pm_clustering::setMember Interface Reference

Compute and return the memberships and minimum distances of a set of input points with respect to the an input set of cluster centers.
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Detailed Description

Compute and return the memberships and minimum distances of a set of input points with respect to the an input set of cluster centers.

The membership ID of the ith sample sample(:,i) is determined by computing the distance of the sample from each cluster and choosing the cluster ID j whose center(:,j) has the minimum distance from the sample among all clusters.
This minimum squared distance is output in disq(:,i).
The metric used within this generic interface is the Euclidean distance.

Parameters

[out]	membership	: The output scalar or vector of shape (1:nsam) of type integer of default kind IK, containing the membership of each input sample in sample from its nearest cluster center, such that cluster(membership(i)) is the nearest cluster center to the ith sample sample(:, i) at a squared-distance of disq(i).
[out]	disq	: The output scalar or vector of shape (1:nsam) of the same type and kind as the input argument sample, containing the Euclidean squared distance of each input sample in sample from its nearest cluster center.
[in]	sample	: The input scalar, vector, or matrix of, type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128), containing the sample of nsam points in a ndim-dimensional space whose memberships and minimum distances with respect to the input centers must be computed. If sample is a scalar and center is a vector of shape (1 : ncls), then the input sample must be the coordinate of a single sample in (univariate space) whose distance from ncls cluster centers must be computed. If sample is a vector of shape (1 : ndim) and center is a matrix of shape (1 : ndim, 1 : ncls), then the input sample must be a single sample (in ndim-dimensional space) whose distance from ncls cluster centers must be computed. If sample is a vector of shape (1 : nsam) and center is a vector of shape (1 : ncls), then the input sample must be a collection of nsam points (in univariate space) whose distances from ncls cluster centers must be computed. If sample is a matrix of shape (1 : ndim, 1 : nsam) and center is a matrix of shape (1 : ndim, 1 : ncls), then the input sample must be a collection of nsam points (in ndim-dimensional space) whose distances from ncls cluster centers must be computed.
[in]	center	: The input vector of shape (1:ncls) or matrix of shape (1 : ndim, 1 : ncls) of the same type and kind as the input argument sample, containing the set of ncls cluster centers (centroids) with respect to which the sample memberships and minimum distances must be computed.

Possible calling interfaces ⛓

use pm_clustering, only: setMember
 
call setMember(membership           , disq          , sample                    , center(1 : ncls))
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : nsam)          , center(1 : ncls))
call setMember(membership           , disq          , sample(1 : ndim)          , center(1 : ndim, 1 : ncls))
call setMember(membership(1 : nsam) , disq(1 : nsam), sample(1 : ndim, 1 : nsam), center(1 : ndim, 1 : ncls))

Warning

The condition ubound(center, rank(center)) > 0 must hold for the corresponding input arguments.
The condition ubound(sample, rank(sample)) == ubound(disq, 1) must hold for the corresponding input arguments.
The condition ubound(sample, rank(sample)) == ubound(membership, 1) must hold for the corresponding input arguments.
The condition ubound(sample, 1) == ubound(center, 1) .or. rank(sample) == 0 .or. rank(center) == 1 must hold for the corresponding input arguments.
These conditions are verified only if the library is built with the preprocessor macro CHECK_ENABLED=1.

The pure procedure(s) documented herein become impure when the ParaMonte library is compiled with preprocessor macro CHECK_ENABLED=1.
By default, these procedures are pure in release build and impure in debug and testing builds.

Remarks

This generic interface implements one of the two major steps involved in Kmeans clustering.

