In [3]:
import numpy as np
import networkx as nx
from Queue import Queue
from threading import Thread
from threading import current_thread
from sklearn.manifold import MDS
from sklearn.metrics.pairwise import euclidean_distances
def distances(X, d):
return euclidean_distances(X[:,:d])
def stress(distances, Ds, tri):
return np.sqrt(np.sum((distances[tri] - np.sqrt(Ds[tri])) ** 2) / np.sum(Ds[tri]))
def classic_mds(Ds):
#centering matrix
n = len(Ds)
C = np.identity(n) - np.ones((n, n)) / n
#double centered similarity matrix
K = - 0.5 * np.dot(np.dot(C, Ds), C)
#eigen decompose K
l, U = np.linalg.eigh(K)
mask = l > 0
l = l[mask]
U = U[:, mask]
##sort eigenvalues (and eigenvectors) into ascending order
idx = l.argsort()[::-1]
l = l[idx]
U = U[:,idx]
# if k < 1:
# print "attempting to preserve 95% of variance"
# total = sum(l)
# k = 0
# var = sum(l[:k]) / total
# while var < variance_preserved:
# k += 1
# var = sum(l[:k]) / total
# print "embedding to {} dimensions".format(k)
#position matrix
X = np.dot(U, np.diag(l ** 0.5))
#upper triangle
tri = np.triu_indices(n=len(Ds), k = 1, m=len(Ds))
#determine the k that minimised stress
stresses = np.array([stress(distances(X, d), Ds, tri) for d in range(1, min(50, U.shape[1]))])
k = stresses.argmin() + 1
print "embedding to {} dimensions with stress {}".format(k, stresses[k-1])
return X[:,:k], stresses
##function to generate benchmark graph
def benchmark_hierarchical_graph(edge_path, c1_path, c2_path):
#construct graph from edge list
G = nx.read_edgelist(edge_path)
#create dictionarys of attributes
c1 = read_attributes(c1_path)
c2 = read_attributes(c2_path)
#set attributes of G
nx.set_node_attributes(G, 'firstlevelcommunity', c1)
nx.set_node_attributes(G, 'secondlevelcommunity', c2)
#return graph
return G
##function to generate benchmark graph
def benchmark_graph(edge_path, c_path):
#construct graph from edge list
G = nx.read_edgelist(edge_path)
#create dictionarys of attributes
c = read_attributes(c_path)
#set attributes of G
nx.set_node_attributes(G, 'firstlevelcommunity', c)
#return graph
return G
##function to read in attributes from file and return a dictionary
def read_attributes(filepath):
#initialise dictionary
d = {}
#open file
with open(filepath) as f:
#iterate over lines in f
for l in f:
#separate into key and value
k, v = l.split()
#add to dictionary
d[k] = v
#return
return d
def filter_nodes_with_no_embedding(G, D):
for n in G.nodes():
if n not in D.keys():
print "{} not in D, removing it from the network".format(n)
G.remove_node(n)
##save embedding to graph
def set_embedding(G, X):
embedding = {k: v for k, v in zip(G.nodes(), X)}
nx.set_node_attributes(G, "embedding", embedding)
## get embedding
def get_embedding(G):
return np.array([v for k, v in nx.get_node_attributes(G, "embedding").items()])
def main_hierarchical(network, first_level, second_level, filename):
#import graph from file
G = benchmark_hierarchical_graph(network, first_level, second_level)
#only embed largest subgraph
H = max(nx.connected_component_subgraphs(G), key=len)
#embed into X
D = nx.floyd_warshall(H)
#remove nodes from H with no embedding
filter_nodes_with_no_embedding(H, D)
##to array
Ds = np.array([[D[i][j] ** 2 for j in D.keys()] for i in D.keys()])
#mds
X, stresses = classic_mds(Ds)
