def plot_powerlaw_combined(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
plot_pdf(data, ax=ax1, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax1, linestyle=':', color='g')
p = fit.power_law.pdf()
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax1, linestyle='--', color='g')
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontsize=14)
ax1.set_ylabel(r"$p(X)$")# (10^n)")
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax2, linestyle='--', color='r')
fit.plot_pdf(ax=ax2, color='b', linewidth=2)
ax2.set_ylim(ax1.get_ylim())
ax2.set_yticks(ax2.get_yticks()[::2])
ax2.set_xlim(ax1.get_xlim())
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontsize=14)
ax2.set_xlabel(units)
def plot_basics(data, data_inst, fig, units):
'''
This function is the main plotting function. Adapted from Newman's powerlaw package.
'''
import pylab
pylab.rcParams['xtick.major.pad'] = '8'
pylab.rcParams['ytick.major.pad'] = '8'
pylab.rcParams['font.sans-serif'] = 'Arial'
from matplotlib import rc
rc('font', family='sans-serif')
rc('font', size=10.0)
rc('text', usetex=False)
from matplotlib.font_manager import FontProperties
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(12.0)
panel_label_font.set_family("sans-serif")
n_data = 1
n_graphs = 4
from powerlaw import plot_pdf, Fit, pdf
ax1 = fig.add_subplot(n_graphs, n_data, data_inst)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5, label='data')
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2, label='PDF')
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
plt.legend(loc='bestloc')
ax2 = fig.add_subplot(n_graphs, n_data, n_data + data_inst, sharex=ax1)
plot_pdf(data[data > 0], ax=ax2, color='b', linewidth=2, label='PDF')
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g', label='w/o xmin')
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True, xmin=3)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g', label='w xmin')
from pylab import setp
setp(ax2.get_xticklabels(), visible=False)
plt.legend(loc='bestloc')
ax3 = fig.add_subplot(n_graphs, n_data,
n_data * 2 + data_inst) #, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g', label='powerlaw')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r', label='exp')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
plt.legend(loc='bestloc')
ax3.set_xlabel(units)
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
from pylab import setp
setp( ax2.get_xticklabels(), visible=False)
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)")# (10^n)")
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
if data_inst==1:
ax3.annotate("C", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
ax3.set_xlabel(units)
def draw_plots(self):
from matplotlib import pyplot as plt
fig = plt.figure(figsize=(4, 4))
ax = fig.add_subplot(111)
data = self.on_data()
from powerlaw import Fit
experimental = Fit(data, xmin=min(data))
experimental.plot_ccdf(ax=ax)
plt.show()
def main():
""" Computes various graph statistics """
#Load subgraph here
#G = nx.read_adjlist("data/sub_graph_networkx_graph")
#G = G.to_directed()
#Load graph
#name = 'data/internal-references-pdftotext.json.gz'
name = '../../data/internal-references-pdftotext.json.gz'
q = ia.loaddata(fname=name)
G = ia.makegraph(q)
#basic stats
N_nodes, N_edges = G.number_of_nodes(), G.number_of_edges()
#Degree
t1 = time.time()
in_deg = [d for n, d in G.in_degree()]
out_deg = [d for n, d in G.out_degree()]
np.savetxt('../../data/in_degree.txt', in_deg)
np.savetxt('../../data/out_degree.txt', out_deg)
mean_k = 2 * np.mean(in_deg)
t2 = time.time()
print('degree took ' + str((t2 - t1) / 60.0) + ' mins')
#Find powerlaw fits
fit_in, fit_out = Fit(in_deg, xmin=0), Fit(out_deg, xmin=0)
alpha_in = np.round(fit_in.power_law.alpha, 2)
xmin_in = np.round(fit_in.power_law.xmin, 2)
alpha_out = np.round(fit_out.power_law.alpha, 2)
xmin_out = np.round(fit_out.power_law.xmin, 2)
print('For power law fitting in-degree: x_min = ' + str(xmin_in))
print('For power law fitting out-degree: x_min = ' + str(xmin_out) + '\n')
#Clustering coeff
t1 = time.time()
cs = list(nx.clustering(G).values())
np.savetxt('../../data/clustering_c.txt', cs)
mean_C = np.round(np.mean(cs), 2)
t2 = time.time()
print('cluster coeff took ' + str((t2 - t1) / 60.0) + ' mins')
#Size-biggest
t1 = time.time()
comps = nx.weakly_connected_components(G)
biggest = max(comps, key=len)
G_cc = G.subgraph(biggest)
size_WCC = 1.0 * G_cc.number_of_nodes()
fraction_WCC = np.round(size_WCC / N_nodes, 2)
#Num isolated
num_isolated = 0
comps = nx.weakly_connected_components(G)
for cc in comps:
if len(cc) == 1:
num_isolated += 1
fraction_isolated = np.round((1.0 * num_isolated) / N_nodes, 2)
t2 = time.time()
print('cluster size dist ' + str((t2 - t1) / 60.0) + ' mins')
#results
stats = [
N_nodes, N_edges, mean_k, alpha_in, alpha_out, mean_C, fraction_WCC,
fraction_isolated
]
print(stats)
#Stuff for tables
OpenArXiv = ['openArXiv']
OpenArXiv.extend(map(lambda n: '{:.3f}'.format(n), stats))
