In [1]:

    

from collections import defaultdict
import networkx as nx
#from Exceptions import ValueError
from random import sample
from itertools import combinations
from math import log

from scipy.stats import entropy 
from phoenix.helpers import *
from phoenix.SortedKeyCollections import *

import numpy as np


def jsd2(dist1, dist2, i=None, debug=False): #Jensen-shannon divergence
    import warnings
    warnings.filterwarnings("ignore", category = RuntimeWarning)

    x = []
    y = []
    if len(dist1) < len(dist2):
        #x = np.append(x, [0 for r in range(dif)])
        for key, val in dist2.items():
            x.append(dist1.get(key, 0))
            y.append(val)
            
    elif len(dist1) >= len(dist2): 
        #y = np.append(y, [0 for r in range(dif)])
        #x = np.array(x)
        for key, val in dist1.items():
            x.append(val)
            y.append(dist2.get(key, 0))
            

    x = np.array(x)
    y = np.array(y)
    #print(x,y)
    d1 = x*np.log2(2*x/(x+y))
    d2 = y*np.log2(2*y/(x+y))
    #print(x, y)
    d1[np.isnan(d1)] = 0
    d2[np.isnan(d2)] = 0
    d = 0.5*np.sum(d1+d2)    
    return d

def avg_jsd2(dists1, dists2, i=None):
    ttl_js_div = sum([jsd2(dist1, dists2.get(key, {}), i) 
                      for key, dist1 in dists1.items()])
    
    if i: print(i)
    
    return ttl_js_div/len(dists1)

def decompress_generate(ref_clq_num_dist, ref_clq2clq_dist, node_count, kl_threshold, iteration_cap=100, debug=False):
    """In the greedy step (decision process), we choose the operation
    that most minimizes the kl divergence."""
    nodes = list(range(node_count))
    ### Initialize clqs with a clique of random selected size 
    clqs = []
    clq_size = get_weighted_random_value(ref_clq_num_dist)
    clq_nodes = sample(nodes, clq_size)
    clqs.append(clq_nodes)
    ### Initialize hypergraph's distributions
    clq_num_dist = clique_number_distribution(clqs)
    clq2clq_dist = cliques_x_cliques_distribution(clqs)
    ### Initialize kl divergence scores
    avg_js = 100
    ###
    i = 0
    
    if debug: print("i | clique-number kl | clqXclq intxn size kl")
    while avg_js > kl_threshold and i < iteration_cap:
        if debug:
            if i%10==0: 
                print(i)
        # climb down from arbitrarily high KL value
        min_clq_num_js = 100
        min_clq2clq_js = 100
        min_clq = []
        
        ### Fully Exhaustive Greedy Decision Process (GDP) ###
        for r in range(1, max(ref_clq_num_dist)+1):
            #random_clq_of_size_r = sample(list(combinations(nodes, r)), 1)
            #assert len(random_clq_of_size_r[0]) > 0
            if debug: print(i, r)
            for potential_next_clq in combinations(nodes, r):
                if debug: print(potential_next_clq)
                # update dists to represent one step forward
                new_clq_num_dist = normalize_distribution(clique_number_distribution(clqs+[potential_next_clq]))
                new_clq2clq_dist = normalize_distributions(cliques_x_cliques_distribution(clqs+[potential_next_clq]))
            
                # calculate the kl divergences of next step
                js_1 = jsd2(ref_clq_num_dist, new_clq_num_dist)
                js_2 = avg_jsd2(ref_clq2clq_dist, new_clq2clq_dist)
                
                # if debug: print("jsd:", js_1, "avg_jsd:", js_2)
                    
                ## king of the valley(?)-type of minimization
                #if (kl_1 < min_clq_num_js and
                #    kl_2 < min_clq_x_clq_js):
                    
                if (js_1+js_2 <= min_clq_num_js + min_clq2clq_js):
                    min_clq_num_js = js_1
                    min_clq2clq_js = js_2
                    min_clq = potential_next_clq
                    
                    #if debug: print("jsd:", js_1, "avg_jsd:", js_2)
        ######### End of GDP ########
        
