scipy.spatial 距离计算模块

在scipy.spatial中最重要的模块应该就是距离计算模块distance了。

from scipy import spatial

距离计算

矩阵距离计算函数

矩阵参数每行代表一个观测值，计算结果就是每行之间的metric距离。Distance matrix computation from a collection of raw observation vectors stored in a rectangular array.

向量距离计算函数Distance functions between two vectors u and v

Distance functions between two vectors u and v. Computingdistances over a large collection of vectors is inefficient for thesefunctions. Use pdist for this purpose.

输入的参数应该是向量，也就是维度应该是(n, )，当然也可以是(1, n)它会使用squeeze自动去掉维度为1的维度；但是如果是多维向量，至少有两个维度>1就会出错。

e.g. spatial.distance.correlation(u, v)    #计算向量u和v之间的相关系数（pearson correlation coefficient, Centered Cosine）

Note: 如果向量u和v元素数目都只有一个或者某个向量中所有元素相同（分母norm(u - u.mean())为0），那么相关系数当然计算无效，会返回nan。

braycurtis(u, v)Computes the Bray-Curtis distance between two 1-D arrays.canberra(u, v)Computes the Canberra distance between two 1-D arrays.chebyshev(u, v)Computes the Chebyshev distance.cityblock(u, v)Computes the City Block (Manhattan) distance.correlation(u, v)Computes the correlation distance between two 1-D arrays.cosine(u, v)Computes the Cosine distance between 1-D arrays.dice(u, v)Computes the Dice dissimilarity between two boolean 1-D arrays.euclidean(u, v)Computes the Euclidean distance between two 1-D arrays.hamming(u, v)Computes the Hamming distance between two 1-D arrays.jaccard(u, v)Computes the Jaccard-Needham dissimilarity between two boolean 1-D arrays.kulsinski(u, v)Computes the Kulsinski dissimilarity between two boolean 1-D arrays.mahalanobis(u, v, VI)Computes the Mahalanobis distance between two 1-D arrays.matching(u, v)Computes the Matching dissimilarity between two boolean 1-D arrays.minkowski(u, v, p)Computes the Minkowski distance between two 1-D arrays.rogerstanimoto(u, v)Computes the Rogers-Tanimoto dissimilarity between two boolean 1-D arrays.russellrao(u, v)Computes the Russell-Rao dissimilarity between two boolean 1-D arrays.seuclidean(u, v, V)Returns the standardized Euclidean distance between two 1-D arrays.sokalmichener(u, v)Computes the Sokal-Michener dissimilarity between two boolean 1-D arrays.sokalsneath(u, v)Computes the Sokal-Sneath dissimilarity between two boolean 1-D arrays.sqeuclidean(u, v)Computes the squared Euclidean distance between two 1-D arrays.wminkowski(u, v, p, w)Computes the weighted Minkowski distance between two 1-D arrays.yule(u, v)Computes the Yule dissimilarity between two boolean 1-D arrays.[距离和相似度计算 ]

scipy.spatial.distance.pdist(X, metric=’euclidean’, p=2, w=None, V=None, VI=None)

pdist(X[, metric, p, w, V, VI])Pairwise distances between observations in n-dimensional space.观测值（n维）两两之间的距离。Pairwise distances between observations in n-dimensional space.距离值越大，相关度越小。

注意，距离转换成相似度时，由于自己和自己的距离是不会计算的默认为0，所以要先通过dist = spatial.distance.squareform(dist)转换成dense矩阵，再通过1 - dist计算相似度。

metric：

1 距离计算可以使用自己写的函数。Y = pdist(X, f) Computes the distance between all pairs of vectors in Xusing the user supplied 2-arity function f.

如欧式距离计算可以这样：

dm = pdist(X, lambda u, v: np.sqrt(((u-v)**2).sum()))

但是如果scipy库中有相应的距离计算函数的话，就不要使用dm = pdist(X, sokalsneath)这种方式计算，sokalsneath调用的是python自带的函数，会调用c(n, 2)次；而应该使用scipy中的optimized C version，使用dm = pdist(X, 'sokalsneath')。

再如矩阵行之间的所有cause effect值的计算可以这样：

def causal_effect(m):    effect = lambda u, v: u.dot(v) / sum(u) - (1 - u).dot(v) / sum(1 - u)    return spatial.distance.squareform(spatial.distance.pdist(m, metric=effect))

2 这里计算的是两两之间的距离，而不是相似度，如计算cosine距离后要用1-cosine才能得到相似度。从下面的consine计算公式就可以看出。

Y = pdist(X, ’euclidean’)    #d=sqrt((x1-x2)^2+(y1-y2)^2+(z1-z2)^2)

Y = pdist(X, ’minkowski’, p)

scipy.spatial.distance.cdist(XA, XB, metric=’euclidean’, p=2, V=None, VI=None, w=None)

cdist(XA, XB[, metric, p, V, VI, w])Computes distance between each pair of the two collections of inputs.

当然XA\XB最简单的形式是一个二维向量（也必须是，否则报错ValueError: XA must be a 2-dimensional array.），计算的就是两个向量之间的metric距离度量。

scipy.spatial.distance.squareform(X, force=’no’, checks=True)

squareform(X[, force, checks])Converts a vector-form distance vector to a square-form distance matrix, and vice-versa.

将向量形式的距离表示转换成dense矩阵形式。Converts a vector-form distance vector to a square-form distance matrix, and vice-versa.

注意：Distance matrix 'X' must be symmetric&diagonal must be zero.