# Automatically make table!
datenow = str(datetime.now()).split()[0]
with open('graph-stats-{}.tex'.format(datenow), 'w') as fout:
fout.write(make_latex_table([Header, OpenArXiv, WoS, CiteSeer, ArXiv]))
#### MAKE FIGURE
tick_size = 20
axis_size = 30
label_size = 28
label_y_position = 1.10
inset_size = 18
plt.figure(figsize=(20, 5))
#Histogram in-degree
n_bins = 30
ax1 = plt.subplot(131)
plt.hist(in_deg, alpha=0.75, bins=n_bins)
#plt.hist(out_deg, alpha=0.75,bins=n_bins)
plt.xlabel('$k_{in}$', fontsize=axis_size)
plt.xticks(fontsize=tick_size)
plt.yticks(fontsize=tick_size)
plt.rc('font', size=15)
ax1.set_xscale('log')
ax1.set_yscale('log')
ax1.spines["top"].set_visible(False)
ax1.spines["right"].set_visible(False)
ax1.text(-0.025,
label_y_position,
'a',
transform=ax1.transAxes,
fontsize=label_size,
fontweight='bold',
va='top',
ha='right')
ax1.text(0.9,
0.55,
'',
transform=ax1.transAxes,
fontsize=inset_size,
va='top',
ha='right')
#Histogram out-degree
ax2 = plt.subplot(132)
plt.hist(out_deg, alpha=0.75, bins=n_bins)
plt.xlabel('$k_{out}$', fontsize=axis_size)
plt.xticks(fontsize=tick_size)
plt.yticks(fontsize=tick_size)
plt.rc('font', size=15)
ax2.set_xscale('log')
ax2.set_yscale('log')
ax2.spines["top"].set_visible(False)
ax2.spines["right"].set_visible(False)
ax2.text(-0.025,
label_y_position,
'b',
transform=ax2.transAxes,
fontsize=label_size,
fontweight='bold',
va='top',
ha='right')
ax2.text(0.9,
0.55,
'',
transform=ax1.transAxes,
fontsize=inset_size,
va='top',
ha='right')
#Histogram clustering coefficients
ax3 = plt.subplot(133)
plt.hist(cs, alpha=0.75, bins=n_bins)
ax3.set_xscale('log')
ax3.set_yscale('log')
plt.xlabel('$C$', fontsize=axis_size)
plt.xticks(fontsize=tick_size)
plt.yticks(fontsize=tick_size)
plt.rc('font', size=15)
ax3.spines["top"].set_visible(False)
ax3.spines["right"].set_visible(False)
ax3.text(-0.025,
label_y_position,
'c',
transform=ax3.transAxes,
fontsize=label_size,
fontweight='bold',
va='top',
ha='right')
ax3.text(0.9,
0.55,
'',
transform=ax2.transAxes,
fontsize=inset_size,
va='top',
ha='right')
plt.tight_layout()
if not os.path.exists('figures'):
os.makedirs('figures')
plt.savefig('figures/histograms_onerow-{}.pdf'.format(datenow))
print "sum :%g, mean :%g" % (np.sum(data), np.mean(data))
return data
#--------------------------------------------------------------#
fig, ax = pl.subplots(1, figsize=(8, 10))
N = 5000
n = -2.6
xmin, xmax = 2.0, 10000.0
seed = 1234785
data = generate_power_law_dist(N, n, xmin, xmax, seed)
counter = collections.Counter(data)
pk = counter.values()
k = counter.keys()
pk = np.asarray(pk) / float(np.sum(pk))
fit = Fit(data)
fit.power_law.plot_pdf(ax=ax, linestyle=':', color='g')
# fit = Fit(data)
print fit.power_law.alpha
print fit.power_law.sigma
ax.loglog(k, pk, '.')
