Implement barcode diagram

[mathemonads]

A barcode is a graphical representation as a collection of horizontal line segments in a plane whose horizontal axis corresponds to the parameter and whose vertical axis represents an (arbitrary) ordering of homology generators. [1]

I'd be happy to contribute my implementation.

[1] Barcodes: The Persistent Topology of Data

[sauln]

That’d be great! By all means, submit a PR. I’ll review asap.

[tmelorc]

Some months ago I created the program below to plot some barcodes. Maybe it could be useful to be implemented in your program.

'''
Created by Thiago de Melo
'''


import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import pandas as pd
import subprocess
#import os

def circle_pts(N, R=1):
    theta_list = np.random.random_sample(N)
    pts = np.zeros((N,2))
    #print theta_list
    for i in range(len(theta_list)):
        pts[i,0] = R*np.cos(2*np.pi*theta_list[i])
        pts[i,1] = R*np.sin(2*np.pi*theta_list[i])
    return pts

def sphere_pts(N, R=1):
    angle_list = 2*np.pi * np.random.sample((N,2))
    #phi_list   = np.random.random_sample(N)
    pts = np.zeros((N,3))
    for i in range(len(angle_list)):
        pts[i,0] = R*np.cos(angle_list[i,0])*np.cos(angle_list[i,1])
        pts[i,1] = R*np.cos(angle_list[i,0])*np.sin(angle_list[i,1])
        pts[i,2] = R*np.sin(angle_list[i,0])
    return pts

def figure_eight_pts(N, a=1):
    theta_list = 2 * np.pi * np.random.sample(N)
    pts = np.zeros((N,2))
    print theta_list
    for i in range(len(theta_list)):
        pts[i,0] = a * np.cos(theta_list[i]) * np.sqrt(2*np.cos(2*theta_list[i]))
        pts[i,1] = a * np.sin(theta_list[i]) * np.sqrt(2*np.cos(2*theta_list[i]))
    return pts

def annulus_pts(N, R=2, r=1):
    theta_list = np.random.random_sample(N)
    radius_list = r + np.random.random_sample(N) * (R-r)
    pts = np.zeros((N,2))
    for i in range(len(theta_list)):
        pts[i,0] = radius_list[i] * np.cos(2*np.pi*theta_list[i])
        pts[i,1] = radius_list[i] * np.sin(2*np.pi*theta_list[i])
    return pts

def random_pts(N,d):
    pts = np.random.random_sample((N, d))
    return pts

def cube_pts(N):
    npts = N/6
    faces = {}
    for i in range(3):
        data0 = np.random.random((npts,3))
        data1 = np.random.random((npts,3))
        data0[:,i] = 0
        data1[:,i] = 1
        faces[i]   = data0
        faces[i+3] = data1
    cube = np.concatenate([faces[i] for i in range(6)])
    return cube

def adjust_spines(ax, spines):
    for loc, spine in ax.spines.items():
        if loc in spines:
            spine.set_position(('outward', 5))  # outward by 10 points
            spine.set_smart_bounds(True)
        else:
            spine.set_color('none')  # don't draw spine

    # turn off ticks where there is no spine
    if 'left' in spines:
        ax.yaxis.set_ticks_position('left')
    else:
        # no yaxis ticks
        ax.yaxis.set_ticks([])

    if 'bottom' in spines:
        ax.xaxis.set_ticks_position('bottom')
    else:
        # no xaxis ticks
        ax.xaxis.set_ticks([])

def plot_bar(p,q,c='b',linestyle='-'):
    plt.plot([p[0],q[0]],[p[1],q[1]], c=c,linestyle=linestyle, linewidth=1)


''' DATA SET SECTION '''
''' cant use dash - in variable name (use _ instead)'''
VR = './examples/VR.point_cloud'
mds_weight = './examples/mds-weight.point_cloud'
mds_size = './examples/mds-size.point_cloud'
input_file = mds_weight
pts_file = './pts.point_cloud'

'''choose pts below'''
#pts = np.loadtxt(input_file, delimiter=',')
pts = circle_pts(50, 2)
#pts = annulus_pts(400, 4, 1)
#pts = random_pts(100,3)
#pts = cube_pts(30)
#pts = figure_eight_pts(400, 3)
#pts = sphere_pts(100)

np.savetxt(pts_file, pts, delimiter=' ', fmt='%.3f')
num_pts, dim_pts = pts.shape

#print pts

#plt.scatter(pts[:,0],pts[:,1])
#plt.show()
#quit()

''' RIPSER SECTION '''
ripser_bin = ['/home/thiago/Dropbox/Programacao/ripser/ripser']
ripser_input_file = pts_file
ripser_output_file = 'ripser.out'
ripser_format = 'point-cloud'
ripser_threshold = 1.4
ripser_dim = 2
ripser_opt = ['--format', ripser_format, '--threshold', str(ripser_threshold), '--dim', str(ripser_dim), '--output', ripser_output_file, ripser_input_file]
ripser_cmd = ripser_bin + ripser_opt

print "Executing Ripser..."
subprocess.call(ripser_cmd),
print "Done!"

