def average_consensus(G, fig_id, loc=100, scale=50, state=[]):
n = len(G.nodes())
# laplacian matrix
L, eps = graph_util(G)
# initial state
if len(state) == 0:
state = random_initialize(n, loc, scale)
else:
state = np.matrix(state).transpose()
"""
generating a n*1 matrix with all elements being the average point
for the later convergency check
"""
avg = np.asmatrix(state.mean() * np.ones((n, 1)))
"""
records: record all the state during the
iterative process until convergency
"""
records = state
# update the state iteratively
for k in range(MAX_ITERATIVE_LIMIT):
state = (np.identity(n) - eps * L) * state
# check convergency
# if np.array_equal(state, state_tmp):
if np.allclose(state, avg, rtol=0, atol=1e-2):
break
# concatenate the states vertically
records = np.asmatrix(np.concatenate((records, state), axis=1))
np.savetxt("../records/" + fig_id + ".csv", records, delimiter=",")
return records
def dp_avg_consensus(G, fig_id, c, q, s, state=[]):
n = len(G.nodes())
'''
calculate the k-th scales of the laplacian noise vector
with each scale being c_i*q_i^k
q_ = 0(one-shot) is also supported
'''
def gen_kth_scales(k, c, q):
kth_scales = [c_i * (q[idx]**k) for idx, c_i in enumerate(c)]
return np.array(kth_scales)
# both the type of c, q are list
def gen_kth_laplacian_noise(k, c, q, n):
kth_scales = gen_kth_scales(k, c, q)
return np.asmatrix(np.random.laplace(scale=kth_scales,
size=n)).transpose()
L, eps = graph_util(G)
if len(state) == 0:
state = random_initialize(n)
else:
state = np.matrix(state).transpose()
records = state
state_ = state # tmp state for convergency check
for k in range(MAX_ITERATIVE_LIMIT):
# noise
eta = gen_kth_laplacian_noise(k, c, q, n)
# print(eta)
message = state + eta
state = state_ - eps * L * message + np.diag(s) * eta
'''
check convergency
'''
if np.allclose(state_, state, atol=0.5 * 1e-1, rtol=0):
# print("convergency happens")
break
state_ = state
# concatenate the states vertically
records = np.asmatrix(np.concatenate((records, state), axis=1))
# print(
# "true average:", np.mean(records[:, 0]), "convergency average:",
# np.mean(records[:, -1]), "privacy rate:",
# abs(np.mean(records[:, -1]) - np.mean(records[:, 0])) /
# np.mean(records[:, 0]), "convergency time:", np.size(records, 1))
return records
# delta = 1.0
'''
for all the experiments in this part, q_i(for all i), and s_i(for all i) are equal
'''
q_ = 0 # one-shot adding
s_ = 1.0
eps_swp = [10**step for step in np.arange(-2, 2.1, 0.2)]
unique_id = str(datetime.datetime.now().strftime('%m%d-%H%M%S'))
for n in [50, 100, 150, 200]:
# for n in [50]:
state = random_initialize(n, 50, 100)
fig = plt.figure()
# set_xscale only supported in add_subplot
ax = fig.add_subplot(111)
x_cords = []
y_cords = []
var_cords = []
for eps in eps_swp:
# x_cord is filed with the same eps
x_cord = []
y_cord = []
# optimal setting
c_ = set_c(eps, q_, s_)
def cmp_netsz_iternumbers(unique_id, dp_eps_):
fig = plt.figure()
plt.rc('text', usetex=True)
plt.rc('font', family='Times New Roman', weight='normal', size=14)
plt.rcParams['mathtext.fontset'] = 'stix'
# set_xscale only supported in add_subplot
ax = fig.add_subplot(111)
mean_cord = []
for n in size_list:
