sigmoid算法代码
时间: 2023-08-29 19:08:56 浏览: 64
下面是使用Python编写的sigmoid算法的代码示例:
```python
import numpy as np
def sigmoid(x):
return 1 / (1 + np.exp(-x))
# 示例用法
x = np.array([0, 1, 2, 3, 4])
print(sigmoid(x))
```
此代码定义了一个sigmoid函数,它接受一个数值或一个数组作为输入,并返回对应的sigmoid函数值。在示例中,我们使用NumPy库创建了一个数组`x`,并将其作为参数传递给sigmoid函数,然后打印输出结果。
请注意,sigmoid函数的输入可以是任意实数或数组。这段代码使用了NumPy库中的`exp`函数来计算指数值,因此需要先安装NumPy库才能运行此代码。
相关问题
用sigmoid算法实现前馈神经网络的代码
当使用sigmoid算法实现前馈神经网络时,需要进行以下几个步骤:
1. 初始化参数:初始化权重和偏置值,可以使用随机数或者其他方法进行初始化。
2. 前向传播:通过计算每一层的加权输入和激活函数的输出,将输入数据从输入层传递到输出层。
3. 计算损失:根据预测值和真实值之间的差异,计算损失函数的值。
4. 反向传播:根据损失函数的值,计算每一层的梯度,并更新参数。
5. 重复步骤2-4,直到达到预定的迭代次数或者损失函数收敛。
下面是一个简单的用sigmoid算法实现前馈神经网络的代码示例:
```python
import numpy as np
# 定义sigmoid函数
def sigmoid(x):
return 1 / (1 + np.exp(-x))
# 初始化参数
def initialize_parameters(layer_dims):
parameters = {}
L = len(layer_dims)
for l in range(1, L):
parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) * 0.01
parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))
return parameters
# 前向传播
def forward_propagation(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for l in range(1, L):
Z = np.dot(parameters['W' + str(l)], A) + parameters['b' + str(l)]
A = sigmoid(Z)
caches.append((Z, A))
ZL = np.dot(parameters['W' + str(L)], A) + parameters['b' + str(L)]
AL = sigmoid(ZL)
caches.append((ZL, AL))
return AL, caches
# 计算损失
def compute_cost(AL, Y):
m = Y.shape
cost = -np.sum(Y * np.log(AL) + (1 - Y) * np.log(1 - AL)) / m
cost = np.squeeze(cost)
return cost
# 反向传播
def backward_propagation(AL, Y, caches):
grads = {}
L = len(caches)
m = AL.shape
Y = Y.reshape(AL.shape)
dAL = - (np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
dZL = dAL * sigmoid(caches[L-1]) * (1 - sigmoid(caches[L-1]))
grads['dW' + str(L)] = np.dot(dZL, caches[L-1].T) / m
grads['db' + str(L)] = np.sum(dZL, axis=1, keepdims=True) / m
for l in reversed(range(L-1)):
dA = np.dot(parameters['W' + str(l+2)].T, dZ)
dZ = dA * sigmoid(caches[l]) * (1 - sigmoid(caches[l]))
grads['dW' + str(l+1)] = np.dot(dZ, caches[l].T) / m
grads['db' + str(l+1)] = np.sum(dZ, axis=1, keepdims=True) / m
return grads
# 更新参数
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2
for l in range(L):
parameters['W' + str(l+1)] -= learning_rate * grads['dW' + str(l+1)]
parameters['b' + str(l+1)] -= learning_rate * grads['db' + str(l+1)]
return parameters
# 定义前馈神经网络模型
def model(X, Y, layer_dims, learning_rate, num_iterations):
parameters = initialize_parameters(layer_dims)
for i in range(num_iterations):
AL, caches = forward_propagation(X, parameters)
cost = compute_cost(AL, Y)
grads = backward_propagation(AL, Y, caches)
parameters = update_parameters(parameters, grads, learning_rate)
if i % 100 == 0:
print("Cost after iteration {}: {}".format(i, cost))
return parameters
# 示例数据
X = np.array([[0, 0, 1, 1], [0, 1, 0, 1]])
Y = np.array([[0, 1, 1, 0]])
# 定义神经网络结构
layer_dims = [2, 4, 1]
# 训练模型
parameters = model(X, Y, layer_dims, learning_rate=0.01, num_iterations=1000)
```
这段代码实现了一个简单的前馈神经网络,其中使用了sigmoid函数作为激活函数。你可以根据自己的需求进行修改和扩展。希望对你有帮助!
