Separations

When linear manifold is formed, a distance from every point of dataset to the manifold is calculated, and a histograms of point distances to each trial manifold are computed. If the resulting histogram contains multiple modes then the mode near zero is isolated in histogram [1]. The isolated part of histogram is used to determine a separation criteria, and the data points are partitioned from the rest of the dataset on the basis of such separation.

The separation properties defined in Separation instance, which is defined as follows:

type Separation
    depth::Float64              # Separation depth (depth between separated histogram modes)
    discriminability::Float64   # Separation discriminability (width between separated histogram modes)
    threshold::Float64          # Distance threshold value
    globalmin::Int              # Global minimum as histogram bin index
    hist_range::Vector{Float64} # Histogram ranges
    hist_count::Vector{UInt32}  # Histogram counts
    bin_index::Vector{UInt32}   # Point to bin assignments
end

Separation criteria and distance threshold value can be accessed through following functions:

criteria(S)

Returns separation criteria value which is product of depth and discriminability.

threshold(S)

Returns distance threshold value for separation calculated on histogram of distances. It is used to determine which points belong to formed cluster.

References

[1]	Kittler & J. Illingworth: “Minimum Error Thresholding”, Pattern Recognition, Vol 19, nr 1. 1986, pp. 41-47, DOI:10.1016/0031-3203(86)90030-0