source: mds-and-trees/mds_plot.py @ 598

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import sys
import numpy as np
from sklearn import manifold

#to make it work in console, http://stackoverflow.com/questions/2801882/generating-a-png-with-matplotlib-when-display-is-undefined
#import matplotlib
#matplotlib.use('Agg')

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import argparse


#http://www.nervouscomputer.com/hfs/cmdscale-in-python/
def cmdscale(D):
    """                                                                                       
    Classical multidimensional scaling (MDS)                                                  
                                                                                               
    Parameters                                                                                
    ----------                                                                                
    D : (n, n) array                                                                          
        Symmetric distance matrix.                                                            
                                                                                               
    Returns                                                                                   
    -------                                                                                   
    Y : (n, p) array                                                                          
        Configuration matrix. Each column represents a dimension. Only the                    
        p dimensions corresponding to positive eigenvalues of B are returned.                 
        Note that each dimension is only determined up to an overall sign,                    
        corresponding to a reflection.                                                        
                                                                                               
    e : (n,) array                                                                            
        Eigenvalues of B.                                                                     
                                                                                               
    """
    # Number of points                                                                        
    n = len(D)
 
    # Centering matrix                                                                        
    H = np.eye(n) - np.ones((n, n))/n
 
    # YY^T                                                                                    
    B = -H.dot(D**2).dot(H)/2
 
    # Diagonalize                                                                             
    evals, evecs = np.linalg.eigh(B)
 
    # Sort by eigenvalue in descending order                                                  
    idx   = np.argsort(evals)[::-1]
    evals = evals[idx]
    evecs = evecs[:,idx]
 
    # Compute the coordinates using positive-eigenvalued components only                      
    w, = np.where(evals > 0)
    L  = np.diag(np.sqrt(evals[w]))
    V  = evecs[:,w]
    Y  = V.dot(L)
 
    return Y, evals

def rand_jitter(arr):
        stdev = arr.max() / 100.
        return arr + np.random.randn(len(arr)) * stdev * 2


def read_file(fname, separator):
        distances = np.genfromtxt(fname, delimiter=separator)
        if np.isnan(distances[0][len(distances[0])-1]):#separator after the last element in row
                distances = np.array([row[:-1] for row in distances])
        return distances


def compute_mds(distance_matrix, dim):
        embed, evals = cmdscale(distance_matrix)
        variances = compute_variances(embed)
        embed = np.asarray([embed[:,i] for i in range(dim)]).T

        percent_variances = [sum(variances[:i+1])/sum(variances) for i in range(dim)]
        for i,pv in enumerate(percent_variances):
                print(i+1,"dimension:",pv)

        return embed


def compute_variances(embed):
        variances = []
        for i in range(len(embed[0])):
                variances.append(np.var(embed[:,i]))
        return variances


def plot(coordinates, dimensions, jitter=0, outname=""):
        fig = plt.figure()

        if dimensions < 3:
                ax = fig.add_subplot(111)
        else:
                ax = fig.add_subplot(111, projection='3d')

        add_jitter = lambda tab : rand_jitter(tab) if jitter==1 else tab

        x_dim = len(coordinates[0])
        y_dim = len(coordinates)

        ax.scatter(*[add_jitter(coordinates[:, i]) for i in range(x_dim)], alpha=0.5)

        plt.title('Phenotypes distances')
        plt.tight_layout()
        plt.axis('tight')

        if outname == "":
                plt.show()

        else:
                plt.savefig(outname+".pdf")
                np.savetxt(outname+".csv", coordinates, delimiter=";")


def main(filename, dimensions=3, outname="", jitter=0, separator='\t'):
        dimensions = int(dimensions)
        distances = read_file(filename, separator)
        embed = compute_mds(distances, dimensions)

        if dimensions == 1:
                embed = np.array([np.insert(e, 0, 0, axis=0) for e in embed])
        
        plot(embed, dimensions, jitter, outname)


if __name__ == '__main__':
        parser = argparse.ArgumentParser()
        parser.add_argument('--in', dest='input', required=True, help='input file with dissimilarity matrix')
        parser.add_argument('--out', dest='output', required=False, help='output file name without extension')
        parser.add_argument('--dim', required=False, help='number of dimensions of the new space')
        parser.add_argument('--sep', required=False, help='separator of the source file')
        parser.add_argument('--j', required=False, help='for j=1 random jitter is added to the plot')

        args = parser.parse_args()
        set_value = lambda value, default : default if value == None else value
        main(args.input, set_value(args.dim, 3), set_value(args.output, ""), set_value(args.j, 0), set_value(args.sep, "\t"))