1 | #!/usr/bin/env python3 |
---|
2 | # -*- coding: utf-8 -*- |
---|
3 | |
---|
4 | import sys |
---|
5 | import 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 | |
---|
12 | import matplotlib.pyplot as plt |
---|
13 | from mpl_toolkits.mplot3d import Axes3D |
---|
14 | from matplotlib import cm |
---|
15 | import argparse |
---|
16 | |
---|
17 | |
---|
18 | #http://www.nervouscomputer.com/hfs/cmdscale-in-python/ |
---|
19 | def 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 | |
---|
65 | def 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 | |
---|
70 | def read_file(fname, separator): |
---|
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("Making it 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 | |
---|
91 | def 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 | percent_variances = [sum(variances[:i+1])/sum(variances) for i in range(len(variances))] |
---|
96 | for i,pv in enumerate(percent_variances): |
---|
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 |
---|
103 | |
---|
104 | |
---|
105 | def plot(coordinates, labels, dimensions, jitter=0, 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 | add_jitter = lambda tab : rand_jitter(tab, jitter) if jitter>0 else tab |
---|
114 | |
---|
115 | x_dim = len(coordinates[0]) |
---|
116 | y_dim = len(coordinates) |
---|
117 | |
---|
118 | points = [add_jitter(coordinates[:, i]) for i in range(x_dim)] |
---|
119 | |
---|
120 | if labels is not None and dimensions==2: |
---|
121 | ax.scatter(*points, alpha=0.1) #barely visible points, because we will show labels anyway |
---|
122 | labelconvert={'velland':'V','velwat':'W','vpp':'P','vpa':'A'} #use this if you want to replace long names with short IDs |
---|
123 | #for point in points: |
---|
124 | # print(point) |
---|
125 | for label, x, y in zip(labels, points[0], points[1]): |
---|
126 | for key in labelconvert: |
---|
127 | if label.startswith(key): |
---|
128 | label=labelconvert[key] |
---|
129 | plt.annotate( |
---|
130 | label, |
---|
131 | xy = (x, y), xytext = (0, 0), |
---|
132 | textcoords = 'offset points', ha = 'center', va = 'center', |
---|
133 | #bbox = dict(boxstyle = 'round,pad=0.5', fc = 'yellow', alpha = 0.5), |
---|
134 | #arrowprops = dict(arrowstyle = '->', connectionstyle = 'arc3,rad=0') |
---|
135 | ) |
---|
136 | else: |
---|
137 | ax.scatter(*points, alpha=0.5) |
---|
138 | |
---|
139 | |
---|
140 | plt.title('Phenotypes distances') #TODO add % variance information |
---|
141 | plt.tight_layout() |
---|
142 | plt.axis('tight') |
---|
143 | |
---|
144 | if outname == "": |
---|
145 | plt.show() |
---|
146 | else: |
---|
147 | plt.savefig(outname+".pdf") |
---|
148 | np.savetxt(outname+".csv", coordinates, delimiter=";") |
---|
149 | |
---|
150 | |
---|
151 | def main(filename, dimensions=3, outname="", jitter=0, separator='\t'): |
---|
152 | distances,labels = read_file(filename, separator) |
---|
153 | embed = compute_mds(distances, dimensions) |
---|
154 | |
---|
155 | if dimensions == 1: |
---|
156 | embed = np.array([np.insert(e, 0, 0, axis=0) for e in embed]) |
---|
157 | |
---|
158 | plot(embed, labels, dimensions, jitter, outname) |
---|
159 | |
---|
160 | |
---|
161 | if __name__ == '__main__': |
---|
162 | parser = argparse.ArgumentParser() |
---|
163 | parser.add_argument('--in', dest='input', required=True, help='input file with dissimilarity matrix') |
---|
164 | parser.add_argument('--out', dest='output', required=False, help='output file name (without extension)') |
---|
165 | parser.add_argument('--dim', required=False, help='number of dimensions of the new space') |
---|
166 | parser.add_argument('--sep', required=False, help='separator of the source file') |
---|
167 | parser.add_argument('--j', required=False, help='for j>0, random jitter is added to points in the plot') |
---|
168 | |
---|
169 | args = parser.parse_args() |
---|
170 | set_value = lambda value, default : default if value == None else value |
---|
171 | main(args.input, int(set_value(args.dim, 3)), set_value(args.output, ""), float(set_value(args.j, 0)), set_value(args.sep, "\t")) |
---|