# for n in [5]:
q = [q_ for _ in range(n)]
s = [s_ for _ in range(n)]
c = [c_ for _ in range(n)]
state = random_initialize(n, 50, 100)
G, fig_id = gen_draw_geograph(n, set_dis(n), unique_id)
y_cord = []
for _ in range(20):
records = dp_avg_consensus(G,
fig_id,
c,
q,
s,
state=np.matrix(state).transpose())
y_cord.append(records.shape[1])
ax.scatter([n for _ in range(20)],
y_cord,
marker='D',
s=160,
facecolors='none',
edgecolors='black')
mean_cord.append(np.mean(y_cord))
ax.scatter(size_list,
mean_cord,
marker='o',
s=80,
color='none',
edgecolors='g',
linewidth=3)
ax.plot(size_list, mean_cord, c='b', lw=1)
# custom legend
legend_elements = [
Line2D([0], [0],
c='none',
marker='D',
markerfacecolor='none',
markeredgecolor='black',
label='Iterative Times of Each Run (PE-IDA)',
markersize=9),
Line2D([0], [0],
c='none',
marker='o',
markerfacecolor='none',
markeredgewidth=3,
markeredgecolor='g',
label='Iterative Times of IDA algorithm',
markersize=9)
]
ax.legend(handles=legend_elements, prop={'size': 15})
plt.xticks([50, 100, 150, 200, 225, 250, 275, 300],
fontsize=20,
weight='bold')
plt.yticks(fontsize=20, weight='bold')
plt.xlabel(r"$|\mathcal{V}|$", fontsize=20)
plt.ylabel(r"Iterative Times", fontsize=25, weight='bold')
ax.grid(ls=':')
ax.set_aspect(1.0 / ax.get_data_ratio() * 0.6)
# plt.show()
# plt.show()
fig_id = unique_id + "_eps_" + str(dp_eps_).replace('.', '') + "_szitt"
plt.savefig("../final_exp_publication/netsz_acc_itertnum/" + fig_id +
'.pdf',
bbox_inches="tight",
pad_inches=0.01)
def cmp_netsz_accuracy(unique_id, dp_eps_):
fig = plt.figure()
plt.rc('text', usetex=True)
plt.rc('font', family='Times New Roman', weight='normal', size=14)
plt.rcParams['mathtext.fontset'] = 'stix'
# set_xscale only supported in add_subplot
ax = fig.add_subplot(111)
mean_cord = []
for n in size_list:
# for n in [5]:
state = random_initialize(n, 50, 100)
G, _ = gen_draw_geograph(n, set_dis(n), unique_id)
y_cord = []
for _ in range(20):
y_cord.append(direct_cal_diff(n, s_, c_))
ax.scatter(
[n for _ in range(20)],
y_cord,
marker='P',
s=160,
# color="#007dff",
# linewidth=2,
color='none',
edgecolors='black')
mean_cord.append(np.mean(y_cord))
ax.scatter(size_list,
mean_cord,
marker='o',
s=80,
color='none',
edgecolors='b',
linewidth=3)
ax.plot(size_list, mean_cord, c='b', lw=1)
# custom legend
legend_elements = [
Line2D([0], [0],
c='none',
marker='P',
markerfacecolor='none',
markeredgecolor='black',
label='Error of Each Run',
markersize=9),
Line2D([0], [0],
c='none',
marker='o',
markerfacecolor='none',
markeredgewidth=3,
markeredgecolor='b',
label='Empirical Mean',
markersize=9)
]
ax.legend(handles=legend_elements, prop={'size': 15})
ax.grid(ls=':')
plt.xticks([50, 100, 150, 200, 225, 250, 275, 300],
fontsize=20,
weight='bold')
plt.yticks(fontsize=20, weight='bold')
# plt.yticks([1, 2])
plt.xlabel(r"$|\mathcal{V}|$", fontsize=20)
plt.ylabel(r"$|x^{*} - \bar{\mathbf{x}}|$", fontsize=25)
ax.set_aspect(1.0 / ax.get_data_ratio() * 0.6)
# plt.show()
fig_id = unique_id + "_eps_" + str(dp_eps_).replace('.', '') + "_szacc"
plt.savefig("../final_exp_publication/netsz_acc_itertnum/" + fig_id +
'.pdf',
bbox_inches="tight",
pad_inches=0.01)