Create Simulated Data for Seriation Evaluation

Several functions to create simulated data to evaluate different aspects of seriation algorithms and criterion functions.

Usage

create_lines_data(n = 250)

create_ordered_data(
  n = 250,
  k = 2,
  size = NULL,
  spacing = 6,
  path = "linear",
  sd1 = 1,
  sd2 = 0
)

Arguments

n: number of data points to create.
k: number of Gaussian components.
size: relative size (number of points) of components (length of k). If NULL then all components have the same size.
spacing: space between the centers of components. The default of 6 means that the components will barely touch at ds1 = 1 (3 standard deviations for each Gaussian component).
path: Are the components arranged along a "linear" or "circular" path?
sd1: variation in the direction along the components. A value greater than one means the components are mixing.
sd2: variation perpendicular to the direction along the components. A value greater than 0 will introduce anti-Robinson violation events.

Value

a data.frame with the created data.

Details

create_lines_data() recreates the lines data set used in for iVAT() in Havens and Bezdek (2012).

create_ordered_data() (Hahsler et al, 2021) is a versatile function which creates "orderable" 2D data using Gaussian components along a linear or circular path. The components are equally spaced (spacing) along the path. The default spacing of 6 ensures that 2 adjacent components with a standard deviation of one along the direction of the path will barely touch. The standard deviation along the path is set by sd1. The standard deviation perpendicular to the path is set by sd2. A value larger than zero will result in the data not being perfectly orderable (i.e., the resulting distance matrix will not be a perfect pre-anti-Robinson matrix and contain anti-Robinson violation events after seriation). Note that a circular path always creates anti-Robinson violation since the circle has to be broken at some point to create a linear order.

References

Havens, T.C. and Bezdek, J.C. (2012): An Efficient Formulation of the Improved Visual Assessment of Cluster Tendency (iVAT) Algorithm, IEEE Transactions on Knowledge and Data Engineering, 24(5), 813–822.

Michael Hahsler, Christian Buchta and Kurt Hornik (2021). seriation: Infrastructure for Ordering Objects Using Seriation. R package version 1.3.2. https://github.com/mhahsler/seriation

Author

Michael Hahsler

Examples

## lines data set from Havens and Bezdek (2011)
x <- create_lines_data(100)
plot(x, xlim = c(-5, 5), ylim = c(-3, 3), cex = .2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "OLO_single"), col = bluered(100, bias = .5), key = TRUE)


## create_ordered_data can produce many types of "orderable" data

## perfect pre-Anti-Robinson matrix (with a single components)
x <- create_ordered_data(100, k = 1)
plot(x, cex = .2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "MDS"), col = bluered(100, bias=.5), key = TRUE)


## separated components
x <- create_ordered_data(100, k = 5)
plot(x, cex =.2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "MDS"), col = bluered(100, bias = .5), key = TRUE)


## overlapping components
x <- create_ordered_data(100, k = 5, sd1 = 2)
plot(x, cex = .2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "MDS"), col = bluered(100, bias = .5), key = TRUE)


## introduce anti-Robinson violations (a non-zero y value)
x <- create_ordered_data(100, k = 5, sd1 = 2, sd2 = 5)
plot(x, cex = .2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "MDS"), col = bluered(100, bias = .5), key = TRUE)


## circular path (has always violations)
x <- create_ordered_data(100, k = 5, path = "circular", sd1 = 2)
plot(x, cex = .2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "OLO"), col = bluered(100, bias = .5), key = TRUE)


## circular path (with more violations violations)
x <- create_ordered_data(100, k = 5, path = "circular", sd1 = 2, sd2 = 1)
plot(x, cex=.2, col = attr(x, "id"))

d <- dist(x)
pimage(d, seriate(d, "OLO"), col = bluered(100, bias = .5), key = TRUE)