This package contains helper functions for working with scipy’s pairwise distance (pdist) functions in scikit-bio, and will eventually be expanded to contain pairwise distance/dissimilarity methods that are not implemented (or planned to be implemented) in scipy.
The functions in this package currently support applying pdist functions to all pairs of samples in a sample by observation count or abundance matrix and returning an skbio.DistanceMatrix object. This application is illustrated below for a few different forms of input.
| pw_distances(counts[, ids, metric]) | Compute distances between all pairs of columns in a counts matrix |
| pw_distances_from_table(table[, metric]) | Compute distances between all pairs of samples in table |
Create a table object containing 7 OTUs and 6 samples.
>>> from skbio.math.diversity.beta import pw_distances
>>> import numpy as np
>>> data = [[23, 64, 14, 0, 0, 3, 1],
... [0, 3, 35, 42, 0, 12, 1],
... [0, 5, 5, 0, 40, 40, 0],
... [44, 35, 9, 0, 1, 0, 0],
... [0, 2, 8, 0, 35, 45, 1],
... [0, 0, 25, 35, 0, 19, 0]]
>>> ids = list('ABCDEF')
Compute Bray-Curtis distances between all pairs of samples and return a DistanceMatrix object.
>>> bc_dm = pw_distances(data, ids, "braycurtis")
>>> print(bc_dm)
6x6 distance matrix
IDs:
A, B, C, D, E, F
Data:
[[ 0. 0.78787879 0.86666667 0.30927835 0.85714286 0.81521739]
[ 0.78787879 0. 0.78142077 0.86813187 0.75 0.1627907 ]
[ 0.86666667 0.78142077 0. 0.87709497 0.09392265 0.71597633]
[ 0.30927835 0.86813187 0.87709497 0. 0.87777778 0.89285714]
[ 0.85714286 0.75 0.09392265 0.87777778 0. 0.68235294]
[ 0.81521739 0.1627907 0.71597633 0.89285714 0.68235294 0. ]]
Compute Jaccard distances between all pairs of samples and return a DistanceMatrix object.
>>> j_dm = pw_distances(data, ids, "jaccard")
>>> print(j_dm)
6x6 distance matrix
IDs:
A, B, C, D, E, F
Data:
[[ 0. 0.83333333 1. 1. 0.83333333 1. ]
[ 0.83333333 0. 1. 1. 0.83333333 1. ]
[ 1. 1. 0. 1. 1. 1. ]
[ 1. 1. 1. 0. 1. 1. ]
[ 0.83333333 0.83333333 1. 1. 0. 1. ]
[ 1. 1. 1. 1. 1. 0. ]]
Determine if the resulting distance matrices are significantly correlated by computing the Mantel correlation between them. Then determine if the p-value is significant based on an alpha of 0.05.
>>> from skbio.math.stats.distance import mantel
>>> r, p_value = mantel(j_dm, bc_dm)
>>> print(r)
-0.209362157621
>>> print(p_value < 0.05)
False
Compute PCoA for both distance matrices, and then find the Procrustes M-squared value that results from comparing the coordinate matrices.
>>> from skbio.math.stats.ordination import PCoA
>>> bc_pc = PCoA(bc_dm).scores()
>>> j_pc = PCoA(j_dm).scores()
>>> from skbio.math.stats.spatial import procrustes
>>> print procrustes(bc_pc.site, j_pc.site)[2]
0.466134984787