1 | #!/usr/bin/env python3 |
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2 | # -*- coding: utf-8 -*- |
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3 | |
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4 | import sys |
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5 | import numpy as np |
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6 | from sklearn import manifold |
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7 | |
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8 | #to make it work in console, http://stackoverflow.com/questions/2801882/generating-a-png-with-matplotlib-when-display-is-undefined |
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9 | #import matplotlib |
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10 | #matplotlib.use('Agg') |
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11 | |
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12 | import matplotlib.pyplot as plt |
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13 | from mpl_toolkits.mplot3d import Axes3D |
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14 | from matplotlib import cm |
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15 | import argparse |
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16 | |
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17 | |
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18 | #http://www.nervouscomputer.com/hfs/cmdscale-in-python/ |
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19 | def cmdscale(D): |
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20 | """ |
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21 | Classical multidimensional scaling (MDS) |
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22 | |
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23 | Parameters |
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24 | ---------- |
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25 | D : (n, n) array |
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26 | Symmetric distance matrix. |
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27 | |
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28 | Returns |
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29 | ------- |
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30 | Y : (n, p) array |
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31 | Configuration matrix. Each column represents a dimension. Only the |
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32 | p dimensions corresponding to positive eigenvalues of B are returned. |
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33 | Note that each dimension is only determined up to an overall sign, |
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34 | corresponding to a reflection. |
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35 | |
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36 | e : (n,) array |
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37 | Eigenvalues of B. |
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38 | |
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39 | """ |
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40 | # Number of points |
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41 | n = len(D) |
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42 | |
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43 | # Centering matrix |
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44 | H = np.eye(n) - np.ones((n, n))/n |
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45 | |
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46 | # YY^T |
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47 | B = -H.dot(D**2).dot(H)/2 |
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48 | |
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49 | # Diagonalize |
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50 | evals, evecs = np.linalg.eigh(B) |
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51 | |
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52 | # Sort by eigenvalue in descending order |
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53 | idx = np.argsort(evals)[::-1] |
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54 | evals = evals[idx] |
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55 | evecs = evecs[:,idx] |
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56 | |
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57 | # Compute the coordinates using positive-eigenvalued components only |
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58 | w, = np.where(evals > 0) |
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59 | L = np.diag(np.sqrt(evals[w])) |
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60 | V = evecs[:,w] |
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61 | Y = V.dot(L) |
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62 | |
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63 | return Y, evals |
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64 | |
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65 | def rand_jitter(arr): |
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66 | stdev = arr.max() / 100. |
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67 | return arr + np.random.randn(len(arr)) * stdev * 2 |
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68 | |
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69 | |
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70 | def read_file(fname, separator): |
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71 | distances = np.genfromtxt(fname, delimiter=separator) |
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72 | if np.isnan(distances[0][len(distances[0])-1]):#separator after the last element in row |
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73 | distances = np.array([row[:-1] for row in distances]) |
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74 | return distances |
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75 | |
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76 | |
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77 | def compute_mds(distance_matrix, dim): |
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78 | embed, evals = cmdscale(distance_matrix) |
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79 | |
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80 | variances = [np.var(embed[:,i]) for i in range(len(embed[0]))] |
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81 | percent_variances = [sum(variances[:i+1])/sum(variances) for i in range(len(variances))] |
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82 | for i,pv in enumerate(percent_variances): |
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83 | print(i+1,"dimension:",pv) |
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84 | |
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85 | dim = min(dim, len(embed[0])) |
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86 | embed = np.asarray([embed[:,i] for i in range(dim)]).T |
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87 | |
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88 | return embed |
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89 | |
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90 | |
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91 | def plot(coordinates, dimensions, jitter=0, outname=""): |
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92 | fig = plt.figure() |
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93 | |
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94 | if dimensions < 3: |
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95 | ax = fig.add_subplot(111) |
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96 | else: |
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97 | ax = fig.add_subplot(111, projection='3d') |
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98 | |
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99 | add_jitter = lambda tab : rand_jitter(tab) if jitter==1 else tab |
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100 | |
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101 | x_dim = len(coordinates[0]) |
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102 | y_dim = len(coordinates) |
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103 | |
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104 | ax.scatter(*[add_jitter(coordinates[:, i]) for i in range(x_dim)], alpha=0.5) |
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105 | |
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106 | plt.title('Phenotypes distances') |
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107 | plt.tight_layout() |
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108 | plt.axis('tight') |
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109 | |
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110 | if outname == "": |
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111 | plt.show() |
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112 | |
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113 | else: |
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114 | plt.savefig(outname+".pdf") |
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115 | np.savetxt(outname+".csv", coordinates, delimiter=";") |
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116 | |
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117 | |
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118 | def main(filename, dimensions=3, outname="", jitter=0, separator='\t'): |
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119 | dimensions = int(dimensions) |
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120 | distances = read_file(filename, separator) |
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121 | embed = compute_mds(distances, dimensions) |
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122 | |
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123 | if dimensions == 1: |
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124 | embed = np.array([np.insert(e, 0, 0, axis=0) for e in embed]) |
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125 | |
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126 | plot(embed, dimensions, jitter, outname) |
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127 | |
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128 | |
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129 | if __name__ == '__main__': |
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130 | parser = argparse.ArgumentParser() |
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131 | parser.add_argument('--in', dest='input', required=True, help='input file with dissimilarity matrix') |
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132 | parser.add_argument('--out', dest='output', required=False, help='output file name without extension') |
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133 | parser.add_argument('--dim', required=False, help='number of dimensions of the new space') |
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134 | parser.add_argument('--sep', required=False, help='separator of the source file') |
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135 | parser.add_argument('--j', required=False, help='for j=1 random jitter is added to the plot') |
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136 | |
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137 | args = parser.parse_args() |
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138 | set_value = lambda value, default : default if value == None else value |
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139 | main(args.input, set_value(args.dim, 3), set_value(args.output, ""), set_value(args.j, 0), set_value(args.sep, "\t")) |
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