See also

setKmeans
setCenter
setMember
setKmeansPP

Example usage ⛓

program example
 
    use pm_kind, only: SK, IK, LK
    use pm_kind, only: RKG => RKS ! all other real kinds are also supported.
    use pm_io, only: display_type
    use pm_distUnif, only: getUnifRand
    use pm_arrayResize, only: setResized
    use pm_clustering, only: setMember
    use pm_arrayRange, only: getRange
 
    implicit none
 
    integer(IK) :: ndim, nsam, ncls
    real(RKG)   , allocatable  :: sample(:,:), center(:,:), disq(:)
    integer(IK) , allocatable  :: membership(:)
    type(display_type) :: disp
 
    disp = display_type(file = "main.out.F90")
 
    call disp%skip
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%show("! Compute memberships of a sample of points from arbitrary dimensional cluster centers.")
    call disp%show("!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%")
    call disp%skip
 
    call disp%skip()
    call disp%show("ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);")
                    ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);
    call disp%show("[ndim, nsam, ncls]")
    call disp%show( [ndim, nsam, ncls] )
    call disp%show("center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.")
                    center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.
    call disp%show("center")
    call disp%show( center )
    call disp%show("sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.")
                    sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.
    call disp%show("sample")
    call disp%show( sample )
    call disp%show("call setResized(disq, nsam)")
                    call setResized(disq, nsam)
    call disp%show("call setResized(membership, nsam)")
                    call setResized(membership, nsam)
    call disp%skip()
 
    call disp%show("call setMember(membership, disq, sample, center) ! sample points memberships.")
                    call setMember(membership, disq, sample, center) ! sample points memberships.
    call disp%show("membership")
    call disp%show( membership )
    call disp%show("disq")
    call disp%show( disq )
    call disp%skip()
 
    call disp%show("call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.")
                    call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.
    call disp%show("membership")
    call disp%show( membership )
    call disp%show("disq")
    call disp%show( disq )
    call disp%skip()
 
    call disp%show("call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.")
                    call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.
    call disp%show("membership")
    call disp%show( membership )
    call disp%show("disq")
    call disp%show( disq )
    call disp%skip()
 
    call disp%show("call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.")
                    call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.
    call disp%show("membership")
    call disp%show( membership )
    call disp%show("disq")
    call disp%show( disq )
    call disp%skip()
 
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    ! Output an example for visualization.
    !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
    block
        integer(IK) :: funit, i
        ndim = 2
        ncls = 5
        nsam = 5000
        center = getUnifRand(0., 1., ndim, ncls)
        sample = getUnifRand(0., 1., ndim, nsam)
        call setResized(disq, nsam)
        call setResized(membership, nsam)
        call setMember(membership, disq, sample, center)
        open(newunit = funit, file = "setMember.center.txt")
            do i = 1, ncls
                write(funit, "(*(g0,:,','))") i, center(:,i)
            end do
        close(funit)
        open(newunit = funit, file = "setMember.sample.txt")
            do i = 1, nsam
                write(funit, "(*(g0,:,','))") membership(i), sample(:,i)
            end do
        close(funit)
    end block
 
end program example

Example Unix compile command via Intel ifort compiler ⛓

#!/usr/bin/env sh
rm main.exe
ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓

del main.exe
set PATH=..\..\..\lib;%PATH%
ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe
main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓

#!/usr/bin/env sh
rm main.exe
gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe
./main.exe

Example output ⛓

 
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
! Compute memberships of a sample of points from arbitrary dimensional cluster centers.
!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
ndim = getUnifRand(1, 5); nsam = getUnifRand(1, 5); ncls = getUnifRand(1, 5);
[ndim, nsam, ncls]
+5, +5, +5
center = getUnifRand(0., 5., ndim, ncls) ! initialize random centers.
center
+2.95287347, +0.873432755, +2.94427490, +4.48586750, +2.38695025
+4.31980324, +2.16027975, +1.91202998, +3.01914549, +0.972197354
+4.63103580, +0.415405929, +2.97512984, +4.01900101, +2.90705252
+0.324255228E-1, +4.30651140, +2.72871852, +2.04859352, +3.20556593
+2.71212721, +0.887698233, +2.62440348, +0.803742111, +2.39284754
sample = getUnifRand(0., 5., ndim, nsam) ! Create a random sample.
sample
+3.16145992, +3.65849543, +3.82833219, +4.83974886, +4.06710815
+3.87250900, +1.49034524, +3.47379589, +1.40087605, +2.95571947
+0.848776400, +2.89913535, +2.59124303, +4.34037304, +3.14335108
+3.55772209, +2.43910432, +4.86771584, +3.81262803, +2.25654960
+1.82135320, +1.59435725, +4.12382507, +4.43122387, +3.55864477
call setResized(disq, nsam)
call setResized(membership, nsam)
 