plot_pdf(data, color='r')
pl.show()
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.1, .95)
# annotate_coord = (1.1, .95)
ax1 = fig.add_subplot(n_graphs, n_data, data_inst, visible=False)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
# ABC
# if data_inst == 1:
# ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontproperties=panel_label_font)
# ax1.set_ylabel(u"p(X)")
# from mpl_toolkits.axes_grid.inset_locator import inset_axes
# ax1in = inset_axes(ax1, width="30%", height="30%", loc=3)
# ax1in.hist(data, density=True, color='b')
# ax1in.set_xticks([])
# ax1in.set_yticks([])
# ax1.set_xlabel(units)
ax2 = fig.add_subplot(n_graphs,
n_data,
n_data + data_inst,
sharex=ax1,
visible=False)
plot_pdf(data, ax=ax2, color='b', linewidth=2, label="pdf of data")
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2,
linestyle=':',
color='g',
label="power law fit")
p = fit.power_law.pdf()
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2,
linestyle='--',
color='g',
label="power law fit--opt xmin")
from pylab import setp
setp(ax2.get_xticklabels(), visible=True)
# if data_inst == 1:
ax2.annotate("B",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)") # (10^n)")
handles, labels = ax2.get_legend_handles_labels()
ax2.legend(handles, labels, loc=3)
ax2.set_xlabel(units)
ax3 = fig.add_subplot(n_graphs, n_data, n_data * 2 +
data_inst) # , sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3,
linestyle='--',
color='g',
label="power law fit\n(opt-min)")
fit.exponential.plot_pdf(ax=ax3,
linestyle='--',
color='r',
label="exponential fit\n(opt-min)")
fit.plot_pdf(ax=ax3, color='b', linewidth=2, label="PDF\n(opt-min)")
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
handles, labels = ax3.get_legend_handles_labels()
ax3.legend(handles, labels, loc=3, fontsize=12)
ax3.set_xlabel(units, fontsize=15)
# if data_inst == 1:
ax3.annotate("C",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax3.set_ylabel(u"p(X)", fontsize=15)
def plot_basics(data, data_inst, fig, units):
### Setup ###
from powerlaw import plot_pdf, Fit, pdf
import pylab
pylab.rcParams['xtick.major.pad'] = '8'
pylab.rcParams['ytick.major.pad'] = '8'
#pylab.rcParams['font.sans-serif']='Arial'
from matplotlib.font_manager import FontProperties
panel_label_font = FontProperties().copy()
panel_label_font.set_weight("bold")
panel_label_font.set_size(30.0)
panel_label_font.set_family("sans-serif")
n_data = 2
n_graphs = 4
annotate_coord = (-.4, .95)
#############
ax1 = fig.add_subplot(n_graphs, n_data, data_inst)
x, y = pdf(data, linear_bins=True)
ind = y > 0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data > 0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp(ax1.get_xticklabels(), visible=False)
if data_inst == 1:
ax1.annotate("A",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2 = fig.add_subplot(n_graphs, n_data, n_data + data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
_ = fit.power_law.pdf()
ax2.set_xlim((1, max(x)))
setp(ax2.get_xticklabels(), visible=False)
if data_inst == 1:
ax2.annotate("B",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax2.set_ylabel(u"p(X)") # (10^n)")
ax3 = fig.add_subplot(n_graphs, n_data,
n_data * 2 + data_inst) #, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.lognormal.plot_pdf(ax=ax3, linestyle=':', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
if data_inst == 1:
ax3.annotate("C",
annotate_coord,
xycoords="axes fraction",
fontproperties=panel_label_font)
ax3.set_xlabel(units)
def _get_fit_obj(self, data, xmin=None):
# NOTE: only keep/use non-zero elements
data = np.nonzero(data) # TODO: confirm data is always of np.ndarray
discrete = False if self.ds.data_nature == 'continuous' else False
xmin = self.__get_xmin(xmin=xmin, data=data)
return Fit(data, discrete=discrete, xmin=xmin)
def clust_powlaw(self, G): # Checks if degree distribution follows power law distribution # Returns value of gamma for graph G gamma = [] fit = Fit(sorted(G.degree().values())) return fit.power_law.alpha
