def stop_grad_ascent(data: np.mat, label: np.mat, k: int, max_iter: int,
alpha: float) -> (float, np.mat, np.mat):
"""利用随机梯度下降法训练FM模型
:param data: 数据特征
:param label: 标签
:param k: v的维度
:param max_iter: 最大迭代次数
:param alpha: 学习率
:return: w0,w,v权重
"""
m, n = np.shape(data)
w = np.random.randn(n).reshape((n, 1))
w0 = 0
v = initialize_v(n, k)
for it in range(max_iter):
for x in range(m):
inter_1 = data[x] * v
inter_2 = np.multiply(data[x], data[x]) * np.multiply(v, v)
inter = np.sum(np.multiply(inter_1, inter_1) - inter_2) / 2.
p = w0 + data[x] * w + inter
loss = sigmoid(label[x] * p[0, 0]) - 1
w0 -= alpha * loss * label[x]
for i in range(n):
if data[x, i] != 0:
w[i, 0] -= alpha * loss * label[x] * data[x, i]
for j in range(k):
v[i, j] -= alpha * loss * label[x] * (
data[x, i] * inter_1[0, j] -
v[i, j] * data[x, i] * data[x, i])
if it % 100 == 0:
pre = get_prediction(np.mat(data), w0, w, v)
print(get_cost(np.mat(pre), label))
return w0, w, v
def get_prediction(data, w0, w, v):
"""预测值
:param data:特征
:param w0:一次项权重
:param w:常数项权重
:param v:交叉项权重
:return:预测结果
"""
m = np.shape(data)[0]
result = []
for x in range(m):
inter_1 = data[x] * v
inter_2 = np.multiply(data[x], data[x]) * np.multiply(v, v)
inter = np.sum(np.multiply(inter_1, inter_1) - inter_2) / 2.
p = w0 + data[x] * w + inter
pre = sigmoid(p[0, 0])
result.append(pre)
return result
def lr_train_bgd(feature: np.array, label: np.array, max_cycle: int,
alpha: float) -> np.mat:
"""利用梯度下降法训练逻辑回归模型（LR）
:param feature:特征
:param label:标签
:param max_cycle:最大迭代次数
:param alpha:学习率
:return:w的权重
"""
n = np.shape(feature)[1] # 特征个数
w = np.random.rand(n).reshape((n, 1)) # 随机初始化权重
i = 0
while i <= max_cycle:
i += 1
h = sigmoid(np.dot(feature, w)) # 做点乘，计算sigmoid值
err = label - h # 误差
if i % 100 == 0:
print(f'error rate: {error_rate(h, label)}')
w += alpha * np.dot(feature.T, err) # wi+ 1= wi+ α·d 梯度下降进行权重修正
return w
def lr_train_bgd(feature: np.array, label: np.array, max_cycle: int,
alpha: float) -> np.mat:
"""利用梯度下降法训练逻辑回归模型（LR）
:param feature:特征
:param label:标签
:param max_cycle:最大迭代次数
:param alpha:学习率
:return:w的权重
"""
n = np.shape(feature)[1] # 特征个数
w = np.random.rand(n).reshape((n, 1)) # 随机初始化权重
i = 0
while i <= max_cycle:
i += 1
h = sigmoid(np.dot(feature, w)) # 做点乘，计算sigmoid值
err = label - h # 误差
if i % 100 == 0:
print(f'error rate: {error_rate(h, label)}')
w += alpha * np.dot(feature.T, err) # wi+ 1= wi+ α·d 梯度下降进行权重修正
return w
if __name__ == '__main__':
weight = lr_train_bgd(TRAIN_DATA, TEST_LABEL, 2000, 0.01)
print(
sigmoid(
np.dot(np.array([[1, 1 / 24, 10 / 60, 32 / 60]], dtype=np.float),
weight)))