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| from scipy.linalg import orth
import matplotlib.pyplot as plt
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
class LISTA(nn.Module):
def __init__(self, n, m, W_e, max_iter, L, theta):
"""
n: 输入维度
m: 稀疏表示的维度
W_e: 字典
max_iter: 最大迭代次数
L: Lipschitz常数
theta: 阈值
"""
super(LISTA, self).__init__()
self._W = nn.Linear(in_features=n, out_features=m, bias=False)
self._S = nn.Linear(in_features=m, out_features=m,
bias=False)
self._S2 = nn.Linear(in_features=m, out_features=m,
bias=False)
self._S3 = nn.Linear(in_features=m, out_features=m,
bias=False)
self.shrinkage = nn.Softshrink(theta)
self.theta = theta
self.max_iter = max_iter
self.A = W_e
self.L = L
def weights_init(self):
"""
按照伪代码来初始化S和W_e
"""
A = self.A.cpu().numpy()
L = self.L
S = torch.from_numpy(np.eye(A.shape[1]) - (1/L)*np.matmul(A.T, A))
S = S.float().to(device)
W = torch.from_numpy((1/L)*A.T)
W = W.float().to(device)
self._S.weight = nn.Parameter(S)
self._S2.weight = nn.Parameter(S)
self._S3.weight = nn.Parameter(S)
self._W.weight = nn.Parameter(W)
def forward(self, y):
"""
前向推断步，利用自动求导机制不需要再求解导数
"""
x = self.shrinkage(self._W(y))
if self.max_iter == 1:
return x
for iter in range(self.max_iter):
x = self.shrinkage(self._W(y) + self._S(x))
x = self.shrinkage(self._W(y) + self._S2(x))
x = self.shrinkage(self._W(y) + self._S3(x))
return x
def train_lista(Y, dictionary, a, L, max_iter=30):
"""
由于需要训练权重，所以还需要使用一个包装函数来训练网络
"""
n, m = dictionary.shape
n_samples = Y.shape[0]
batch_size = 32
steps_per_epoch = n_samples // batch_size
Y = torch.from_numpy(Y)
Y = Y.float().to(device)
W_d = torch.from_numpy(dictionary)
W_d = W_d.float().to(device)
net = LISTA(n, m, W_d, max_iter=30, L=L, theta=a/L)
net = net.float().to(device)
net.weights_init()
learning_rate = 1e-2
criterion1 = nn.MSELoss()
criterion2 = nn.L1Loss()
all_zeros = torch.zeros(batch_size, m).to(device)
optimizer = torch.optim.SGD(
net.parameters(), lr=learning_rate, momentum=0.9)
loss_list = []
for epoch in range(100):
index_samples = np.random.choice(
a=n_samples, size=n_samples, replace=False, p=None)
Y_shuffle = Y[index_samples]
for step in range(steps_per_epoch):
Y_batch = Y_shuffle[step*batch_size:(step+1)*batch_size]
optimizer.zero_grad()
X_h = net(Y_batch)
Y_h = torch.mm(X_h, W_d.T)
loss1 = criterion1(Y_batch.float(), Y_h.float())
loss2 = a * criterion2(X_h.float(), all_zeros.float())
loss = loss1 + loss2
loss.backward()
optimizer.step()
with torch.no_grad():
loss_list.append(loss.detach().data)
print("epoch: {}, loss: {}".format(epoch, loss.detach().data))
return net, loss_list
m, n, k = 1000, 256, 5
N = 128
Psi = np.eye(m)
Phi = np.random.randn(n, m)
Phi = np.transpose(orth(np.transpose(Phi)))
W_d = np.dot(Phi, Psi)
print(W_d.shape)
Z = np.zeros((N, m))
X = np.zeros((N, n))
for i in range(N):
index_k = np.random.choice(a=m, size=k, replace=False, p=None)
Z[i, index_k] = 5 * np.random.randn(k, 1).reshape([-1, ])
X[i] = np.dot(W_d, Z[i, :])
net, err_list = train_lista(X, W_d, 0.1, 2)
X_h = net(torch.from_numpy(X[0:2]).float().to(device))
plt.subplot(2, 1, 1)
plt.plot(X[0])
plt.title("Original")
plt.subplot(2, 1, 2)
plt.plot(X_h.cpu().detach().numpy()[0], label="reconstruction")
plt.title("Reconstruction")
plt.legend()
plt.show()
|