rbf 遗传算法代码
由于RBF(径向基函数)网络的训练需要遗传算法来优化权值和偏置,因此以下是一个简单的RBF网络遗传算法的Python代码示例:
```
import numpy as np
import random
# 初始化参数
num_inputs = 2
num_hidden = 4
num_outputs = 1
population_size = 20
num_generations = 100
mutation_rate = 0.1
crossover_rate = 0.8
# 定义RBF网络类
class RBFNetwork:
def __init__(self, num_inputs, num_hidden, num_outputs):
self.num_inputs = num_inputs
self.num_hidden = num_hidden
self.num_outputs = num_outputs
self.hidden_weights = np.random.rand(num_inputs, num_hidden)
self.hidden_biases = np.random.rand(num_hidden)
self.output_weights = np.random.rand(num_hidden, num_outputs)
self.output_biases = np.random.rand(num_outputs)
def sigmoid(self, x):
return 1 / (1 + np.exp(-x))
def forward(self, inputs):
hidden_inputs = np.dot(inputs, self.hidden_weights) + self.hidden_biases
hidden_outputs = self.sigmoid(hidden_inputs)
output_inputs = np.dot(hidden_outputs, self.output_weights) + self.output_biases
output = self.sigmoid(output_inputs)
return output
# 定义遗传算法类
class GeneticAlgorithm:
def __init__(self, population_size, num_genes):
self.population_size = population_size
self.num_genes = num_genes
self.population = np.random.rand(population_size, num_genes)
def fitness(self, individual):
# 转换为网络的参数
hidden_weights = individual[:num_inputs*num_hidden].reshape(num_inputs, num_hidden)
hidden_biases = individual[num_inputs*num_hidden:num_inputs*num_hidden+num_hidden]
output_weights = individual[num_inputs*num_hidden+num_hidden:num_inputs*num_hidden+num_hidden+num_hidden*num_outputs].reshape(num_hidden, num_outputs)
output_biases = individual[-num_outputs:]
# 初始化RBF网络
network = RBFNetwork(num_inputs, num_hidden, num_outputs)
network.hidden_weights = hidden_weights
network.hidden_biases = hidden_biases
network.output_weights = output_weights
network.output_biases = output_biases
# 计算损失函数(MSE)
inputs = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
targets = np.array([[0], [1], [1], [0]])
outputs = np.array([network.forward(input) for input in inputs])
loss = np.mean((outputs - targets) ** 2)
# 计算适应度(倒数)
fitness = 1 / (loss + 1e-6)
return fitness
def selection(self, fitnesses):
# 选择2个最优个体
indices = np.argsort(fitnesses)[::-1][:2]
parents = self.population[indices]
return parents
def crossover(self, parents):
# 单点交叉
child = np.zeros(self.num_genes)
if random.random() < crossover_rate:
crossover_point = random.randint(1, self.num_genes-1)
child[:crossover_point] = parents[0][:crossover_point]
child[crossover_point:] = parents[1][crossover_point:]
else:
child = parents[0]
return child
def mutation(self, child):
# 随机突变
for i in range(self.num_genes):
if random.random() < mutation_rate:
child[i] += np.random.randn() * 0.1
return child
def evolve(self):
fitnesses = np.array([self.fitness(individual) for individual in self.population])
parents = self.selection(fitnesses)
children = [self.crossover(parents) for _ in range(self.population_size-2)]
children = [self.mutation(child) for child in children]
self.population = np.vstack((parents, children))
# 初始化遗传算法
ga = GeneticAlgorithm(population_size, num_inputs*num_hidden+num_hidden+num_hidden*num_outputs+num_outputs)
# 训练网络
for _ in range(num_generations):
ga.evolve()
best_individual = ga.population[np.argmax([ga.fitness(individual) for individual in ga.population])]
# 输出结果
hidden_weights = best_individual[:num_inputs*num_hidden].reshape(num_inputs, num_hidden)
hidden_biases = best_individual[num_inputs*num_hidden:num_inputs*num_hidden+num_hidden]
output_weights = best_individual[num_inputs*num_hidden+num_hidden:num_inputs*num_hidden+num_hidden+num_hidden*num_outputs].reshape(num_hidden, num_outputs)
output_biases = best_individual[-num_outputs:]
network = RBFNetwork(num_inputs, num_hidden, num_outputs)
network.hidden_weights = hidden_weights
network.hidden_biases = hidden_biases
network.output_weights = output_weights
network.output_biases = output_biases
inputs = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
outputs = np.array([network.forward(input) for input in inputs])
print(outputs)
```
请注意,上述代码中的RBF网络只使用了1个隐藏层和1个输出层。如果需要更复杂的网络,可以增加隐藏层和输出层的数量,并相应地调整遗传算法的参数。此外,为了简化代码,此示例并未使用优化算法(如梯度下降)来训练RBF网络,而是直接计算损失函数和适应度。在实际应用中,建议使用更高级的优化算法来训练网络。
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