def _fit_curr_data(self):
data = self.curr_signed_returns
data = data[np.nonzero(data)] # only use non-zero elements to do Fit
xmin = self.__get_xmin()
self.curr_fit = Fit(data=data, xmin=xmin,
discrete=self.sa.fit_discretely)
def out_degree(adj):
return np.count_nonzero(adj, axis=1)
funcs = [in_sum, out_sum, in_degree, out_degree]
for i in range(len(GRAPH_TYPES)):
g_type = GRAPH_TYPES[i]
g_type_label = GRAPH_TYPE_LABELS[i]
adj = load_everything(g_type, version=BRAIN_VERSION)
for j in range(len(funcs)):
vals = funcs[j](adj)
vals = vals[vals > 0]
plot_ccdf(data=vals, ax=axs[i, j])
results = Fit(vals)
line = results.power_law.plot_ccdf(
ax=axs[i, j],
c="r",
shift_by="original_data",
linestyle="--",
label="Power law",
)
results.lognormal.plot_ccdf(
ax=axs[i, j],
c="g",
shift_by="original_data",
linestyle="--",
label="Lognormal",
)
def main():
timer = Timer()
timer.start()
app_name = 'cyberbullying'
archive_dir = '../data/{0}_out'.format(app_name)
entities = ['user', 'hashtag']
rho = 0.5272
fig, axes = plt.subplots(1, 2, figsize=(10, 3.3))
cc4 = ColorPalette.CC4
blue = cc4[0]
for ax_idx, entity in enumerate(entities):
sample_datefile = open(os.path.join(
archive_dir, '{0}_{1}_all.txt'.format(entity, app_name)),
'r',
encoding='utf-8')
complete_datefile = open(os.path.join(
archive_dir, 'complete_{0}_{1}.txt'.format(entity, app_name)),
'r',
encoding='utf-8')
sample_entity_freq_dict = defaultdict(int)
complete_entity_freq_dict = defaultdict(int)
uni_random_entity_freq_dict = defaultdict(int)
if entity == 'user':
for line in sample_datefile:
sample_entity_freq_dict[line.rstrip().split(',')[1]] += 1
for line in complete_datefile:
complete_entity_freq_dict[line.rstrip().split(',')[1]] += 1
toss = np.random.random_sample()
if toss <= rho:
uni_random_entity_freq_dict[line.rstrip().split(',')
[1]] += 1
else:
for line in sample_datefile:
for item in line.rstrip().split(',')[1:]:
sample_entity_freq_dict[item.lower()] += 1
for line in complete_datefile:
for item in line.rstrip().split(',')[1:]:
complete_entity_freq_dict[item.lower()] += 1
toss = np.random.random_sample()
if toss <= rho:
for item in line.rstrip().split(',')[1:]:
uni_random_entity_freq_dict[item.lower()] += 1
sample_datefile.close()
complete_datefile.close()
# compute the powerlaw fit in the complete set
complete_freq_list = list(complete_entity_freq_dict.values())
complete_powerlaw_fit = Fit(complete_freq_list)
complete_alpha = complete_powerlaw_fit.power_law.alpha
complete_xmin = complete_powerlaw_fit.power_law.xmin
print('{0} complete set alpha {1}, xmin {2}'.format(
entity, complete_alpha, complete_xmin))
plot_ccdf(complete_freq_list,
ax=axes[ax_idx],
color='k',
ls='-',
label='complete')
# compute the powerlaw fit in the sample set
# infer the number of missing entities
sample_freq_list = list(sample_entity_freq_dict.values())
sample_freq_counter = Counter(sample_freq_list)
# we observe the frequency of entities appearing less than 100 times
num_interest = 100
sample_freq_list_top100 = [0] * num_interest
for freq in range(1, num_interest + 1):
sample_freq_list_top100[freq - 1] = sample_freq_counter[freq]
inferred_num_missing = infer_missing_num(sample_freq_list_top100,
rho=rho,
m=num_interest)
corrected_sample_freq_list = sample_freq_list + [
0
] * inferred_num_missing
sample_powerlaw_fit = Fit(corrected_sample_freq_list)
sample_alpha = sample_powerlaw_fit.power_law.alpha
sample_xmin = sample_powerlaw_fit.power_law.xmin
print('{0} sample set alpha {1}, xmin {2}'.format(
entity, sample_alpha, sample_xmin))
plot_ccdf(corrected_sample_freq_list,
ax=axes[ax_idx],
color=blue,
ls='-',
label='sample')
# compute the powerlaw fit in uniform random sample
uni_random_num_missing = len(complete_entity_freq_dict) - len(
uni_random_entity_freq_dict)
uni_random_freq_list = list(uni_random_entity_freq_dict.values())
uni_random_freq_list = uni_random_freq_list + [
0
] * uni_random_num_missing
uni_random_powerlaw_fit = Fit(uni_random_freq_list)
uni_random_alpha = uni_random_powerlaw_fit.power_law.alpha
