

Arguments

a

(required, numeric) Result of psi_cost_path_sum(), the sum of distances of the least cost path between two time series. Default: NULL

b

(required, numeric) Result of psi_auto_sum(), the cumulative sum of the consecutive cases of two time series. Default: NULL

diagonal

(optional, logical) Used to correct psi when diagonals are used during the computation of the least cost path. If the cost matrix and least cost path were computed using diagonal = TRUE, this argument should be TRUE as well. Default: TRUE

Value

numeric value

See also

Other psi_demo: psi_auto_distance(), psi_auto_sum(), psi_cost_matrix(), psi_cost_path(), psi_cost_path_sum(), psi_distance_lock_step(), psi_distance_matrix()

Examples

#distance metric
d <- "euclidean"

#use diagonals in least cost computations
diagonal <- TRUE

#simulate two irregular time series
x <- zoo_simulate(
  name = "x",
  rows = 100,
  seasons = 2,
  seed = 1
  )

y <- zoo_simulate(
  name = "y",
  rows = 80,
  seasons = 2,
  seed = 2
  )

if(interactive()){
  zoo_plot(x = x)
  zoo_plot(x = y)
}

#dynamic time warping

#distance matrix
dist_matrix <- psi_distance_matrix(
  x = x,
  y = y,
  distance = d
)

#cost matrix
cost_matrix <- psi_cost_matrix(
  dist_matrix = dist_matrix,
  diagonal = diagonal
)

#least cost path
cost_path <- psi_cost_path(
  dist_matrix = dist_matrix,
  cost_matrix = cost_matrix,
  diagonal = diagonal
)

if(interactive()){
  utils_matrix_plot(
    m = cost_matrix,
    path = cost_path
    )
}


#computation of psi score

#sum of distances in least cost path
a <- psi_cost_path_sum(
  path = cost_path
  )

#auto sum of both time series
b <- psi_auto_sum(
  x = x,
  y = y,
  distance = d
)

#dissimilarity score
psi_equation(
  a = a,
  b = b,
  diagonal = diagonal
)
#> [1] 6.403623

#full computation with distantia()
tsl <- list(
  x = x,
  y = y
)

distantia(
  tsl = tsl,
  distance = d,
  diagonal = diagonal
)$psi
#> [1] 6.403623

if(interactive()){
  distantia_plot(
    tsl = tsl,
    distance = d,
    diagonal = diagonal
  )
}