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

---

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

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.        ]])
'''