scipy.cluster.hierarchy:标签的顺序似乎不正确，并且被垂直轴的值弄糊涂了 [英] scipy.cluster.hierarchy: labels seems not in the right order, and confused by the value of the vertical axes

问题描述

我知道 scipy.cluster.hierarchy 专注于处理距离矩阵.但是现在我有了一个相似度矩阵……在我使用树状图绘制它之后，发生了一些奇怪的事情.代码如下:

I know that scipy.cluster.hierarchy focused on dealing with the distance matrix. But now I have a similarity matrix... After I plot it by using Dendrogram, something weird just happens. Here is the code:

similarityMatrix = np.array(([1,0.75,0.75,0,0,0,0],
                         [0.75,1,1,0.25,0,0,0],
                         [0.75,1,1,0.25,0,0,0],
                         [0,0.25,0.25,1,0.25,0.25,0],
                         [0,0,0,0.25,1,1,0.75],
                         [0,0,0,0.25,1,1,0.75],
                         [0,0,0,0,0.75,0.75,1]))

这是链接方法

Z_sim = sch.linkage(similarityMatrix)
plt.figure(1)
plt.title('similarity')
sch.dendrogram(
    Z_sim,
    labels=['1','2','3','4','5','6','7']
)
plt.show()

但这是结果:

我的问题是:

1. 为什么这个树状图的标签不正确?
2. 我为链接方法提供了一个相似度矩阵，但我无法完全理解垂直轴的含义.比如最大相似度为1，为什么纵轴的最大值接近1.6?

非常感谢您的帮助！

推荐答案

• linkage 需要距离"，而不是相似性".要将您的矩阵转换为距离矩阵之类的东西，您可以将其从 1 中减去:

  • linkage expects "distances", not "similarities". To convert your matrix to something like a distance matrix, you can subtract it from 1:

    dist = 1 - similarityMatrix
    

  • 链接不接受平方距离矩阵.它期望距离数据采用压缩"形式.您可以使用 scipy.spatial.distance.squareform :

  • linkage does not accept a square distance matrix. It expects the distance data to be in "condensed" form. You can get that using scipy.spatial.distance.squareform:

    from scipy.spatial.distance import squareform
    
    dist = 1 - similarityMatrix
    condensed_dist = squareform(dist)
    Z_sim = sch.linkage(condensed_dist)
    

    (当您将形状为 (m, n) 的二维数组传递给 linkage 时，它会将行视为 n 维空间中的点，并在内部计算距离.)

  (When you pass a two-dimensional array with shape (m, n) to linkage, it treats the rows as points in n-dimensional space, and computes the distances internally.)

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