Module org.scijava.ops.image
Package org.scijava.ops.image.coloc.kendallTau

Class KendallTauBRank<T extends RealType<T>,​U extends RealType<U>>

  • Type Parameters:
    T -
    All Implemented Interfaces:
    BiFunction<Iterable<T>,​Iterable<U>,​Double>
    public class KendallTauBRank<T extends RealType<T>,​U extends RealType<U>>
extends Object
implements BiFunction<Iterable<T>,​Iterable<U>,​Double>
    This algorithm calculates Kendall's Tau-b rank correlation coefficient

    According to this article, Tau-b (appropriate if multiple pairs share the same first, or second, value), the rank correlation of a set of pairs (x_1, y_1), ..., (x_n, y_n): 

     Tau_B = (n_c - n_d) / sqrt( (n_0 - n_1) (n_0 - n_2) )
    where 
     n_0 = n (n - 1) / 2
 n_1 = sum_i t_i (t_i - 1) / 2
 n_2 = sum_j u_j (u_j - 1) / 2
 n_c = #{ i, j; i != j && (x_i - x_j) * (y_i - y_j) > 0 },
   i.e. the number of pairs of pairs agreeing on the order of x and y, respectively
 n_d = #{ i, j: i != j && (x_i - x_j) * (y_i - y_j) < 0 },
   i.e. the number of pairs of pairs where x and y are ordered opposite of each other
 t_i = number of tied values in the i-th group of ties for the first quantity
 u_j = number of tied values in the j-th group of ties for the second quantity
    Author:
    Johannes Schindelin, Ellen T Arena
    Implementation Note:
    op names='coloc.kendallTau'