        ### Update list of cliques, reference models, and average KL score
        if min_clq not in clqs:
            clqs.append(list(min_clq))
            yield min_clq
            
            clq_num_dist = normalize_distribution(clique_number_distribution(clqs))
            clq2clq_dist = normalize_distributions(cliques_x_cliques_distribution(clqs))
            
            assert min_clq_num_js == jsd2(ref_clq_num_dist, clq_num_dist)
            assert min_clq2clq_js == avg_jsd2(ref_clq2clq_dist, clq2clq_dist)
            
            avg_js = (min_clq_num_js+min_clq2clq_js)/2

            if debug:
                print(i, "|", min_clq_num_js, "|", min_clq2clq_js)                    
                print()
        i += 1
        
    yield clqs
    

def generate_edges_from_clique(nodes):
    from itertools import combinations
    for c in combinations(nodes, 2):
        yield c


    

In [2]:

    

%matplotlib inline

from networkx.generators import watts_strogatz_graph, barabasi_albert_graph

#graph = nx.Graph([[0,1], [1,2], [2,3], [1,3], [1,4], [2,6], [0,2]]); graph.add_node(5)
graph = nx.read_gml('../demo_graphs/karate_Zachary.gml')
#graph = barabasi_albert_graph(15, 2)

node_count = graph.number_of_nodes() 
clqs = list(nx.find_cliques(graph))
nx.draw_networkx(graph)


    

    




---------------------------------------------------------------------------
NetworkXError                             Traceback (most recent call last)
<ipython-input-2-78c7676b388e> in <module>()
      4 
      5 #graph = nx.Graph([[0,1], [1,2], [2,3], [1,3], [1,4], [2,6], [0,2]]); graph.add_node(5)
----> 6 graph = nx.read_gml('../demo_graphs/karate_Zachary.gml')
      7 #graph = barabasi_albert_graph(15, 2)
      8 

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in read_gml(path, label, destringizer)

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/utils/decorators.pyc in _open_file(func, *args, **kwargs)
    218         # Finally, we call the original function, making sure to close the fobj.
    219         try:
--> 220             result = func(*new_args, **kwargs)
    221         finally:
    222             if close_fobj:

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in read_gml(path, label, destringizer)
    208             yield line
    209 
--> 210     G = parse_gml_lines(filter_lines(path), label, destringizer)
    211     return G
    212 

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in parse_gml_lines(lines, label, destringizer)
    381 
    382     tokens = tokenize()
--> 383     graph = parse_graph()
    384 
    385     directed = graph.pop('directed', False)

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in parse_graph()
    370 
    371     def parse_graph():
--> 372         curr_token, dct = parse_kv(next(tokens))
    373         if curr_token[0] is not None:  # EOF
    374             unexpected(curr_token, 'EOF')

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in parse_kv(curr_token)
    345             if type == 1 or type == 2:  # reals or ints
    346                 value = curr_token[1]
--> 347                 curr_token = next(tokens)
    348             elif type == 3:  # strings
    349                 value = unescape(curr_token[1][1:-1])

/Users/saguinag/ToolSet/anaconda/lib/python2.7/site-packages/networkx/readwrite/gml.pyc in tokenize()
    321                 else:
    322                     raise NetworkXError('cannot tokenize %r at (%d, %d)' %
--> 323                                         (line[pos:], lineno + 1, pos + 1))
    324             lineno += 1
    325         yield (None, None, lineno + 1, 1)  # EOF

NetworkXError: cannot tokenize u'graph' at (3, 1)

In [ ]:

    

clq_num_dist = normalize_distribution(clique_number_distribution(clqs))

clq2clq_dist = normalize_distributions(cliques_x_cliques_distribution(clqs))

d = list(decompress_generate(clq_num_dist, clq2clq_dist, node_count, 0.5, iteration_cap=36, debug=True))

gen_clqs = d[-1]
model1 = normalize_distribution(clique_number_distribution(gen_clqs))
model2 = normalize_distributions(cliques_x_cliques_distribution(gen_clqs))


    

    




