dtaidistance 笔记：相似度&压缩

UQI-LIUWJ2023-12-06 10:37

1 相似度

相似度：1表示相等，0表示疏远

给定一组时间序列（每一行是一个），计算基于DTW的逐对相似度

python 复制代码

from dtaidistance import dtw, similarity
s = np.array([[0., 0, 1, 2, 1, 0, 1, 0, 0],
              [0., 1, 2, 0, 0, 0, 0, 0, 0],
              [1., 2, 0, 0, 0, 0, 0, 1, 1],
              [0., 0, 1, 2, 1, 0, 1, 0, 0],
              [0., 1, 2, 0, 0, 0, 0, 0, 0],
              [1., 2, 0, 0, 0, 0, 0, 1, 1]])
dis_matrix=dtw.distance_matrix(s)
dis_matrix
'''
array([[0.        , 1.41421356, 2.23606798, 0.        , 1.41421356,
        2.23606798],
       [1.41421356, 0.        , 1.73205081, 1.41421356, 0.        ,
        1.73205081],
       [2.23606798, 1.73205081, 0.        , 2.23606798, 1.73205081,
        0.        ],
       [0.        , 1.41421356, 2.23606798, 0.        , 1.41421356,
        2.23606798],
       [1.41421356, 0.        , 1.73205081, 1.41421356, 0.        ,
        1.73205081],
       [2.23606798, 1.73205081, 0.        , 2.23606798, 1.73205081,
        0.        ]])
'''


sim_matrix=similarity.distance_to_similarity(dis_matrix)
sim_matrix
'''
array([[1.        , 0.53128561, 0.36787944, 1.        , 0.53128561,
        0.36787944],
       [0.53128561, 1.        , 0.46088963, 0.53128561, 1.        ,
        0.46088963],
       [0.36787944, 0.46088963, 1.        , 0.36787944, 0.46088963,
        1.        ],
       [1.        , 0.53128561, 0.36787944, 1.        , 0.53128561,
        0.36787944],
       [0.53128561, 1.        , 0.46088963, 0.53128561, 1.        ,
        0.46088963],
       [0.36787944, 0.46088963, 1.        , 0.36787944, 0.46088963,
        1.        ]])
'''

2 压缩

相似性将高值反转为低值，低值反转为高值。如果要保持方向但将距离压缩到0到1之间，可以使用squash函数

python 复制代码

sq_matrix=similarity.squash(dis_matrix)
sq_matrix
'''
array([[1.        , 0.53128561, 0.36787944, 1.        , 0.53128561,
        0.36787944],
       [0.53128561, 1.        , 0.46088963, 0.53128561, 1.        ,
        0.46088963],
       [0.36787944, 0.46088963, 1.        , 0.36787944, 0.46088963,
        1.        ],
       [1.        , 0.53128561, 0.36787944, 1.        , 0.53128561,
        0.36787944],
       [0.53128561, 1.        , 0.46088963, 0.53128561, 1.        ,
        0.46088963],
       [0.36787944, 0.46088963, 1.        , 0.36787944, 0.46088963,
        1.        ]])
'''