source:mds-and-trees/mds_plot.py@958

Last change on this file since 958 was 616, checked in by Maciej Komosinski, 7 years ago

Introduced an option to swap (exchange) X and Y axes

File size: 8.1 KB
Line
1#!/usr/bin/env python3
2# -*- coding: utf-8 -*-
3
4import sys
5import numpy as np
6#from sklearn import manifold #was needed for manifold MDS http://scikit-learn.org/stable/auto_examples/manifold/plot_compare_methods.html
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, jitter):
66        stdev = (arr.max()-arr.min()) / 100. * jitter #dispersion proportional to range
67        return arr + np.random.randn(len(arr)) * stdev
68
69
71        distances = np.genfromtxt(fname, delimiter=separator)
72        if (distances.shape[0]!=distances.shape[1]):
73                print("Matrix is not square:",distances.shape)
74        if (distances.shape[0]>distances.shape[1]):
75                raise ValueError('More rows than columns?')
76        if (distances.shape[0]<distances.shape[1]):
77                minsize = min(distances.shape[0],distances.shape[1])
78                firstsquarecolumn=distances.shape[1]-minsize
79                distances = np.array([row[firstsquarecolumn:] for row in distances]) #this can only fix matrices with more columns than rows
80                print("Made the matrix square:",distances.shape)
81
82                #if the file has more columns than rows, assume the first extra column on the left of the square matrix has labels
83                labels = np.genfromtxt(fname, delimiter=separator, usecols=firstsquarecolumn-1,dtype=[('label','S10')])
84                labels = [label[0].decode("utf-8") for label in labels]
85        else:
86                labels = None #no labels
87
88        return distances,labels
89
90
91def compute_mds(distance_matrix, dim):
92        embed, evals = cmdscale(distance_matrix)
93
94        variances = [np.var(embed[:,i]) for i in range(len(embed[0]))]
95        variances_fraction = [sum(variances[:i+1])/sum(variances) for i in range(len(variances))]
96        for i,pv in enumerate(variances_fraction):
97                print("In",i+1,"dimensions:",pv)
98
99        dim = min(dim, len(embed[0]))
100        embed = np.asarray([embed[:,i] for i in range(dim)]).T
101
102        return embed, variances_fraction[dim-1]
103
104
105def plot(coordinates, labels, dimensions, variance_fraction, jitter, flipX, flipY, swapXY, outname=""):
106        fig = plt.figure()
107
108        if dimensions < 3:
109                ax = fig.add_subplot(111)
110        else:
111                ax = fig.add_subplot(111, projection='3d')
112
113        x_dim = len(coordinates[0])
114        y_dim = len(coordinates)
115
116        if flipX:
117                coordinates=np.hstack((-coordinates[:, [0]], coordinates[:, [1]]))
118        if flipY:
119                coordinates=np.hstack((coordinates[:, [0]], -coordinates[:, [1]]))
120        if swapXY:
121                coordinates[:,[0, 1]] = coordinates[:,[1, 0]]
122
123        add_jitter = lambda tab: rand_jitter(tab, jitter) if jitter>0 else tab
124        points = [add_jitter(coordinates[:, i]) for i in range(x_dim)]
125
126        if labels is not None and dimensions==2: #could be ported to 3D too
127                ax.scatter(*points, alpha=0) #invisible points, because we will show labels instead
128                labelconvert={'velland_':'V','velwat_':'W','vpp_':'P','vpa_':'A'} #use this if you want to replace long names with short IDs
129                colors={'velland_':'green','velwat_':'blue','vpp_':'red','vpa_':'violet'}
130                #for point in points:
131                #       print(point)
132                for label, x, y in zip(labels, points[0], points[1]):
133                        color='black'
134                        for key in labelconvert:
135                                if label.startswith(key):
136                                        label=labelconvert[key]
137                                        color=colors[key]
138                        plt.annotate(
139                                label,
140                                xy = (x, y), xytext = (0, 0),
141                                textcoords = 'offset points', ha = 'center', va = 'center',
142                                color = color,
143                                alpha = 0.8,
144                                #bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5),
145                                #arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0')
146                                )
147        else:
148                ax.scatter(*points, alpha=0.5)
149
150
151        plt.title('Projection of phenotype distances, variance preserved = %.1f%%' % (variance_fraction*100))
152        plt.tight_layout()
153        plt.axis('tight')
154
155        if outname == "":
156                plt.show()
157        else:
158                plt.savefig(outname+".pdf")
159                np.savetxt(outname+".csv", coordinates, delimiter=";")
160
161
162def main(filename, dimensions=3, outname="", jitter=0, separator='\t', flipX=False, flipY=False, swapXY=False):
163        distances,labels = read_file(filename, separator)
164        embed,variance_fraction = compute_mds(distances, dimensions)
165
166        if dimensions == 1:
167                embed = np.array([np.insert(e, 0, 0, axis=0) for e in embed])
168
169        plot(embed, labels, dimensions, variance_fraction, jitter, flipX, flipY, swapXY, outname)
170
171
172if __name__ == '__main__':
173        parser = argparse.ArgumentParser()
174        parser.add_argument('--in', dest='input', required=True, help='input file with dissimilarity matrix')
175        parser.add_argument('--out', dest='output', required=False, help='output file name (without extension)')
176        parser.add_argument('--dim', required=False, help='number of dimensions of the new space')
177        parser.add_argument('--sep', required=False, help='separator of the source file')
178        parser.add_argument('--j', required=False, help='for j>0, random jitter is added to points in the plot')
179        parser.add_argument('--flipX', required=False, dest='flipX', action='store_true')
180        parser.add_argument('--flipY', required=False, dest='flipY', action='store_true')
181        parser.add_argument('--swapXY', required=False, dest='swapXY', action='store_true')
182        parser.set_defaults(flipX=False)
183        parser.set_defaults(flipY=False)
184        parser.set_defaults(swapXY=False)
185
186        args = parser.parse_args()
187        set_value = lambda value, default: default if value == None else value
188        main(args.input, int(set_value(args.dim, 3)), set_value(args.output, ""), float(set_value(args.j, 0)), set_value(args.sep, "\t"), args.flipX, args.flipY, args.swapXY)
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