i | clique-number kl | clqXclq intxn size kl
0
(0, 1)
(0,)
(1,)
(2,)
(3,)
(4,)
(5,)
(6,)
(7,)
(8,)
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(13,)
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(22,)
(23,)
(24,)
(25,)
(26,)
(27,)
(28,)
(29,)
(30,)
(31,)
(32,)
(33,)
(0, 2)
(0, 1)
(0, 2)
(0, 3)
(0, 4)
(0, 5)
(0, 6)
(0, 7)
(0, 8)
(0, 9)
(0, 10)
(0, 11)
(0, 12)
(0, 13)
(0, 14)
(0, 15)
(0, 16)
(0, 17)
(0, 18)
(0, 19)
(0, 20)
(0, 21)
(0, 22)
(0, 23)
(0, 24)
(0, 25)
(0, 26)
(0, 27)
(0, 28)
(0, 29)
(0, 30)
(0, 31)
(0, 32)
(0, 33)
(1, 2)
(1, 3)
(1, 4)
(1, 5)
(1, 6)
(1, 7)
(1, 8)
(1, 9)
(1, 10)
(1, 11)
(1, 12)
(1, 13)
(1, 14)
(1, 15)
(1, 16)
(1, 17)
(1, 18)
(1, 19)
(1, 20)
(1, 21)
(1, 22)
(1, 23)
(1, 24)
(1, 25)
(1, 26)
(1, 27)
(1, 28)
(1, 29)
(1, 30)
(1, 31)
(1, 32)
(1, 33)
(2, 3)
(2, 4)
(2, 5)
(2, 6)
(2, 7)
(2, 8)
(2, 9)
(2, 10)
(2, 11)
(2, 12)
(2, 13)
(2, 14)
(2, 15)
(2, 16)
(2, 17)
(2, 18)
(2, 19)
(2, 20)
(2, 21)
(2, 22)
(2, 23)
(2, 24)
(2, 25)
(2, 26)
(2, 27)
(2, 28)
(2, 29)
(2, 30)
(2, 31)
(2, 32)
(2, 33)
(3, 4)
(3, 5)
(3, 6)
(3, 7)
(3, 8)
(3, 9)
(3, 10)
(3, 11)
(3, 12)
(3, 13)
(3, 14)
(3, 15)
(3, 16)
(3, 17)
(3, 18)
(3, 19)
(3, 20)
(3, 21)
(3, 22)
(3, 23)
(3, 24)
(3, 25)
(3, 26)
(3, 27)
(3, 28)
(3, 29)
(3, 30)
(3, 31)
(3, 32)
(3, 33)
(4, 5)
(4, 6)
(4, 7)
(4, 8)
(4, 9)
(4, 10)
(4, 11)
(4, 12)
(4, 13)
(4, 14)
(4, 15)
(4, 16)
(4, 17)
(4, 18)
(4, 19)
(4, 20)
(4, 21)
(4, 22)
(4, 23)
(4, 24)
(4, 25)
(4, 26)
(4, 27)
(4, 28)
(4, 29)
(4, 30)
(4, 31)
(4, 32)
(4, 33)
(5, 6)
(5, 7)
(5, 8)
(5, 9)
(5, 10)
(5, 11)
(5, 12)
(5, 13)
(5, 14)
(5, 15)
(5, 16)
(5, 17)
(5, 18)
(5, 19)
(5, 20)
(5, 21)
(5, 22)
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(5, 24)
(5, 25)
(5, 26)
(5, 27)
(5, 28)
(5, 29)
(5, 30)
(5, 31)
(5, 32)
(5, 33)
(6, 7)
(6, 8)
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(6, 11)
(6, 12)
(6, 13)
(6, 14)
(6, 15)
(6, 16)
(6, 17)
(6, 18)
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(6, 24)
(6, 25)
(6, 26)
(6, 27)
(6, 28)
(6, 29)
(6, 30)
(6, 31)
(6, 32)
(6, 33)
(7, 8)
(7, 9)
(7, 10)
(7, 11)
(7, 12)
(7, 13)
(7, 14)
(7, 15)
(7, 16)
(7, 17)
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(7, 24)
(7, 25)
(7, 26)
(7, 27)
(7, 28)
(7, 29)
(7, 30)
(7, 31)
(7, 32)
(7, 33)
(8, 9)
(8, 10)
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(8, 13)
(8, 14)
(8, 15)
(8, 16)
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(8, 18)
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(8, 27)
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(8, 30)
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(8, 32)
(8, 33)
(9, 10)
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(9, 13)
(9, 14)
(9, 15)
(9, 16)
(9, 17)
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(9, 19)
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(9, 25)
(9, 26)
(9, 27)
(9, 28)
(9, 29)
(9, 30)
(9, 31)
(9, 32)
(9, 33)
(10, 11)
(10, 12)
(10, 13)
(10, 14)
(10, 15)
(10, 16)
(10, 17)
(10, 18)
(10, 19)
(10, 20)
(10, 21)
(10, 22)
(10, 23)
(10, 24)
(10, 25)
(10, 26)
(10, 27)
(10, 28)
(10, 29)
(10, 30)
(10, 31)
(10, 32)
(10, 33)
(11, 12)
(11, 13)
(11, 14)
(11, 15)
(11, 16)
(11, 17)
(11, 18)
(11, 19)
(11, 20)
(11, 21)
(11, 22)
(11, 23)
(11, 24)
(11, 25)
(11, 26)
(11, 27)
(11, 28)
(11, 29)
(11, 30)
(11, 31)
(11, 32)
(11, 33)
(12, 13)
(12, 14)
(12, 15)
(12, 16)
(12, 17)
(12, 18)
(12, 19)
(12, 20)
(12, 21)
(12, 22)
(12, 23)