uni_random_xmin = uni_random_powerlaw_fit.power_law.xmin
print('{0} uniform random sampling alpha {1}, xmin {2}'.format(
entity, uni_random_alpha, uni_random_xmin))
plot_ccdf(uni_random_freq_list,
ax=axes[ax_idx],
color='k',
ls='--',
label='uniform random')
print('inferred missing', inferred_num_missing)
print('empirical missing',
len(complete_entity_freq_dict) - len(sample_entity_freq_dict))
print('uniform random missing', uni_random_num_missing)
print('KS test (sample, uniform)')
print(stats.ks_2samp(corrected_sample_freq_list, uni_random_freq_list))
print('KS test (sample, complete)')
print(stats.ks_2samp(corrected_sample_freq_list, complete_freq_list))
print('KS test (uniform, complete)')
print(stats.ks_2samp(uni_random_freq_list, complete_freq_list))
axes[ax_idx].set_xscale('symlog')
axes[ax_idx].set_yscale('log')
axes[ax_idx].set_xlabel('frequency', fontsize=16)
axes[ax_idx].tick_params(axis='both', which='major', labelsize=16)
axes[0].set_xticks([0, 1, 100, 10000])
axes[0].set_yticks([1, 0.01, 0.0001, 0.000001])
axes[0].set_ylabel('$P(X \geq x)$', fontsize=16)
axes[0].legend(frameon=False,
fontsize=16,
ncol=1,
fancybox=False,
shadow=True,
loc='lower left')
axes[0].set_title('(a) user posting', fontsize=18, pad=-3 * 72, y=1.0001)
axes[1].set_xticks([0, 1, 100, 10000, 1000000])
axes[1].set_yticks([1, 0.1, 0.001, 0.00001])
axes[1].set_title('(b) hashtag', fontsize=18, pad=-3 * 72, y=1.0001)
hide_spines(axes)
timer.stop()
plt.tight_layout(rect=[0, 0.05, 1, 1])
plt.savefig('../images/entity_freq_dist.pdf', bbox_inches='tight')
if not platform.system() == 'Linux':
plt.show()
def main():
# == == == == == == Part 1: Set up environment == == == == == == #
timer = Timer()
timer.start()
data_prefix = '../data/'
target_day_indices = [0, 15, 30, 45]
color_cycle_4 = ColorPalette.CC4
date_labels = [
'Sep 01, 2018', 'Sep 16, 2018', 'Oct 01, 2018', 'Oct 16, 2018'
]
# == == == == == == Part 2: Load video views == == == == == == #
data_loader = DataLoader()
data_loader.load_video_views()
embed_view_dict = data_loader.embed_view_dict
embed_avg_view_dict = data_loader.embed_avg_view_dict
num_videos = data_loader.num_videos
target_day_view_list = [[], [], [], []]
for embed in range(num_videos):
for target_idx, target_day in enumerate(target_day_indices):
target_day_view_list[target_idx].append(
embed_view_dict[embed][target_day])
# == == == == == == Part 3: Load dynamic network snapshot == == == == == == #
embed_indegree_dict = {
embed: np.zeros((T, ))
for embed in np.arange(num_videos)
} # daily indegree for each embed
zero_indegree_list = [] # percentage of zero indegree for each day
num_edges_list = [] # number of total edges for each day
for t in range(T):
filename = 'network_{0}.p'.format(
(datetime(2018, 9, 1) + timedelta(days=t)).strftime('%Y-%m-%d'))
indegree_list = []
with open(os.path.join(data_prefix, 'network_pickle', filename),
'rb') as fin:
network_dict = pickle.load(fin)
# embed_tar: [(embed_src, pos_src, view_src), ...]
for tar_embed in range(num_videos):
indegree_value = len(
[1 for x in network_dict[tar_embed] if x[1] < NUM_REL])
embed_indegree_dict[tar_embed][t] = indegree_value
indegree_list.append(indegree_value)
indegree_counter = Counter(indegree_list)
zero_indegree_list.append(indegree_counter[0] / num_videos)
num_edges_list.append(sum(indegree_list))
print('>>> Finish loading day {0}...'.format(t + 1))
print('>>> Network structure has been loaded!')
print('\n>>> Average number of edges: {0:.0f}, max: {1:.0f}, min: {2:.0f}'.
format(
sum(num_edges_list) / len(num_edges_list), max(num_edges_list),
min(num_edges_list)))
fig, axes = plt.subplots(1, 3, figsize=(12, 4.5))
ax1, ax2, ax3 = axes.ravel()
# == == == == == == Part 4: Plot ax1 indegree CCDF == == == == == == #
embed_avg_indegree_dict = defaultdict(float)
for t in range(T):
for embed in range(num_videos):
embed_avg_indegree_dict[embed] += embed_indegree_dict[embed][t] / T
indegree_ranked_embed_list = [
x[0] for x in sorted(embed_avg_indegree_dict.items(),
key=lambda kv: kv[1],