#quit()

''' DIAGRAMS SECTION '''
cols_name = ['dim', 'birth', 'death']
df = pd.read_csv(ripser_output_file, delim_whitespace = True, header = None, names = cols_name)
dimensions = df.drop_duplicates('dim')['dim'].tolist()
birth_max = df['birth'].max()
death_max = df['death'].max()
infinity = ripser_threshold #1.05 * np.maximum(birth_max,death_max)
print "Creating persistent diagram for dimensions", dimensions

diagrams = {} 
diagrams_inf = {}
bar_num = {}
bar_inf_num = {}
for dim in dimensions:
    diagrams[dim] = df[ (df.dim == dim) & (df.death != -1) ]
    diagrams[dim] = diagrams[dim].sort_values(['birth','death'], ascending=[True,True]).reset_index()
    diagrams_inf[dim] = df[ (df.dim == dim) & (df.death == -1) ]
    diagrams_inf[dim] = diagrams_inf[dim].sort_values(['birth','death'], ascending=[True,True]).reset_index()
    bar_num[dim] = diagrams[dim].shape[0]
    bar_inf_num[dim] = diagrams_inf[dim].shape[0]
    #print dim, bar_num[dim], bar_inf_num[dim]
    #print diagrams[dim]


''' PLOTS SECTION '''

#'''
fig = plt.figure()

# dataset
if dim_pts >= 3:
    ax = fig.add_subplot(1,2,2, projection='3d')
    ax.plot3D(pts[:,0],pts[:,1],pts[:,2],".")
    ax.set_title(r'$X$ with $%d$ points' % num_pts, fontsize = 10)
    ax.set_zticks([1])
    ax.set_yticks([0,1])
    ax.set_xticks([0,1])
if dim_pts == 2:
    ax = fig.add_subplot(1, 2, 2)
    ax.set_title(r'$X$ with $%d$ points' % num_pts, fontsize = 10)
    plt.scatter(pts[:,0],pts[:,1], s=10)
if dim_pts == 1:
    ax = fig.add_subplot(1, 2, 2)
    ax.set_title(r'$X$ with $%d$ points' % num_pts, fontsize = 10)
    plt.scatter(pts,0*pts, s=10)


# diagrams
ax = fig.add_subplot(1, 2, 1)
ax.set_title(r'$\mathrm{Dgm}_k(X)$  $\epsilon = %.2f$' % float(ripser_threshold), fontsize = 10)
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
plt.xlabel('birth', fontsize=10)
plt.ylabel('death', fontsize=10)
adjust_spines(ax, ['left', 'bottom'])
plt.plot([0,infinity],[0,infinity], c='k', linewidth=1)
colors = ['r', 'b', 'g']
markers = ['o', 's', 'x']
labels = [r'$k = %d$' % x for x in range(len(dimensions))]

for dim in dimensions:
    #print diagrams_inf[dim]
    plt.scatter(diagrams[dim].birth, diagrams[dim].death, s=10, c=colors[dim], label=labels[dim], marker=markers[dim])
    if len(diagrams_inf[dim].index) > 0:
        plt.scatter(diagrams_inf[dim].birth, -infinity*diagrams_inf[dim].death, s=15, c=colors[dim], marker=markers[dim], label='') 
plt.legend(loc="lower right")


# barcodes
for dim in dimensions:
    print "Number of bars in dimension %d: %d" % (dim, bar_num[dim] + bar_inf_num[dim])
    fig = plt.figure()
    ax = plt.subplot("111")
    ax.set_title("%d-dimensional bars: %d finite, %d infinite" % (dim, bar_num[dim], bar_inf_num[dim]), fontsize = 10)
    # infinite bars
    if bar_inf_num[dim] > 0:
        for i in range(bar_inf_num[dim]):
                h=i+bar_num[dim]
                plot_bar([diagrams_inf[dim].birth[i],h],[-infinity*diagrams_inf[dim].death[i],h])
                plt.scatter([-infinity*diagrams_inf[dim].death[i]],[h], c='b', s=10, marker='>')
    # finite bars
    if bar_num[dim] > 0:
        for i in range(bar_num[dim]):
                plot_bar([diagrams[dim].birth[i],i],[diagrams[dim].death[i],i])
                plt.plot([diagrams[dim].death.max(),diagrams[dim].death.max()],[0,bar_num[dim]], c='r', linestyle='--', linewidth=0.5)
        #plt.xticks(list(plt.xticks()[0]) + [diagrams[dim].death.max()])

plt.show()
#'''

[sauln]

Looks great! If you'd submit the barcodes portion as a PR, I'd gladly do a code review and incorporate the implementation.