(12, 24)
(12, 25)
(12, 26)
(12, 27)
(12, 28)
(12, 29)
(12, 30)
(12, 31)
(12, 32)
(12, 33)
(13, 14)
(13, 15)
(13, 16)
(13, 17)
(13, 18)
(13, 19)
(13, 20)
(13, 21)
(13, 22)
(13, 23)
(13, 24)
(13, 25)
(13, 26)
(13, 27)
(13, 28)
(13, 29)
(13, 30)
(13, 31)
(13, 32)
(13, 33)
(14, 15)
(14, 16)
(14, 17)
(14, 18)
(14, 19)
(14, 20)
(14, 21)
(14, 22)
(14, 23)
(14, 24)
(14, 25)
(14, 26)
(14, 27)
(14, 28)
(14, 29)
(14, 30)
(14, 31)
(14, 32)
(14, 33)
(15, 16)
(15, 17)
(15, 18)
(15, 19)
(15, 20)
(15, 21)
(15, 22)
(15, 23)
(15, 24)
(15, 25)
(15, 26)
(15, 27)
(15, 28)
(15, 29)
(15, 30)
(15, 31)
(15, 32)
(15, 33)
(16, 17)
(16, 18)
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(16, 20)
(16, 21)
(16, 22)
(16, 23)
(16, 24)
(16, 25)
(16, 26)
(16, 27)
(16, 28)
(16, 29)
(16, 30)
(16, 31)
(16, 32)
(16, 33)
(17, 18)
(17, 19)
(17, 20)
(17, 21)
(17, 22)
(17, 23)
(17, 24)
(17, 25)
(17, 26)
(17, 27)
(17, 28)
(17, 29)
(17, 30)
(17, 31)
(17, 32)
(17, 33)
(18, 19)
(18, 20)
(18, 21)
(18, 22)
(18, 23)
(18, 24)
(18, 25)
(18, 26)
(18, 27)
(18, 28)
(18, 29)
(18, 30)
(18, 31)
(18, 32)
(18, 33)
(19, 20)
(19, 21)
(19, 22)
(19, 23)
(19, 24)
(19, 25)
(19, 26)
(19, 27)
(19, 28)
(19, 29)
(19, 30)
(19, 31)
(19, 32)
(19, 33)
(20, 21)
(20, 22)
(20, 23)
(20, 24)
(20, 25)
(20, 26)
(20, 27)
(20, 28)
(20, 29)
(20, 30)
(20, 31)
(20, 32)
(20, 33)
(21, 22)
(21, 23)
(21, 24)
(21, 25)
(21, 26)
(21, 27)
(21, 28)
(21, 29)
(21, 30)
(21, 31)
(21, 32)
(21, 33)
(22, 23)
(22, 24)
(22, 25)
(22, 26)
(22, 27)
(22, 28)
(22, 29)
(22, 30)
(22, 31)
(22, 32)
(22, 33)
(23, 24)
(23, 25)
(23, 26)
(23, 27)
(23, 28)
(23, 29)
(23, 30)
(23, 31)
(23, 32)
(23, 33)
(24, 25)
(24, 26)
(24, 27)
(24, 28)
(24, 29)
(24, 30)
(24, 31)
(24, 32)
(24, 33)
(25, 26)
(25, 27)
(25, 28)
(25, 29)
(25, 30)
(25, 31)
(25, 32)
(25, 33)
(26, 27)
(26, 28)
(26, 29)
(26, 30)
(26, 31)
(26, 32)
(26, 33)
(27, 28)
(27, 29)
(27, 30)
(27, 31)
(27, 32)
(27, 33)
(28, 29)
(28, 30)
(28, 31)
(28, 32)
(28, 33)
(29, 30)
(29, 31)
(29, 32)
(29, 33)
(30, 31)
(30, 32)
(30, 33)
(31, 32)
(31, 33)
(32, 33)
(0, 3)
(0, 1, 2)
(0, 1, 3)
(0, 1, 4)
(0, 1, 5)
(0, 1, 6)
(0, 1, 7)
(0, 1, 8)
(0, 1, 9)
(0, 1, 10)
(0, 1, 11)
(0, 1, 12)
(0, 1, 13)
(0, 1, 14)
(0, 1, 15)
(0, 1, 16)
(0, 1, 17)
(0, 1, 18)
(0, 1, 19)
(0, 1, 20)
(0, 1, 21)
(0, 1, 22)
(0, 1, 23)
(0, 1, 24)
(0, 1, 25)
(0, 1, 26)
(0, 1, 27)
(0, 1, 28)
(0, 1, 29)
(0, 1, 30)
(0, 1, 31)
(0, 1, 32)
(0, 1, 33)
(0, 2, 3)
(0, 2, 4)
(0, 2, 5)
(0, 2, 6)
(0, 2, 7)
(0, 2, 8)
(0, 2, 9)
(0, 2, 10)
(0, 2, 11)
(0, 2, 12)
(0, 2, 13)
(0, 2, 14)
(0, 2, 15)
(0, 2, 16)
(0, 2, 17)
(0, 2, 18)
(0, 2, 19)
(0, 2, 20)
(0, 2, 21)
(0, 2, 22)
(0, 2, 23)
(0, 2, 24)
(0, 2, 25)
(0, 2, 26)
(0, 2, 27)
(0, 2, 28)
(0, 2, 29)
(0, 2, 30)
(0, 2, 31)
(0, 2, 32)
(0, 2, 33)
(0, 3, 4)
(0, 3, 5)
(0, 3, 6)
(0, 3, 7)
(0, 3, 8)
(0, 3, 9)
(0, 3, 10)
(0, 3, 11)
(0, 3, 12)
(0, 3, 13)
(0, 3, 14)
(0, 3, 15)
(0, 3, 16)
(0, 3, 17)
(0, 3, 18)
(0, 3, 19)
(0, 3, 20)
(0, 3, 21)
(0, 3, 22)
(0, 3, 23)
(0, 3, 24)
(0, 3, 25)
(0, 3, 26)
(0, 3, 27)
(0, 3, 28)
(0, 3, 29)
(0, 3, 30)
(0, 3, 31)
(0, 3, 32)
(0, 3, 33)
(0, 4, 5)
(0, 4, 6)
(0, 4, 7)
(0, 4, 8)
(0, 4, 9)
(0, 4, 10)
(0, 4, 11)
(0, 4, 12)
(0, 4, 13)
(0, 4, 14)
(0, 4, 15)
(0, 4, 16)
(0, 4, 17)
(0, 4, 18)
(0, 4, 19)
(0, 4, 20)
(0, 4, 21)
(0, 4, 22)
(0, 4, 23)
(0, 4, 24)
(0, 4, 25)
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(1, 7, 12, 24)
(1, 7, 12, 25)
(1, 7, 12, 26)
(1, 7, 12, 27)

