In [1]:
import numpy as np
import matplotlib.pyplot as plt
from Util import gen_five_clusters, visualize2d
class MultiPerceptron:
def __init__(self):
# 注意这里的 self._w 将来会是（n x K 的）矩阵
self._w = None
def fit(self, x, y, lr=1e-3, epoch=1000):
x, y = np.asarray(x, np.float32), np.asarray(y, np.float32)
# x.shape[1] 即为 n、y.shape[1] 即为 K
self._w = np.zeros([x.shape[1], y.shape[1]])
for _ in range(epoch):
# 依公式进行梯度下降
y_pred = x.dot(self._w)
dw = 2 * x.T.dot(y_pred - y)
self._w -= lr * dw
def predict(self, x):
# 依公式计算模型输出向量
y_pred = np.asarray(x, np.float32).dot(self._w)
# 预测类别时对输出的 K 维向量用 argmax 即可
return np.argmax(y_pred, axis=1).astype(np.float32)
In [2]:
x, y = gen_five_clusters()
label = np.argmax(y, axis=1)
perceptron = MultiPerceptron()
perceptron.fit(x, y)
visualize2d(perceptron, x, label, draw_background=True)
print("准确率：{:8.6} %".format((perceptron.predict(x) == label).mean() * 100))
In [3]:
class NaiveNN:
def __init__(self, ws=None):
# 这里的 self._ws 将会是一个存储着两个权值矩阵的列表
self._ws = ws
@staticmethod
def relu(x):
# 利用 numpy 相应函数直接写出 ReLU 的实现
return np.maximum(0, x)
# hidden_dim 即为隐藏层神经元个数 m
def fit(self, x, y, hidden_dim=4, lr=1e-3, epoch=1000):
input_dim, output_dim = x.shape[1], y.shape[1]
if self._ws is None:
# 随机初始化权值矩阵
self._ws = [
np.random.random([input_dim, hidden_dim]),
np.random.random([hidden_dim, output_dim])
]
# 定义一个列表存储训练过程中的损失
losses = []
for _ in range(epoch):
# 依公式算出各个值
h = x.dot(self._ws[0]); h_relu = NaiveNN.relu(h)
y_pred = h_relu.dot(self._ws[1])
# 利用 np.linalg.norm 算出损失
losses.append(np.linalg.norm(y_pred - y, ord="fro"))
# 依公式算出各个梯度
d1 = 2 * (y_pred - y)
dw2 = h_relu.T.dot(d1)
dw1 = x.T.dot(d1.dot(self._ws[1].T) * (h_relu != 0))
# 走一步梯度下降
self._ws[0] -= lr * dw1; self._ws[1] -= lr * dw2
# 把诸模型损失返回
return losses
def predict(self, x):
h = x.dot(self._ws[0]); h_relu = NaiveNN.relu(h)
# 用 argmax 预测类别
return np.argmax(h_relu.dot(self._ws[1]), axis=1)
In [4]:
x, y = gen_five_clusters()
label = np.argmax(y, axis=1)
nn = NaiveNN()
losses = nn.fit(x, y, 32, 1e-5)
visualize2d(nn, x, label, draw_background=True)
print("准确率：{:8.6} %".format((nn.predict(x) == label).mean() * 100))
plt.figure()
plt.plot(np.arange(1, len(losses)+1), losses)
plt.show()
In [5]:
class NN:
def __init__(self, ws=None):
self._ws = ws
@staticmethod
def relu(x):
return np.maximum(0, x)
@staticmethod
def softmax(x):
exp_x = np.exp(x - np.max(x, axis=1, keepdims=True))
return exp_x / np.sum(exp_x, axis=1, keepdims=True)
@staticmethod
def cross_entropy(y_pred, y_true):
return -np.average(
y * np.log(np.maximum(y_pred, 1e-12)) +
(1 - y) * np.log(np.maximum(1 - y_pred, 1e-12))
)
def fit(self, x, y, hidden_dim=4, lr=1e-3, epoch=1000):
input_dim, output_dim = x.shape[1], y.shape[1]
if self._ws is None:
self._ws = [
np.random.random([input_dim, hidden_dim]),
np.random.random([hidden_dim, output_dim])
]
losses = []
for _ in range(epoch):
h = x.dot(self._ws[0]); h_relu = NN.relu(h)
y_pred = NN.softmax(h_relu.dot(self._ws[1]))
losses.append(NN.cross_entropy(y_pred, y))
d1 = y_pred - y
dw2 = h_relu.T.dot(d1)
dw1 = x.T.dot(d1.dot(self._ws[1].T) * (h_relu != 0))
self._ws[0] -= lr * dw1; self._ws[1] -= lr * dw2
return losses
def predict(self, x):
h = x.dot(self._ws[0]); h_relu = NaiveNN.relu(h)
# 由于 Softmax 不影响 argmax 的结果，所以这里直接 argmax 即可
return np.argmax(h_relu.dot(self._ws[1]), axis=1)
In [6]:
nn = NN()
losses = nn.fit(x, y, 32, 1e-4)
visualize2d(nn, x, label, draw_background=True)
print("准确率：{:8.6} %".format((nn.predict(x) == label).mean() * 100))
plt.figure()
plt.plot(np.arange(1, len(losses)+1), losses)
plt.show()