reverse=True)
]
top_20_indegree_embeds = indegree_ranked_embed_list[:20]
popular_ranked_embed_list = [
x[0] for x in sorted(
embed_avg_view_dict.items(), key=lambda kv: kv[1], reverse=True)
]
top_20_popular_embeds = popular_ranked_embed_list[:20]
for target_idx, target_day in enumerate(target_day_indices):
indegree_list = []
for embed in range(num_videos):
indegree_list.append(embed_indegree_dict[embed][target_day])
print(
'video with 10 indegree has more in-links than {0:.2f}% videos on date {1}'
.format(percentileofscore(indegree_list, 10),
date_labels[target_idx]))
print(
'video with 20 indegree has more in-links than {0:.2f}% videos on date {1}'
.format(percentileofscore(indegree_list, 20),
date_labels[target_idx]))
plot_ccdf(indegree_list,
ax=ax1,
color=color_cycle_4[target_idx],
label=date_labels[target_idx])
# compute the powerlaw fit
powerlaw_fit = Fit(list(embed_avg_indegree_dict.values()))
infer_alpha = powerlaw_fit.power_law.alpha
p = powerlaw_fit.power_law.ccdf()
ins_x_axis = powerlaw_fit.power_law.__dict__['parent_Fit'].__dict__[
'data'][:int(0.9 * len(p))]
ins_y_axis = 0.1 * p[:int(0.9 * len(p))]
ax1.plot(ins_x_axis, ins_y_axis, 'k:')
ax1.text(0.4,
0.6,
r'$x^{{{0:.2f}}}$'.format(-infer_alpha + 1),
size=12,
ha='right',
va='bottom',
transform=ax1.transAxes)
ax1.set_xscale('log')
ax1.set_yscale('log')
ax1.set_xlabel('indegree', fontsize=11)
ax1.set_ylabel('$P(X) \geq x$', fontsize=11)
ax1.tick_params(axis='both', which='major', labelsize=10)
ax1.set_title('(a) indegree distribution', fontsize=12)
ax1.legend(frameon=False, fontsize=11, ncol=1, fancybox=False, shadow=True)
mean_zero_indegree = sum(zero_indegree_list) / len(zero_indegree_list)
ax1.axhline(y=1 - mean_zero_indegree, color='k', linestyle='--', zorder=30)
ax1.text(0.96,
0.9,
'{0:.0f}% with 0 indegree'.format(mean_zero_indegree * 100),
size=11,
transform=ax1.transAxes,
ha='right',
va='top')
# == == == == == == Part 5: Plot ax2 views distribution == == == == == == #
for target_idx, views_list in enumerate(target_day_view_list):
x_values = range(100)
y_values = [np.percentile(views_list, x) for x in x_values]
ax2.plot(x_values,
y_values,
color=color_cycle_4[target_idx],
label=date_labels[target_idx])
ax2.set_yscale('log')
ax2.set_xlabel('views percentile', fontsize=11)
ax2.set_ylabel('num of views', fontsize=11)
ax2.tick_params(axis='both', which='major', labelsize=10)
ax2.set_title('(b) daily views vs. its percentile', fontsize=12)
avg_views_list = sorted(list(embed_avg_view_dict.values()), reverse=True)
gini_coef = gini(avg_views_list)
print('top 1% videos occupy {0:.2f}% views'.format(
sum(avg_views_list[:int(0.01 * num_videos)]) / sum(avg_views_list) *
100))
print('top 10% videos occupy {0:.2f}% views'.format(
sum(avg_views_list[:int(0.1 * num_videos)]) / sum(avg_views_list) *
100))
print('Gini coef: {0:.3f}'.format(gini_coef))
spearman_degree = [
embed_avg_indegree_dict[embed] for embed in range(num_videos)
]
spearman_views = [
embed_avg_view_dict[embed] for embed in range(num_videos)
]
print(
'Spearman correlation between views and indegree: {0:.4f}, pvalue: {1:.2f}'
.format(*spearmanr(spearman_views, spearman_degree)))
median_views = np.median(avg_views_list)
top_views_90th = np.percentile(avg_views_list, 90)
top_views_99th = np.percentile(avg_views_list, 99)
ax2_xmin = ax2.get_xlim()[0]
ax2_ymin = ax2.get_ylim()[0]
ax2.plot((50, 50), (ax2_ymin, median_views),
color='k',
linestyle='--',
zorder=30)
ax2.plot((ax2_xmin, 50), (median_views, median_views),
color='k',
linestyle='--',
zorder=30)
ax2.text(0.49,
0.45,
'median views {0:,.0f}'.format(median_views),
size=11,
transform=ax2.transAxes,
ha='right',
va='bottom')
ax2.plot((90, 90), (ax2_ymin, top_views_90th),
color='k',
linestyle='--',
zorder=30)
ax2.plot((ax2_xmin, 90), (top_views_90th, top_views_90th),
color='k',
linestyle='--',
zorder=30)
ax2.text(0.88,
0.75,
'90th views {0:,.0f}'.format(top_views_90th),
size=11,
transform=ax2.transAxes,
ha='right',
va='bottom')
ax2.plot((99, 99), (ax2_ymin, top_views_99th),