#save embedding to nodes of G
set_embedding(H, X)
#write gml file
nx.write_gpickle(H, filename)
return X, Ds, stresses
def main_binary(network, first_level, filename):
#import graph from file
G = benchmark_graph(network, first_level)
#only embed largest subgraph
H = max(nx.connected_component_subgraphs(G), key=len)
#embed into X
D = nx.floyd_warshall(H)
#remove nodes from H with no embedding
filter_nodes_with_no_embedding(H, D)
##to array
Ds = np.array([[D[i][j] ** 2 for j in D.keys()] for i in D.keys()])
#mds
X, stresses = custom_mds(Ds)
# print "embedding to {} dimensions".format(k)
# mds = MDS(n_components = k, dissimilarity = "precomputed", n_jobs=-1, max_iter=10000)
# X = mds.fit_transform(D)
#save embedding to nodes of G
set_embedding(H, X)
#write gml file
nx.write_gpickle(H, filename)
return X, Ds, stresses
def main(txt, filename, D=None, delimiter="\t"):
#import graph from file
G = nx.read_edgelist(txt, delimiter=delimiter)
#only embed largest subgraph
H = max(nx.connected_component_subgraphs(G), key=len)
#embed into X
if D == None:
#if no precomuped distance matrix then use floyd
D = nx.floyd_warshall(H)
#remove nodes from H with no embedding
filter_nodes_with_no_embedding(H, D)
##array of squared shortest path distances
Ds = np.array([[D[i][j] ** 2 for j in D.keys()] for i in D.keys()])
print "computed distance matrix"
# #validation testing for best dimension
# stresses = np.array([])
# for k in range(min_k, max_k + 1):
# mds = MDS(n_components = k, dissimilarity = "precomputed", n_jobs=-1, max_iter=10000)
# mds.fit(D)
# stress = mds.stress_
# X = mds.embedding_
# print stress
# stresses = np.append(stresses, stress)
# if len(stresses) > 1:
# gradient = np.gradient(stresses, 5)[-1]
# print "k={}, stress={}, gradient={}".format(k, stress, gradient)
# if np.abs(gradient) < eps:
# print "BREAK"
# break
# mds = MDS(n_components = k, dissimilarity = "precomputed", n_jobs=-1, max_iter=10000)
# mds.fit(D)
# stress = mds.stress_
# X = mds.embedding_
X, stresses = classic_mds(Ds)
#save embedding to nodes of G
set_embedding(H, X)
#write gml file
nx.write_gpickle(H, filename)
return X, Ds, stresses
In [3]:
X, D, stresses = main("Uetz_screen.txt", "embedded_yeast_uetz.gpickle", delimiter="\t")
computed distance matrix
embedding to 10 dimensions with stress 0.0827381995922
In [4]:
X, D, stresses = main_hierarchical("benchmarks/network.dat", "benchmarks/community_first_level.dat",
"benchmarks/community_second_level.dat", "benchmarks/hierarchical_benchmark.gpickle")
embedding to 32 dimensions with stress 0.164205746756
In [ ]:
stresses
In [34]:
G = nx.read_gpickle("benchmarks/hierarchical_benchmark.gpickle")
In [35]:
X = get_embedding(G)
In [36]:
X.shape
Out[36]:
(512, 39)
In [37]:
G.nodes(data=True)
Out[37]:
[(u'344',
{'embedding': array([ 3.49051661e-01, -3.19418447e-01, 1.09063765e-01,
-1.16078364e-01, 2.09129704e-01, -1.71228473e-02,
4.34386387e-02, -7.15931860e-02, 2.00001430e-01,
-3.23126125e-01, 8.64329535e-02, -2.42280602e-01,
1.37117559e-01, -1.93248824e-02, 7.07096772e-02,
-1.50439014e-01, -7.93745584e-03, 5.94446806e-02,
-1.27927115e-01, 1.47864264e-01, -1.66557114e-01,
2.62281413e-01, -2.53536794e-02, 2.07000031e-04,
-4.86950644e-02, 2.32102072e-01, -1.95973752e-01,
1.02894272e-01, -9.60744416e-02, 8.14593478e-02,