In [ ]:

    

gen_edges = [e for c in gen_clqs for e in generate_edges_from_clique(c)]

gen_graph = nx.Graph(gen_edges)

for r in range(node_count):
    gen_graph.add_node(r)

nx.draw_networkx(gen_graph)


    

In [ ]:

    

from scipy.stats import entropy 

ref_dist = {(2, 2): Counter({0: 0.9, 1: 0.1}),
 (2, 3): Counter({0: 0.8, 1: 0.2}),
 (2, 4): Counter({0: 0.7, 1: 0.3})}

# this dist is perfect as each internal distribution 
# is of the same key size (feature(?), length)
good_dist = {(2, 2): Counter({0: 0.5, 1: 0.5}),
 (2, 3): Counter({0: 0.5, 1: 0.5}),
 (2, 4): Counter({0: 0.9, 1: 0.1})}

# this dist breaks bc one internal dist is of diff. size
# to its respective internal reference dist.
bad_dist = {(2, 2): Counter({0: 0.7, 1: 0.3}),
            (2, 3): Counter({0: 0.1, 1: 0.5, 2:0.4}), 
            (2, 4): Counter({0:1.0})
           } # breaks here

#print(avg_kl_div(ref_dist, good_dist))

print(avg_jsd(bad_dist, ref_dist))