# source:mds-and-trees/mds_plot.py@600

Last change on this file since 600 was 600, checked in by oriona, 7 years ago

Number of returned dimensions set to minimum of desired number and the number returned by mds.

File size: 5.5 KB
Line
1#!/usr/bin/env python3
2# -*- coding: utf-8 -*-
3
4import sys
5import numpy as np
6from sklearn import manifold
7
8#to make it work in console, http://stackoverflow.com/questions/2801882/generating-a-png-with-matplotlib-when-display-is-undefined
9#import matplotlib
10#matplotlib.use('Agg')
11
12import matplotlib.pyplot as plt
13from mpl_toolkits.mplot3d import Axes3D
14from matplotlib import cm
15import argparse
16
17
18#http://www.nervouscomputer.com/hfs/cmdscale-in-python/
19def cmdscale(D):
20    """
21    Classical multidimensional scaling (MDS)
22
23    Parameters
24    ----------
25    D : (n, n) array
26        Symmetric distance matrix.
27
28    Returns
29    -------
30    Y : (n, p) array
31        Configuration matrix. Each column represents a dimension. Only the
32        p dimensions corresponding to positive eigenvalues of B are returned.
33        Note that each dimension is only determined up to an overall sign,
34        corresponding to a reflection.
35
36    e : (n,) array
37        Eigenvalues of B.
38
39    """
40    # Number of points
41    n = len(D)
42
43    # Centering matrix
44    H = np.eye(n) - np.ones((n, n))/n
45
46    # YY^T
47    B = -H.dot(D**2).dot(H)/2
48
49    # Diagonalize
50    evals, evecs = np.linalg.eigh(B)
51
52    # Sort by eigenvalue in descending order
53    idx   = np.argsort(evals)[::-1]
54    evals = evals[idx]
55    evecs = evecs[:,idx]
56
57    # Compute the coordinates using positive-eigenvalued components only
58    w, = np.where(evals > 0)
59    L  = np.diag(np.sqrt(evals[w]))
60    V  = evecs[:,w]
61    Y  = V.dot(L)
62
63    return Y, evals
64
65def rand_jitter(arr):
66        stdev = arr.max() / 100.
67        return arr + np.random.randn(len(arr)) * stdev * 2
68
69
71        distances = np.genfromtxt(fname, delimiter=separator)
72        if np.isnan(distances[0][len(distances[0])-1]):#separator after the last element in row
73                distances = np.array([row[:-1] for row in distances])
74        return distances
75
76
77def compute_mds(distance_matrix, dim):
78        embed, evals = cmdscale(distance_matrix)
79
80        variances = [np.var(embed[:,i]) for i in range(len(embed[0]))]
81        percent_variances = [sum(variances[:i+1])/sum(variances) for i in range(len(variances))]
82        for i,pv in enumerate(percent_variances):
83                print(i+1,"dimension:",pv)
84
85        dim = min(dim, len(embed[0]))
86        embed = np.asarray([embed[:,i] for i in range(dim)]).T
87
88        return embed
89
90
91def plot(coordinates, dimensions, jitter=0, outname=""):
92        fig = plt.figure()
93
94        if dimensions < 3:
96        else:
98
99        add_jitter = lambda tab : rand_jitter(tab) if jitter==1 else tab
100
101        x_dim = len(coordinates[0])
102        y_dim = len(coordinates)
103
104        ax.scatter(*[add_jitter(coordinates[:, i]) for i in range(x_dim)], alpha=0.5)
105
106        plt.title('Phenotypes distances')
107        plt.tight_layout()
108        plt.axis('tight')
109
110        if outname == "":
111                plt.show()
112
113        else:
114                plt.savefig(outname+".pdf")
115                np.savetxt(outname+".csv", coordinates, delimiter=";")
116
117
118def main(filename, dimensions=3, outname="", jitter=0, separator='\t'):
119        dimensions = int(dimensions)
121        embed = compute_mds(distances, dimensions)
122
123        if dimensions == 1:
124                embed = np.array([np.insert(e, 0, 0, axis=0) for e in embed])
125
126        plot(embed, dimensions, jitter, outname)
127
128
129if __name__ == '__main__':
130        parser = argparse.ArgumentParser()
131        parser.add_argument('--in', dest='input', required=True, help='input file with dissimilarity matrix')
132        parser.add_argument('--out', dest='output', required=False, help='output file name without extension')
133        parser.add_argument('--dim', required=False, help='number of dimensions of the new space')
134        parser.add_argument('--sep', required=False, help='separator of the source file')
135        parser.add_argument('--j', required=False, help='for j=1 random jitter is added to the plot')
136
137        args = parser.parse_args()
138        set_value = lambda value, default : default if value == None else value
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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