-8.62704274e-02, 3.50756428e-03, -3.28906988e-02,
-1.89287610e-01, 2.37095125e-01, -2.35965601e-01,
1.02799014e-01, -2.29461923e-01, -2.39295936e-02]),
'firstlevelcommunity': '11',
'secondlevelcommunity': '3'}),
(u'345',
{'embedding': array([ 0.29818963, -0.36094679, 0.13751338, -0.10214628, 0.09621445,
0.05197943, 0.1053855 , -0.19393805, 0.09629912, -0.04079251,
-0.00387543, -0.21007438, 0.10970806, -0.06775092, 0.16233489,
0.33160612, 0.134439 , 0.03609869, -0.32007996, -0.07635691,
-0.08414982, 0.25167537, 0.26508365, -0.02585255, 0.08048947,
0.13200637, -0.09316784, -0.10115442, 0.24345383, -0.30985711,
-0.06292389, -0.18642189, -0.04322954, -0.02078861, -0.06089916,
0.22003393, 0.12788929, -0.1738507 , -0.18979306]),
'firstlevelcommunity': '11',
'secondlevelcommunity': '3'}),
(u'346',
{'embedding': array([ 3.16830769e-01, -7.06414915e-02, 3.57237174e-01,
2.29470023e-01, -3.35646088e-01, -9.66574242e-02,
6.50195615e-02, 8.20798244e-02, 2.05868868e-01,
3.40714835e-02, 3.17506578e-01, 1.55588097e-01,
2.29242160e-01, 1.18689445e-01, 5.03697953e-02,
-5.28456381e-02, -2.19015192e-02, 4.21066660e-02,
1.16771963e-01, -1.49685696e-01, 2.70364907e-04,
2.33853326e-01, -1.10324261e-01, 8.64870646e-02,
-3.60350483e-02, 2.13356689e-02, -1.51185189e-01,
-1.78488602e-01, -2.08292440e-01, -5.81183551e-02,
-5.90766054e-02, -4.45561773e-02, 1.31151729e-01,
2.18727429e-01, -4.22458900e-02, 1.25812629e-01,
-2.29035850e-02, -2.03254839e-03, -9.82439119e-02]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'347',
{'embedding': array([ 0.28532025, -0.19794634, 0.13958798, 0.21861442, 0.1064123 ,
-0.1086652 , 0.25717137, -0.05848093, 0.11283661, -0.03299402,
-0.37535256, 0.00579036, 0.04193845, -0.18126621, 0.00696302,
0.01413577, 0.35549308, -0.0533577 , 0.16455627, 0.26335966,
0.13622005, -0.03040382, 0.05071156, -0.26113707, 0.09178651,
-0.2056359 , 0.01220097, 0.00938219, -0.0376328 , -0.00472201,
-0.08833982, -0.15058817, 0.09174372, 0.01484142, 0.13178322,
-0.18080605, 0.05637908, 0.00289633, 0.00977426]),
'firstlevelcommunity': '10',
'secondlevelcommunity': '3'}),
(u'340',
{'embedding': array([ 0.34196391, -0.03721214, 0.26308185, -0.03331104, -0.38387975,
-0.24767901, 0.05953375, -0.07070351, -0.10696257, -0.09093811,
0.22270751, 0.04227748, 0.03840132, 0.063881 , -0.24275479,
0.04624779, -0.33623728, -0.16784856, -0.07704269, 0.24151277,
0.18111338, -0.18235302, 0.14571299, 0.03043082, -0.0559344 ,
0.05598172, 0.11084874, 0.15171644, -0.01069494, 0.33635894,
-0.10354625, 0.00394981, 0.02353827, -0.12798257, -0.11812958,
-0.06487234, 0.10625552, -0.27085729, 0.1649545 ]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'341',
{'embedding': array([ 0.26080591, -0.16613206, 0.27166635, 0.1546751 , 0.25015774,
-0.01893892, 0.13307864, -0.12056191, 0.13506881, 0.22808254,
-0.14555977, -0.09695786, -0.07068516, -0.17908314, -0.25499403,
0.10148342, 0.01739161, 0.15345183, 0.05669683, -0.16197466,
-0.09263437, 0.07800941, 0.03442027, -0.13304297, -0.16471147,
0.1003682 , -0.00961841, -0.01488739, -0.19085726, -0.03257603,
-0.10415172, 0.19926672, 0.32061629, -0.21346372, 0.07870165,
0.31599896, -0.12901217, 0.01989376, -0.0067197 ]),
'firstlevelcommunity': '10',
'secondlevelcommunity': '3'}),
(u'342',
