def gfl_cvx_2():
''' Graph Fused Lasso '''
numNode = 100
data = np.zeros((numNode, 2))
for k in range(11):
data[k] = data[k] + np.array([1, 1])
data[k + 11] = data[k + 11] + np.array([-1, 1])
data[k + 22] = data[k + 22] + np.array([2, 2])
data[k + 33] = data[k + 33] + np.array([-1, -1])
np.random.seed(1)
noise = 0.5 * np.random.normal(0, 1, (numNode, 2))
data = data + noise
edgelist = [[k, k + 1] for k in range(numNode - 1)]
graph = nx.Graph()
graph.add_edges_from(edgelist)
coloredge(graph)
graph0, graph1 = decompose_graph(graph)
runtime = []
objerror = []
rho_set = [2**k for k in range(7)]
# rho_set = [1]
_, obj, _, _ = solve_GroupFL(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=3000,
rho=8,
lam=0.1)
optobj = obj[-1]
for rho in rho_set:
clock_time = time.time()
_, tevolution, obj, _ = solve_GroupFL_pool(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=250,
rho=rho,
lam=0.1)
print('GraphLasso_pool:', time.time() - clock_time, ',rho:', rho)
objerror.append([i - optobj for i in obj])
runtime.append(tevolution)
# plotting
plt.figure()
plt.plot(runtime[0], objerror[0], label=r'$\rho=2^0$')
plt.plot(runtime[1], objerror[1], label=r'$\rho=2^1$')
plt.plot(runtime[2], objerror[2], label=r'$\rho=2^2$')
plt.plot(runtime[3], objerror[3], label=r'$\rho=2^3$')
plt.plot(runtime[4], objerror[4], label=r'$\rho=2^4$')
plt.plot(runtime[5], objerror[5], label=r'$\rho=2^5$')
plt.plot(runtime[6], objerror[6], label=r'$\rho=2^6$')
plt.legend(loc='upper right')
plt.xlim((0, 50))
plt.ylim((1e-5, 1e2))
# plt.title('Graph Fused Lasso Algorithm-cvxpy (lambda=0.1)')
plt.title(r'Graph Fused Lasso Algorithm '
r'(cvx, $\lambda=0.1$)',
fontsize=12)
plt.xlabel('Running time (seconds)', fontsize=12)
plt.ylabel('Objective Value Error', fontsize=12)
plt.yscale('log')
plt.savefig('Figures/ChainGraph_cvx/GraphFL_lamb=01_chain_graph_cvx',
bbox_inches='tight')
def gfl_explicit_1():
''' group fused lasso algorithm with explicit updates '''
# img = mpimg.imread('Data/ABC.png')
# img = np.ones((10,10,3))
img = np.zeros((10, 10, 3))
for i in range(10):
for j in range(10):
if (i - 4)**2 + (j - 4)**2 < 5:
img[i][j] = np.array([0.5, 0.5, 0.5])
imgsize1, imgsize2, _ = img.shape
# img=img.astype(float)/255
noise = 0.2 * np.random.normal(0, 1, (imgsize1, imgsize2, 3))
imgnoise = img + noise
data = np.reshape(imgnoise, (-1, 3))
nodes = imgsize1 * imgsize2
# graph settings
graph = nx.grid_2d_graph(imgsize1, imgsize2)
graph = nx.convert_node_labels_to_integers(graph)
temp_edges = []
for k in range(0, imgsize1 * imgsize2):
for j in graph.neighbors(k):
if j == k + 1:
temp_edges.append([k, j])
graph0_edges = []
graph0_edges.append(temp_edges[0])
for edge in temp_edges:
if (edge[0] != graph0_edges[-1][1]) and (edge != graph0_edges[-1]):
graph0_edges.append(edge)
graph1_edges = [
edge for edge in list(graph.edges()) if edge not in graph0_edges
]
graph1_edges.sort()
graph0_nodes = np.unique(np.array(graph0_edges))
graph1_nodes = np.unique(np.array(graph1_edges))
graph0 = nx.Graph()
graph1 = nx.Graph()
graph0.add_nodes_from(graph0_nodes)
graph1.add_nodes_from(graph1_nodes)
graph0.add_edges_from(graph0_edges)
graph1.add_edges_from(graph1_edges)
runtime = []
objerror = []
rho_set = [2**k for k in range(7)]
# rho_set = [32]
_, obj, _, _ = solve_GroupFL(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=10000,
rho=4,
lam=0.5)
optobj = obj[-1]
for rho in rho_set:
clock_time = time.time()
_, obj, _, tevolution = solve_GroupFL(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=3000,
rho=rho,
lam=0.5)
print('running time GraphLasso_explicit:',