call setMember(membership, disq, sample, center) ! sample points memberships.
membership
+3, +3, +3, +3, +3
disq
+9.74416351, +1.83857572, +10.1916142, +10.1574488, +3.47409105
 
call setMember(membership(1), disq(1), sample(:,1), center) ! single point membership.
membership
+3, +3, +3, +3, +3
disq
+9.74416351, +1.83857572, +10.1916142, +10.1574488, +3.47409105
 
call setMember(membership, disq, sample(1,:), center(1,:)) ! sample points memberships in one-dimension.
membership
+1, +1, +4, +4, +4
disq
+0.435083099E-1, +0.497902334, +0.432352692, +0.125232011, +0.175359383
 
call setMember(membership(1), disq(1), sample(1,1), center(1,:)) ! single point membership in one-dimension.
membership
+1, +1, +4, +4, +4
disq
+0.435083099E-1, +0.497902334, +0.432352692, +0.125232011, +0.175359383
 
 

Postprocessing of the example output ⛓

#!/usr/bin/env python
 
import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
import glob
import sys
import os
 
fontsize = 17
fig = plt.figure(figsize = 1.25 * np.array([6.4, 4.8]), dpi = 200)
ax = plt.subplot()
 
parent = os.path.basename(os.path.dirname(__file__))
pattern = parent + "*.txt"
 
fileList = glob.glob(pattern)
legends = []
if len(fileList) == 2:
    for file in fileList:
 
        kind = file.split(".")[1]
        prefix = file.split(".")[0]
        df = pd.read_csv(file, delimiter = ",", header = None)
 
        if kind == "center":
            ax.scatter  ( df.values[:,1]
                        , df.values[:,2]
                        , zorder = 100
                        , marker = "*"
                        , c = "red"
                        , s = 50
                        )
            legends.append("center")
        elif kind == "sample":
            ax.scatter  ( df.values[:,1]
                        , df.values[:,2]
                        , c = df.values[:, 0]
                        , s = 10
                        )
            legends.append("sample")
        else:
            sys.exit("Ambiguous file exists: {}".format(file))
 
    ax.legend(legends, fontsize = fontsize)
    plt.xticks(fontsize = fontsize - 2)
    plt.yticks(fontsize = fontsize - 2)
    ax.set_xlabel("X", fontsize = 17)
    ax.set_ylabel("Y", fontsize = 17)
    ax.set_title("Membership Scatter Plot", fontsize = fontsize)
 
    plt.axis('equal')
    plt.grid(visible = True, which = "both", axis = "both", color = "0.85", linestyle = "-")
    ax.tick_params(axis = "y", which = "minor")
    ax.tick_params(axis = "x", which = "minor")
    ax.set_axisbelow(True)
    plt.tight_layout()
 
    plt.savefig(prefix + ".png")
else:
    sys.exit("Ambiguous file list exists.")

Visualization of the example output ⛓

Test:

test_pm_clustering

Final Remarks ⛓

---

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

1. If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
   
2. If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.
   

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, September 1, 2012, 12:00 AM, National Institute for Fusion Studies, The University of Texas at Austin

Definition at line 126 of file pm_clustering.F90.

---

The documentation for this interface was generated from the following file:

• src/fortran/main/pm_clustering.F90