{'embedding': array([ 0.19592246, -0.07692668, 0.42425171, -0.14499186, -0.14907685,
-0.4072018 , 0.14842199, 0.02961773, 0.02107018, 0.20059848,
0.01977353, 0.11913435, 0.26778097, 0.08083776, -0.17809967,
0.04121814, -0.11692168, -0.16978904, 0.02914408, -0.04235114,
0.17788486, -0.15682884, 0.20048263, 0.21828695, -0.05067866,
-0.126847 , 0.12925337, 0.08792752, 0.1286842 , 0.11673329,
0.1329202 , 0.08288348, 0.30542851, 0.17161865, -0.09302483,
0.10646655, 0.0745298 , -0.0533275 , -0.08122306]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'343',
{'embedding': array([ 0.36494726, -0.07936712, 0.29408004, -0.23981575, -0.3792642 ,
-0.15014912, 0.29166992, 0.11398422, -0.11265487, -0.08307458,
0.02483888, 0.08598883, -0.04892522, -0.16734597, -0.21667047,
0.02036138, -0.09101604, -0.12535777, 0.31823373, -0.00764098,
-0.10239306, 0.08483746, 0.07326039, -0.10174343, 0.18717421,
0.06403682, -0.18749968, 0.10343105, -0.17775568, -0.11479738,
0.05251677, -0.04347868, -0.25043165, 0.03051657, 0.06828778,
-0.10183483, -0.11405592, -0.17197704, -0.1037967 ]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'348',
{'embedding': array([ 0.27891268, -0.12761302, 0.24071537, 0.13966997, 0.25414745,
0.22423458, 0.12022204, -0.12277819, 0.18639413, 0.39981819,
-0.13945545, -0.28537458, -0.09025745, -0.13499628, 0.01521542,
-0.21093158, -0.29007089, -0.13593111, 0.07155978, -0.01773126,
0.15040156, 0.09049192, 0.02290281, 0.0705628 , 0.06354535,
-0.04906335, 0.17386882, -0.12961896, -0.22090305, 0.06193459,
0.15063519, -0.06678692, 0.01947141, -0.19782859, 0.05435377,
0.1609649 , 0.01097388, 0.10968014, 0.02815747]),
'firstlevelcommunity': '10',
'secondlevelcommunity': '3'}),
(u'349',
{'embedding': array([ 0.22257937, -0.1754796 , 0.31140969, -0.32541311, -0.08101421,
0.19700912, -0.13936496, 0.22032871, 0.05705019, -0.08219882,
-0.05658281, 0.16951991, -0.06563739, 0.21928421, -0.10283364,
0.05625585, -0.10037746, 0.36853454, 0.10857624, -0.01904001,
0.21615293, 0.10515444, 0.13006591, -0.08400911, -0.15141221,
0.20437626, 0.1190438 , -0.18048683, -0.16025982, -0.00400912,
-0.08657994, 0.09125469, -0.05785377, 0.16370207, 0.12212425,
0.24120849, 0.02720362, 0.05899525, 0.04579412]),
'firstlevelcommunity': '12',
'secondlevelcommunity': '3'}),
(u'298',
{'embedding': array([-0.2039211 , 0.34638822, 0.21381569, 0.11974408, -0.11749444,
0.01623875, 0.21800685, 0.1209619 , -0.01924405, -0.07206845,
-0.53111705, -0.07555325, 0.1026602 , -0.08683242, -0.30343273,
-0.32367983, -0.07550718, 0.15291627, -0.01396879, -0.0482572 ,
-0.12463609, 0.16715863, 0.18866266, 0.15309051, -0.03437989,
-0.15771456, -0.03655288, -0.08894549, -0.20151219, 0.19828155,
-0.13110964, 0.11864031, 0.10033721, -0.10188687, -0.00618412,
-0.00878205, -0.05782167, -0.02228704, 0.06185079]),
'firstlevelcommunity': '11',
'secondlevelcommunity': '3'}),
(u'299',
{'embedding': array([ 0.3818633 , -0.08867935, 0.20112112, -0.23733174, 0.1861926 ,
-0.17326332, 0.11879116, -0.2945351 , 0.03680789, -0.0741051 ,
0.16539571, -0.03124884, -0.02603025, -0.08851397, 0.3364013 ,
0.4019559 , -0.1396333 , -0.29385621, 0.05953245, 0.06592903,
-0.01821353, 0.04621572, 0.23590654, 0.09352492, -0.03077433,
0.05715226, -0.22429279, 0.03430363, -0.13003783, -0.07678714,