color='k',
linestyle='--',
zorder=30)
ax2.plot((ax2_xmin, 99), (top_views_99th, top_views_99th),
color='k',
linestyle='--',
zorder=30)
ax2.text(0.91,
0.95,
'99th views {0:,.0f}'.format(top_views_99th),
size=11,
transform=ax2.transAxes,
ha='right',
va='bottom')
# == == == == == == Part 7: Plot ax3 video uploading trend == == == == == == #
x_axis = range(2009, 2018)
x_labels = ["'09", "'10", "'11", "'12", "'13", "'14", "'15", "'16", "'17"]
upload_mat = np.zeros((len(x_axis), 8))
target_topics = [
'Pop_music', 'Rock_music', 'Hip_hop_music', 'Independent_music',
'Country_music', 'Electronic_music', 'Soul_music', 'Others'
]
topic_labels = [
'Pop', 'Rock', 'Hip hop', 'Independent', 'Country', 'Electronic',
'Soul', 'Others'
]
color_cycle_8 = ColorPalette.CC8
data_loader.load_embed_content_dict()
embed_title_dict = data_loader.embed_title_dict
embed_uploadtime_dict = data_loader.embed_uploadtime_dict
embed_genre_dict = data_loader.embed_genre_dict
for embed in range(num_videos):
upload_year = int(embed_uploadtime_dict[embed][:4])
if 2009 <= upload_year <= 2017:
year_idx = upload_year - 2009
genres = embed_genre_dict[embed]
if len(genres) == 0:
# add one to "Others" genre
upload_mat[year_idx, 7] += 1
else:
for genre in genres:
upload_mat[year_idx,
target_topics.index(genre)] += 1 / len(genres)
print()
print([
'{0}: {1}'.format(topic, int(num))
for topic, num in zip(target_topics, np.sum(upload_mat, axis=0))
])
stackedBarPlot(ax=ax3,
data=upload_mat,
cols=color_cycle_8,
edgeCols=['#000000'] * 8,
xlabel='uploaded year',
ylabel='num of videos',
scale=False,
endGaps=True)
ax3.tick_params(axis='both', which='major', labelsize=9)
ax3.set_xticks(np.arange(len(x_axis)))
ax3.set_xticklabels(x_labels)
ax3.yaxis.set_major_formatter(FuncFormatter(concise_fmt))
ax3.legend([
plt.Rectangle((0, 0), 1, 1, fc=c, ec='k', alpha=0.6)
for c in color_cycle_8
],
topic_labels,
fontsize=9,
frameon=False,
handletextpad=0.2,
columnspacing=0.3,
ncol=4,
bbox_to_anchor=(1, -0.12),
bbox_transform=ax3.transAxes,
fancybox=False,
shadow=True)
ax3.set_title('(c) VEVO videos uploading trend', fontsize=12)
union_top_set = set(top_20_indegree_embeds).union(top_20_popular_embeds)
print('\n>>> Size of the union set at cutoff 15:', len(union_top_set))
print('{0:>24} | {1:>17} | {2:>5} | {3:>8} | {4:>6} | {5:>10} | {6:>5}'.
format('Video title', 'Artist', 'Age', 'Indegree', '-rank', 'Views',
'-rank'))
for embed in top_20_indegree_embeds:
print(
'{0:>24} & {1:>17} & {2:>5} & {3:>8} & {4:>6} & {5:>10} & {6:>5} \\\\'
.format(
embed_title_dict[embed].split(
' - ', 1)[1].split('(')[0].split('ft')[0].strip(),
embed_title_dict[embed].split(
' - ',
1)[0].split('&')[0].split(',')[0].strip(), '{0:,}'.format(
(datetime(2018, 11, 2) -
str2obj(embed_uploadtime_dict[embed])).days),
'{0:,}'.format(int(embed_avg_indegree_dict[embed])),
'{0:,}'.format(top_20_indegree_embeds.index(embed) + 1),
'{0:,}'.format(int(embed_avg_view_dict[embed])),
'{0:,}'.format(popular_ranked_embed_list.index(embed) + 1)))
print('\n{0:>24} | {1:>17} | {2:>5} | {3:>8} | {4:>6} | {5:>10} | {6:>5}'.
format('Video title', 'Artist', 'Age', 'Indegree', '-rank', 'Views',
'-rank'))
for embed in top_20_popular_embeds:
print(
'{0:>24} & {1:>17} & {2:>5} & {3:>8} & {4:>6} & {5:>10} & {6:>5} \\\\'
.format(
embed_title_dict[embed].split(
' - ', 1)[1].split('(')[0].split('ft')[0].strip(),
embed_title_dict[embed].split(
' - ',
1)[0].split('&')[0].split(',')[0].strip(), '{0:,}'.format(
(datetime(2018, 11, 2) -
str2obj(embed_uploadtime_dict[embed])).days),
'{0:,}'.format(int(embed_avg_indegree_dict[embed])),
'{0:,}'.format(indegree_ranked_embed_list.index(embed) + 1),
'{0:,}'.format(int(embed_avg_view_dict[embed])),
'{0:,}'.format(top_20_popular_embeds.index(embed) + 1)))
hide_spines(axes)
timer.stop()
plt.tight_layout()
plt.savefig('../images/measure_basic_statistics.pdf', bbox_inches='tight')
if not platform.system() == 'Linux':
plt.show()
def plplot(data, title, save=False, save_path=None):
data = np.array(data)
fig = plt.figure(figsize=(18,6))
