def mini_banch_SGD(matX, matY, cf):
'''
function:批量随机梯度下降
:param matX:
:param matY:
:return:
'''
count = 0 # 当前迭代次数
matA = np.random.randn(cf.k)
old_matA = matA
# 确认最小梯度
if cf.n/10 > 1:
least_banch = int(cf.n/10)
else:
least_banch = 1
while count < cf.loop_max:
sum_m = np.zeros(cf.k) # 记录一批数据的梯度差
count += 1
chosen = np.random.randint(0, cf.n, least_banch) # 生成随机数
for i in chosen:
# 计算梯度
diff = matX[i].dot(matX[i].dot(matA.T) - matY[i])
sum_m = sum_m + diff # 计算梯度和
sum_m = sum_m/len(chosen)
if np.linalg.norm(sum_m) < cf.epsilon:
break
# 带有正则化的loss
matA = matA*(1-cf.theta*cf.alpha/len(chosen)) - cf.alpha*sum_m
# 提前结束
if np.linalg.norm(matA - old_matA) < cf.epsilon:
break
old_matA = matA
print('count=', count, 'loss=', function.RMSE(matX, matY, matA))
return matA
def SGD(matX, matY, cf):
count = 0 # 当前迭代次数
matA = np.zeros(cf.k)
old_matA = matA
while count < cf.loop_max:
count += 1
for i in range(cf.n):
# 计算梯度
diff = matX[i].dot(matX[i].dot(matA.T) - matY[i])
# 带有正则化的loss
matA = matA * (1 - cf.theta * cf.alpha) - cf.alpha * diff
# 提前结束
if np.linalg.norm(matA-old_matA) < cf.epsilon:
break
old_matA = matA
print('count=',count,'loss=',function.RMSE(matX,matY,matA))
return matA
def fitting(matX,matY,cf):
#计算X.T*X
squareX = np.dot(matX.T, matX)
invX = np.linalg.inv(squareX)
MatA = (invX.dot(matX.T)).dot(matY)
return MatA
# 加入正则化的最小二乘法
def fittingRegular(matX,matY,cf):
#计算X.T*X+NRI
squareX = np.dot(matX.T, matX) + cf.n*cf.theta*np.eye(cf.k, cf.k)
invX = np.linalg.inv(squareX)
MatA = (invX.dot(matX.T)).dot(matY)
return MatA
if __name__ == '__main__':
cf = function.config(-20, 20, 200, 25, 3e-7, 150000, 1e-20, 0.0)
x,y = function.create_data(cf.x0, cf.x1, cf.n)
#print(x,y)
matX, matY = function.create_mat(x,y,cf.k)
#print(matX)
#print(matY)
#print(matA)
matA = fitting(matX,matY,cf)
#print(matA)
err = function.RMSE(matX,matY,matA)
print(err)
plt.title('Least Squares with Regular')
function.show(x,y,matX, matA)
# 梯度下降法，无正则项
cf.theta = 0
matA3 = gd.SGD(matX, matY, cf)
# 梯度下降法，有正则项
cf.theta = 0.3
matA4 = gd.SGD(matX, matY, cf)
# 共轭梯度法
matA5 = cg.CG(matX, matY, cf)
plt.plot(x, y, color='b', linestyle='', marker='.')
plt.plot(x, matX.dot(matA1), color='R', linestyle='-', marker='', label='least squares')
plt.plot(x, matX.dot(matA2), color='b', linestyle='-', marker='', label='least squares with regular')
plt.plot(x, matX.dot(matA3), color='c', linestyle='-', marker='', label='gradient descent')
plt.plot(x, matX.dot(matA4), color='m', linestyle='-', marker='', label='gradient descent with regular')
plt.plot(x, matX.dot(matA5), color='g', linestyle='-', marker='', label='conjugate gradient')
plt.legend(loc='upper right')
print('least squares =', function.RMSE(matX,matY,matA1))
print('least squares with regular =', function.RMSE(matX, matY, matA2))
print('gradient descent =', function.RMSE(matX, matY, matA3))
print('gradient descent with regular =', function.RMSE(matX, matY, matA4))
print('conjugate gradient =', function.RMSE(matX, matY, matA5))
plt.show()