import numpy as np def mlwf(alpha, beta, t_i, t_j): g = abs(int(t_i) - int(t_j)) a = -alpha * (g - beta) exp = math.exp(a) omaga = 1 / (1 + exp) return omaga def dtw_mahalanobis(s1, s2): s1, s2 = np.array(s1), np.array(s2) n1, n2 = len(s1), len(s2) d = np.zeros((n1 + 1, n2 + 1)) d[1:, 0] = np.inf d[0, 1:] = np.inf # 计算样本的协方差矩阵 X = np.vstack([s1, s2]) S = np.cov(X.T) S_inv = np.linalg.inv(S) for i in range(1, n1 + 1): for j in range(1, n2 + 1): cost = mahalanobis(s1[i - 1], s2[j - 1], S_inv) d[i, j] = cost + min(d[i - 1, j], d[i, j - 1], d[i - 1, j - 1]) return d[n1, n2] def mahalanobis(x, y, S_inv): diff = x - y return np.sqrt(np.dot(np.dot(diff, S_inv), diff.T)) s1=[[7,9,11,12,8],[6,8,9,11,13],[7,10,13,10,7]] s2 = [[7,8,11,10,9],[9,8,7,14,13],[8,10,8,10,9]] s3 = [[7,9,15,14,9],[9,8,8,14,3],[8,11,8,15,9]] result1 = dtw_mahalanobis(s1, s2) result2 = dtw_mahalanobis(s1, s3) print(result1) print(result2)如何将代码时间权重融入其中

要将时间权重融入DTW算法中，可以在计算距离矩阵时，在每个时间点的距离值上乘以时间权重系数。具体实现方式如下：

1. 在计算距离矩阵之前，先计算出每个时间点的时间权重系数，可以使用mlwf函数来计算。

2. 在计算距离矩阵时，将每个时间点的距离值乘以其对应的时间权重系数，得到加权距离值。

3. 在计算DTW路径时，同样需要使用加权距离值来计算。具体实现方式可以参考DTW算法的标准实现。

下面是修改后的代码：

import numpy as np
import math

def mlwf(alpha, beta, t_i, t_j):
g = abs(int(t_i) - int(t_j))
a = -alpha * (g - beta)
exp = math.exp(a)
omaga = 1 / (1 + exp)
return omaga

def dtw_mahalanobis(s1, s2, alpha, beta):
s1, s2 = np.array(s1), np.array(s2)
n1, n2 = len(s1), len(s2)
d = np.zeros((n1 + 1, n2 + 1))
d[1:, 0] = np.inf
d[0, 1:] = np.inf

# 计算样本的协方差矩阵
X = np.vstack([s1, s2])
S = np.cov(X.T)
S_inv = np.linalg.inv(S)

# 计算时间权重系数
w1 = np.zeros(n1)
w2 = np.zeros(n2)
for i in range(n1):
w1[i] = mlwf(alpha, beta, i, 0)
for j in range(n2):
w2[j] = mlwf(alpha, beta, 0, j)

for i in range(1, n1 + 1):
for j in range(1, n2 + 1):
cost = mahalanobis(s1[i - 1], s2[j - 1], S_inv)
# 计算加权距离值
cost *= w1[i-1] * w2[j-1]
d[i, j] = cost + min(d[i - 1, j], d[i, j - 1], d[i - 1, j - 1])

return d[n1, n2]

def mahalanobis(x, y, S_inv):
diff = x - y
return np.sqrt(np.dot(np.dot(diff, S_inv), diff.T))

s1=[[7,9,11,12,8],[6,8,9,11,13],[7,10,13,10,7]]
s2 = [[7,8,11,10,9],[9,8,7,14,13],[8,10,8,10,9]]
s3 = [[7,9,15,14,9],[9,8,8,14,3],[8,11,8,15,9]]

alpha = 0.5
beta = 2

result1 = dtw_mahalanobis(s1, s2, alpha, beta)
result2 = dtw_mahalanobis(s1, s3, alpha, beta)

print(result1)
print(result2)