time.time() - clock_time, ',rho:', rho)
objerror.append([i - optobj for i in obj])
runtime.append(tevolution)
# plotting
plt.figure()
plt.plot(runtime[0], objerror[0], label=r'$\rho=2^0$')
plt.plot(runtime[1], objerror[1], label=r'$\rho=2^1$')
plt.plot(runtime[2], objerror[2], label=r'$\rho=2^2$')
plt.plot(runtime[3], objerror[3], label=r'$\rho=2^3$')
plt.plot(runtime[4], objerror[4], label=r'$\rho=2^4$')
plt.plot(runtime[5], objerror[5], label=r'$\rho=2^5$')
plt.plot(runtime[6], objerror[6], label=r'$\rho=2^6$')
plt.legend(loc='upper right')
plt.xlim((0, 20))
plt.ylim((1e-12, 1e1))
# plt.title('Graph Fused Lasso Algorithm (explict)')
plt.title(r'Graph Fused Lasso Algorithm '
r'(explicit, $\lambda=0.5$)',
fontsize=12)
plt.xlabel('Running time (seconds)', fontsize=12)
# plt.xlabel('Number of Iterations')
plt.ylabel('Objective Value Error', fontsize=12)
plt.yscale('log')
plt.savefig('Figures/GridGraph/GraphFL_lamb=05_grid_graph_explicit',
bbox_inches='tight')
def gfl_cvx_1():
''' group fused lasso algorithm with explicit updates '''
# img = mpimg.imread('Data/ABC.png')
img = np.zeros((10, 10, 3))
for i in range(10):
for j in range(10):
if (i - 4)**2 + (j - 4)**2 < 5:
img[i][j] = np.array([0.5, 0.5, 0.5])
imgsize1, imgsize2, _ = img.shape
# img=img.astype(float)/255
np.random.seed(1)
noise = 0.2 * np.random.normal(0, 1, (imgsize1, imgsize2, 3))
imgnoise = img + noise
data = np.reshape(imgnoise, (-1, 3))
nodes = imgsize1 * imgsize2
# graph settings
graph = nx.grid_2d_graph(imgsize1, imgsize2)
graph = nx.convert_node_labels_to_integers(graph)
graph0_edges = []
for k in range(0, nodes, 2):
for j in graph.neighbors(k):
if j == k + 1:
graph0_edges.append([k, j])
graph1_edges = [edge for edge in list(
graph.edges()) if edge not in graph0_edges]
graph1_edges.sort()
# print(graph1_edges)
# return
graph0_nodes = np.unique(np.array(graph0_edges))
graph1_nodes = np.unique(np.array(graph1_edges))
graph0 = nx.Graph()
graph1 = nx.Graph()
graph0.add_nodes_from(graph0_nodes)
graph1.add_nodes_from(graph1_nodes)
graph0.add_edges_from(graph0_edges)
graph1.add_edges_from(graph1_edges)
runtime = []
objerror = []
rho_set = [2**k for k in range(7)]
# rho_set = [2]
_, obj, _, _ = solve_GroupFL(
y=data, G=graph, G0=graph0, G1=graph1, maxsteps=4500, rho=8, lam=0.5)
optobj = obj[-1]
print(optobj)
# with open('Figures/GridGraph_cvx/optobj.csv', newline='') as csvfile:
# spamreader = csv.reader(csvfile, delimiter=' ', quotechar='|')
# for value in spamreader:
# obj = value
for rho in rho_set:
clock_time = time.time()
x_hat, tevolution, obj, _ = solve_GroupFL_pool(
y=data, G=graph, G0=graph0, G1=graph1, maxsteps=800, rho=rho, lam=0.5)
print('GraphLasso_cvx:',
time.time() - clock_time, ',rho:', rho)
objerror.append([i - optobj for i in obj])
# objerror.append([i - obj[-1] for i in obj])
runtime.append(tevolution)
# print(obj)
# print('obj:',obj)
# print('time:',runtime)
# print('obj_cvx:', obj)
# img_recovered = np.reshape(x_hat, (imgsize1, imgsize2, 3))
#
# fig = plt.figure()
# fig.add_subplot(1, 3, 1)
# plt.imshow(img)
# fig.add_subplot(1, 3, 2)
# plt.imshow(imgnoise)
# fig.add_subplot(1, 3, 3)
# plt.imshow(img_recovered)
# plt.savefig(
# 'Figures/GridGraph_cvx/img', bbox_inches='tight')
# plotting
plt.figure()
plt.plot(runtime[0], objerror[0], label=r'$\rho=2^0$')
plt.plot(runtime[1], objerror[1], label=r'$\rho=2^1$')
plt.plot(runtime[2], objerror[2], label=r'$\rho=2^2$')
plt.plot(runtime[3], objerror[3], label=r'$\rho=2^3$')
plt.plot(runtime[4], objerror[4], label=r'$\rho=2^4$')
plt.plot(runtime[5], objerror[5], label=r'$\rho=2^5$')
