bigMap (version 2.3.1)

bdm.pakde: Perplexity-adaptive kernel density estimation

Description

Starts the paKDE algorithm (second step of the mapping protocol).

Usage

bdm.pakde(bdm, layer = 1, threads = 2, type = "SOCK", ppx = 100,
  itr = 100, tol = 1e-05, g = 200, g.exp = 3)

Arguments

bdm

A bdm instance as generated by bdm.init().

layer

The number of the t-SNE layer (1 by default).

threads

The number of parallel threads (in principle only limited by hardware resources, i.e. number of cores and available memory)

type

The type of cluster: 'SOCK' (default) for intra-node parallelization, 'MPI' (message passing interface) for inter-node parallelization.

ppx

The value of perplexity to compute similarities in the low-dimensional embedding (100 by default).

itr

The number of iterations for computing input similarities (100 by default).

tol

The tolerance lower bound for computing input similarities (1e-05 by default).

g

The resolution of the density space grid (\(g*g\) cells, 200 by default).

g.exp

A numeric factor to avoid border effects. The grid limits will be expanded so as to enclose the density of the kernel of the most extreme embedded datapoints up to g.exp times \(\sigma\). By default, (g.exp = 3) the grid limits are expanded so as to enclose the 0.9986 of the probability mass of the most extreme kernels.

Value

A copy of the input bdm instance with new element bdm$pakde (paKDE output). bdm$pakde[[layer]]$layer = 'NC' stands for not computed layers.

Details

When computing the paKDE the embedding area is discretized as a grid of size g*g cells. In order to avoid border effects, the limits of the grid are expanded by default so as to enclose at least the 0.9986 of the cumulative distribution function (\(3 \sigma\)) of the kernels of the most extreme mapped points in each direction.

The presence of outliers in the embedding can lead to undesired expansion of the grid limits. We can overcome this using lower values of g.exp. By setting g.exp = 0 the grid limits will be equal to the range of the embedding.

The values g.exp = c(1, 2, 3, 4, 5, 6) enclose cdf values of 0.8413, 0.9772, 0.9986, 0.99996, 0.99999, 1.0 respectively.

Examples

# NOT RUN {
# --- load mapped dataset
bdm.example()
# --- run paKDE
# }
# NOT RUN {
exMap <- bdm.pakde(exMap, threads = 4, ppx = 200, g = 200, g.exp = 3)
# }
# NOT RUN {
# --- plot paKDE output
bdm.pakde.plot(exMap)
# }