Thanks!

[tmelorc]

I have no experience with Git, sorry. I have just added the .py file and two images to my git here: https://github.com/tmelorc/ripser I'd be glad to help (according to my limitations :-) )

[sauln]

I'd rather walk you through the process than do it for you. The process is as follows.

1. Fork Persim
2. Clone locally: `git clone https://github.com/tmelorc/persim
3. cd into the repo: cd persim
4. Add a function plot_barcode with just the barcodes visualization code to the file persim/visuals.py.
5. Commit the changes: git add persim/visuals.py; git commit -m "added barcode visualization"
6. Push changes back to github: git push origin master
7. Head back to github and click "New pull request"
8. You can then select your fork and branch and submit the PR.
9. This will initiate a bunch of build scripts that will confirm the code didn't break anything.

[tmelorc]

Oh, interesting. Thanks for your help and explanation. I'll try to do that as soon as possible. Since the program I created was very locally (I mean, works for my examples) there are many parts that can be improved. For example, it runs ripser instead of using the Python version (which I just discovered). So the code should be cleaned. Did you see the screenshot I uploaded? Was it good? Regards.

[sauln]

Yeah! I'm not sure what screenshot unless you mean the code snipped posted above?

There'll be a little bit of working getting the interface right, but overall it looks good (I haven't actually tried running it).

I imagine this chunk of code will be most of what is needed in the new function:

def plot_bar(p,q,c='b',linestyle='-'):
    plt.plot([p[0],q[0]],[p[1],q[1]], c=c,linestyle=linestyle, linewidth=1)

# barcodes
for dim in dimensions:
    print "Number of bars in dimension %d: %d" % (dim, bar_num[dim] + bar_inf_num[dim])
    fig = plt.figure()
    ax = plt.subplot("111")
    ax.set_title("%d-dimensional bars: %d finite, %d infinite" % (dim, bar_num[dim], bar_inf_num[dim]), fontsize = 10)
    # infinite bars
    if bar_inf_num[dim] > 0:
        for i in range(bar_inf_num[dim]):
                h=i+bar_num[dim]
                plot_bar([diagrams_inf[dim].birth[i],h],[-infinity*diagrams_inf[dim].death[i],h])
                plt.scatter([-infinity*diagrams_inf[dim].death[i]],[h], c='b', s=10, marker='>')
    # finite bars
    if bar_num[dim] > 0:
        for i in range(bar_num[dim]):
                plot_bar([diagrams[dim].birth[i],i],[diagrams[dim].death[i],i])
                plt.plot([diagrams[dim].death.max(),diagrams[dim].death.max()],[0,bar_num[dim]], c='r', linestyle='--', linewidth=0.5)
        #plt.xticks(list(plt.xticks()[0]) + [diagrams[dim].death.max()])

plt.show()

Once you submit a first PR, I can help by editing the PR directly.

[tmelorc]

Good. I meant https://github.com/tmelorc/ripser/blob/master/barcode.png

Also, the functions you have cited are the main one. The most difficulty part is to work with the ripser output. The original Ripser outputs only the intervals (like [0,.3) for example).

What I did was to change it to save the output to a file and read that file to create the bars. I defined an option --output filename.

For example, the output I need is like

0 0 0.764629
0 0 -1
1 1.19803 -1

showing (-1 means infinity) dimension birth death.

So, I have to study the output of ripser.py to adapt to my functions. Hopefully it would be possible. Regards.

[sauln]

The link to the .png is dead now.

The difference is now that the return will be a list of numpy arrays. The index of the list is the dimension and each array is n x 2 with the first column being birth times and the second being deaths.

[tmelorc]

I'm working on the file now. I think it is going well.

The barcode.png is here: https://github.com/tmelorc/ripser

[sauln]

Looks great to start. I think the way infinity bars are handled could be made a little cleaner, but we can play with a few different options there.

[tmelorc]

Good, so please, wait a little bit and I think I can do a good starting point. Maybe tomorrow I could make a PR. I am learning with your code.

[tmelorc]

So, I think I'm done. Lets see how to improve it. Thanks for attention.

[tmelorc]

Does anybody tested the function to plot barcode I sent?

[DeliciousHair]

I have pushed this a little further with #24 just now. Hopefully something gets accepted.