plt.plot(runtime[6], objerror[6], label=r'$\rho=2^6$')
plt.legend(loc='upper right')
plt.xlim((0, 120))
plt.ylim((1e-6, 1e1))
# plt.title('Graph Fused Lasso Algorithm (cvx)')
plt.title(r'Graph Fused Lasso Algorithm ' r'(cvx, $\lambda=0.5$)', fontsize=12)
plt.xlabel('Running time (seconds)', fontsize=12)
# plt.xlabel('Number of Iterations')
plt.ylabel('Objective Value Error', fontsize=12)
plt.yscale('log')
plt.savefig(
'Figures/GridGraph_cvx/GraphFL_lamb=05_grid_graph_cvx', bbox_inches='tight')
def obj_find():
''' find optimal objective vlaue '''
# img = mpimg.imread('Data/ABC.png')
# imgsize1, imgsize2, _ = img.shape
img = np.ones(16, 16, 3)
np.random.seed(1)
noise = 0.2 * np.random.normal(0, 1, (imgsize1, imgsize2, 3))
imgnoise = img + noise
data = np.reshape(imgnoise, (-1, 3))
nodes = imgsize1 * imgsize2
# graph settings
graph = nx.grid_2d_graph(imgsize1, imgsize2)
graph = nx.convert_node_labels_to_integers(graph)
# print(list(graph.edges()))
temp_edges = []
for k in range(0, imgsize1 * imgsize2):
for j in graph.neighbors(k):
if j == k + 1:
temp_edges.append([k, j])
graph0_edges = []
graph0_edges.append(temp_edges[0])
for edge in temp_edges:
if (edge[0] != graph0_edges[-1][1]) and (edge != graph0_edges[-1]):
graph0_edges.append(edge)
graph_edges = list(graph.edges())
graph_edges.sort()
graph1_edges = [edge for edge in list(
graph.edges()) if edge not in graph0_edges]
graph1_edges.sort()
graph0_nodes = np.unique(np.array(graph0_edges))
graph1_nodes = np.unique(np.array(graph1_edges))
graph = nx.Graph()
graph0 = nx.Graph()
graph1 = nx.Graph()
graph0.add_nodes_from(graph0_nodes)
graph1.add_nodes_from(graph1_nodes)
graph0.add_edges_from(graph0_edges)
graph1.add_edges_from(graph1_edges)
graph.add_nodes_from(range(imgsize1 * imgsize2))
graph.add_edges_from(graph_edges)
# print(list(graph.edges()))
_, obj, _, _ = solve_GroupFL(
y=data, G=graph, G0=graph0, G1=graph1, maxsteps=1000, rho=2, lam=10)
optobj = obj[-1]
print(obj)
_, obj, _, _ = solve_NetworkLasso(
y=data, G=graph, maxsteps=1000, rho=2, lam=10)
optobj = obj[-1]
print(obj)
return
plt.switch_backend('TkAgg')
plt.figure()
plt.plot(obj - obj[-1])
# plt.ylim((1e-4, 1e3))
plt.title('Graph Fused Lasso Algorithm (cvx)')
plt.ylabel('error')
plt.yscale('log')
plt.show()
with open('Figures/GridGraph_cvx/optobj.csv', 'w', newline='') as csvfile:
objwriter = csv.writer(csvfile, delimiter=' ',
quotechar='|', quoting=csv.QUOTE_MINIMAL)
objwriter.writerow([optobj] + ['lambda:'] + [10])
def gfl_cvx_1():
''' group fused lasso algorithm with explicit updates '''
img = np.random.normal(0, 1, (10, 10, 3))
imgsize1, imgsize2, _ = img.shape
# img=img.astype(float)/255
np.random.seed(1)
noise = 0.2 * np.random.normal(0, 1, (imgsize1, imgsize2, 3))
imgnoise = img + noise
data = np.reshape(imgnoise, (-1, 3))
nodes = imgsize1 * imgsize2
# graph settings
graph = nx.grid_2d_graph(imgsize1, imgsize2)
graph = nx.convert_node_labels_to_integers(graph)
graph0_edges = []
for k in range(0, nodes, 2):
for j in graph.neighbors(k):
if j == k + 1:
graph0_edges.append([k, j])
graph1_edges = [
edge for edge in list(graph.edges()) if edge not in graph0_edges
]
graph1_edges.sort()
graph0_nodes = np.unique(np.array(graph0_edges))
graph1_nodes = np.unique(np.array(graph1_edges))
graph0 = nx.Graph()
graph1 = nx.Graph()
graph0.add_nodes_from(graph0_nodes)
graph1.add_nodes_from(graph1_nodes)
graph0.add_edges_from(graph0_edges)
graph1.add_edges_from(graph1_edges)
runtime = []
objerror = []
# rho_set = [2**k for k in range(7)]
rho_set = [1]