fig.suptitle(title)
# === A ===
ax1 = fig.add_subplot(1,3,1)
# 线性x轴
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
# 双log-绘制概率密度曲线
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
ax1.set_xlabel('A')
# 绘制histogram小图
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
# === A ===
# === B ===
annotation = ''
ax2 = fig.add_subplot(1,3,2, sharey=ax1)
# 双log-绘制概率密度曲线
print(title)
print(pdf(data))
print()
plot_pdf(data, ax=ax2, color='b', linewidth=2)
# 拟合power-law函数并绘图
fit = Fit(data, xmin=1, discrete=True, parameter_range={'alpha':[None,None]})
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
params1 = (fit.power_law.alpha, fit.power_law.xmin, fit.power_law.sigma)
# alpha为拟合系数
# xmin表示最小的x值(使不为0)，此处指定为1
# sigma为标准差
annotation += '\':\' - alpha={:.2f}, xmin= {}, sigma={:.2f}'.format(*params1)
# p = fit.power_law.pdf()
fit = Fit(data, discrete=True, parameter_range={'alpha':[-5,10]})
# 区别于ax2中的第一条拟合线 - 此处的xmin并非指定，而是自动计算的optimal
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
params2 = (fit.power_law.alpha, fit.power_law.xmin, fit.power_law.sigma)
annotation += '\n\'--\' - alpha={:.2f}, xmin= {}, sigma={:.2f}'.format(*params2)
ax2.set_xlabel('B')
ax2.set_ylabel(u"p(X)")# (10^n)")
ax2.set_xlim(ax1.get_xlim())
annotate_coord = (0.05, 0.88)
ax2.annotate(annotation, annotate_coord, xycoords="axes fraction")
# === B ===
# === C ===
ax3 = fig.add_subplot(1,3,3, sharey=ax1)#, sharex=ax1)#, sharey=ax2)
plot_pdf(data[data>0], ax=ax3, color='b', linewidth=2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
ax3.set_ylim(ax2.get_ylim())
ax3.set_xlim(ax1.get_xlim())
ax3.set_xlabel('C')
# === C ===
if save:
plt.savefig(save_path)
else:
plt.show()
return params1, params2
def plot_basics(data, data_inst, fig, units):
from powerlaw import plot_pdf, Fit, pdf
annotate_coord = (-.4, .95)
ax1 = fig.add_subplot(n_graphs,n_data,data_inst)
plot_pdf(data[data>0], ax=ax1, linear_bins=True, color='r', linewidth=.5)
x, y = pdf(data, linear_bins=True)
ind = y>0
y = y[ind]
x = x[:-1]
x = x[ind]
ax1.scatter(x, y, color='r', s=.5)
plot_pdf(data[data>0], ax=ax1, color='b', linewidth=2)
from pylab import setp
setp( ax1.get_xticklabels(), visible=False)
#ax1.set_xticks(ax1.get_xticks()[::2])
ax1.set_yticks(ax1.get_yticks()[::2])
locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax1.annotate("A", annotate_coord, xycoords="axes fraction", fontsize=14)
from mpl_toolkits.axes_grid.inset_locator import inset_axes
ax1in = inset_axes(ax1, width = "30%", height = "30%", loc=3)
ax1in.hist(data, normed=True, color='b')
ax1in.set_xticks([])
ax1in.set_yticks([])
ax2 = fig.add_subplot(n_graphs,n_data,n_data+data_inst, sharex=ax1)
plot_pdf(data, ax=ax2, color='b', linewidth=2)
fit = Fit(data, xmin=1, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle=':', color='g')
p = fit.power_law.pdf()
#ax2.set_ylim(min(p), max(p))
ax2.set_xlim(ax1.get_xlim())
fit = Fit(data, discrete=True)
fit.power_law.plot_pdf(ax=ax2, linestyle='--', color='g')
from pylab import setp
setp( ax2.get_xticklabels(), visible=False)
#ax2.set_xticks(ax2.get_xticks()[::2])
if ax2.get_ylim()[1] >1:
ax2.set_ylim(ax2.get_ylim()[0], 1)
ax2.set_yticks(ax2.get_yticks()[::2])
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax2.annotate("B", annotate_coord, xycoords="axes fraction", fontsize=14)
ax2.set_ylabel(r"$p(X)$")# (10^n)")
ax3 = fig.add_subplot(n_graphs,n_data,n_data*2+data_inst)#, sharex=ax1)#, sharey=ax2)
fit.power_law.plot_pdf(ax=ax3, linestyle='--', color='g')
fit.exponential.plot_pdf(ax=ax3, linestyle='--', color='r')
fit.plot_pdf(ax=ax3, color='b', linewidth=2)
#p = fit.power_law.pdf()
ax3.set_ylim(ax2.get_ylim())
ax3.set_yticks(ax3.get_yticks()[::2])
ax3.set_xlim(ax1.get_xlim())
#locs,labels = yticks()
#yticks(locs, map(lambda x: "%.0f" % x, log10(locs)))
if data_inst==1:
ax3.annotate("C", annotate_coord, xycoords="axes fraction", fontsize=14)
#if ax2.get_xlim()!=ax3.get_xlim():
# zoom_effect01(ax2, ax3, ax3.get_xlim()[0], ax3.get_xlim()[1])
ax3.set_xlabel(units)