-0.19249773, 0.09864759, 0.03742902, -0.14923917, -0.04945421,
0.08973502, -0.10884111, -0.08705774, -0.07332696]),
'firstlevelcommunity': '11',
'secondlevelcommunity': '3'}),
(u'296',
{'embedding': array([ 0.31667806, -0.15876498, 0.25629883, -0.00980376, 0.1706098 ,
-0.10047575, 0.13555955, -0.2568816 , 0.0317436 , -0.27554342,
0.10206442, 0.28760203, -0.02094384, 0.19587072, 0.26291827,
0.11950827, -0.06045654, 0.2900732 , -0.11578424, -0.00711719,
-0.20290921, 0.16066085, -0.02427946, 0.15914148, 0.04884466,
-0.09125777, -0.12904442, 0.17507911, -0.00521135, 0.07928987,
-0.05051648, 0.08252682, -0.22289656, -0.19552203, -0.13340619,
0.17353619, 0.20479748, 0.01341715, -0.02013855]),
'firstlevelcommunity': '10',
'secondlevelcommunity': '3'}),
(u'297',
{'embedding': array([ 0.25539845, -0.1668382 , 0.38013756, 0.15536991, -0.02549769,
-0.18233194, -0.24293535, -0.0818743 , 0.07612977, 0.25726897,
-0.09493295, 0.00752488, -0.25656903, -0.05125913, -0.05729154,
0.13565727, -0.19318582, 0.35648243, 0.03615464, -0.16949298,
-0.0300282 , -0.16395874, 0.08482002, -0.23285546, 0.27386953,
0.0442651 , 0.30001475, -0.26061885, 0.17005755, -0.16044275,
0.17270832, 0.09853888, 0.16043944, -0.31199521, -0.03683272,
0.13257937, -0.12417719, 0.03609197, -0.02342987]),
'firstlevelcommunity': '12',
'secondlevelcommunity': '3'}),
(u'294',
{'embedding': array([ 0.38654877, -0.13021307, 0.16020634, -0.03145993, 0.05433921,
0.04809084, -0.23176954, 0.23812056, 0.14218778, -0.11840643,
0.04125137, 0.21537264, -0.12451443, 0.22974825, 0.04979999,
-0.22792962, -0.0333217 , -0.20224092, 0.05527579, 0.09183279,
0.04996795, -0.18144198, 0.19915747, 0.08082846, 0.250003 ,
-0.13680595, -0.07840376, 0.21586123, -0.01976052, 0.10910235,
-0.3406877 , 0.04214262, -0.06137334, -0.10859126, 0.10959018,
0.07506558, -0.05057474, -0.09920623, 0.02409841]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'295',
{'embedding': array([ 0.43406336, -0.20948072, 0.02347318, 0.08721503, -0.22513493,
-0.07776719, -0.03923205, 0.16639108, 0.12199975, -0.0275946 ,
0.09546761, 0.31476581, 0.20282619, -0.17948351, -0.2274246 ,
0.07153101, -0.0060686 , 0.00486315, -0.10865047, 0.09505772,
-0.32338238, 0.10312605, -0.13903388, 0.32084928, -0.256953 ,
-0.11863534, -0.17441212, -0.1572743 , -0.08205196, 0.02560718,
0.02504713, -0.18089311, -0.09053479, -0.12612643, -0.11037528,
0.11469911, -0.07804661, 0.32384255, 0.03585952]),
'firstlevelcommunity': '9',
'secondlevelcommunity': '3'}),
(u'292',
{'embedding': array([ 0.21581511, -0.29592151, 0.27446039, 0.13951611, -0.16901983,
-0.13727182, -0.07021935, 0.05746342, -0.06359538, 0.16258959,
0.30688061, 0.12509773, 0.30670117, 0.04848099, -0.12708315,
0.11935013, -0.10436718, -0.03165357, -0.00818711, -0.05545515,
0.18103414, -0.03141902, 0.08279363, 0.08263288, -0.15743738,
-0.45466906, 0.20946162, 0.10938484, 0.10969157, -0.3188407 ,
0.00259286, 0.08727834, 0.18552316, -0.27343152, 0.08090788,
-0.17967889, 0.04881993, 0.03412301, 0.14523525]),
'firstlevelcommunity': '12',
'secondlevelcommunity': '3'}),
(u'293',
{'embedding': array([ 0.29238756, -0.20870371, 0.23352474, -0.13293596, -0.061373 ,
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In [ ]:
Content source: DavidMcDonald1993/ghsom
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