x_hat1, obj, _, _ = solve_GroupFL(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=50,
rho=1,
lam=10)
optobj = obj[-1]
print("obj_exp:", obj)
# lam = 10
# objtemp = (np.linalg.norm(x_hat1 - data))**2
#
# for node1, node2 in graph.edges():
# objtemp = objtemp + lam * np.linalg.norm(x_hat1[node1] - x_hat1[node2])
#
# print(objtemp)
obj = []
for rho in rho_set:
clock_time = time.time()
x_hat2, tevolution, obj, _ = solve_GroupFL_pool(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=50,
rho=rho,
lam=10)
print('GraphLasso_cvx:', time.time() - clock_time, ',rho:', rho)
objerror.append([i - optobj for i in obj])
runtime.append(tevolution)
# print('x_cvx:',x_hat)
# lam = 10
# objtemp = (np.linalg.norm(x_hat2 - data))**2
#
# for node1, node2 in graph.edges():
# objtemp = objtemp + lam * \
# np.linalg.norm(x_hat2[node1] - x_hat2[node2])
#
# print(objtemp)
# print("x1-x2", x_hat1 - x_hat2)
print('obj_cvx:', obj)
def gfl_cvx_2():
''' Graph Fused Lasso '''
numNode = 100
data = np.zeros((numNode, 2))
for k in range(11):
data[k] = data[k] + np.array([1, 1])
data[k + 11] = data[k + 11] + np.array([-1, 1])
data[k + 22] = data[k + 22] + np.array([2, 2])
data[k + 33] = data[k + 33] + np.array([-1, -1])
np.random.seed(1)
noise = 0.5 * np.random.normal(0, 1, (numNode, 2))
data = data + noise
graph = nx.grid_2d_graph(10, 10)
graph = nx.convert_node_labels_to_integers(graph)
print('graph:', list(graph.edges()))
temp_edges = []
for k in range(0, numNode):
for j in graph.neighbors(k):
if j == k + 1:
temp_edges.append([k, j])
graph0_edges = []
graph0_edges.append(temp_edges[0])
for edge in temp_edges:
if (edge[0] != graph0_edges[-1][1]) and (edge != graph0_edges[-1]):
graph0_edges.append(edge)
graph1_edges = [
edge for edge in list(graph.edges()) if edge not in graph0_edges
]
graph1_edges.sort()
graph0_nodes = np.unique(np.array(graph0_edges))
graph1_nodes = np.unique(np.array(graph1_edges))
graph0 = nx.Graph()
graph1 = nx.Graph()
graph0.add_nodes_from(graph0_nodes)
graph1.add_nodes_from(graph1_nodes)
graph0.add_edges_from(graph0_edges)
graph1.add_edges_from(graph1_edges)
print("graph0:", graph0_edges, "graph1:", graph1_edges)
# edgelist = [[k, k + 1] for k in range(numNode - 1)]
# graph = nx.Graph()
# graph.add_edges_from(edgelist)
# coloredge(graph)
# graph0, graph1 = decompose_graph(graph)
runtime = []
objerror = []
# rho_set = [2**k for k in range(7)]
rho_set = [1]
x_hat1, obj1, _, _ = solve_GroupFL(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=20,
rho=1,
lam=1)
optobj = obj1[-1]
print(obj1[:20])
for rho in rho_set:
clock_time = time.time()
x_hat2, tevolution, obj, _ = solve_GroupFL_pool(y=data,
G=graph,
G0=graph0,
G1=graph1,
maxsteps=20,
rho=rho,
lam=1)
print('GraphLasso_pool:', time.time() - clock_time, ',rho:', rho)
objerror.append([i - optobj for i in obj])
runtime.append(tevolution)
print(obj[:20])
print((x_hat1 - x_hat2)[:10])
print([obj1[i] - obj[i] for i in range(len(obj))])
# plotting
plt.switch_backend('TkAgg')
plt.figure()
plt.plot(runtime[0], objerror[0], label=r'$\rho=2^0$')
# plt.plot(runtime[1], objerror[1], label=r'$\rho=2^1$')
# plt.plot(runtime[2], objerror[2], label=r'$\rho=2^2$')
# plt.plot(runtime[3], objerror[3], label=r'$\rho=2^3$')
# plt.plot(runtime[4], objerror[4], label=r'$\rho=2^4$')
# plt.plot(runtime[5], objerror[5], label=r'$\rho=2^5$')
# plt.plot(runtime[6], objerror[6], label=r'$\rho=2^6$')
plt.legend()
plt.xlim((0, 50))
plt.ylim((1e-5, 1e2))
plt.title('Graph Fused Lasso Algorithm (cvxpy)')
plt.xlabel('Running time (seconds)', fontsize=12)
plt.ylabel('Objective Value Error', fontsize=12)
plt.yscale('log')