# This code is part of the Biopython distribution and governed by its
# license. Please see the LICENSE file that should have been included
# as part of this package.
#
"""Cluster Analysis.
The Bio.Cluster provides commonly used clustering algorithms and was
designed with the application to gene expression data in mind. However,
this module can also be used for cluster analysis of other types of data.
Bio.Cluster and the underlying C Clustering Library is described in
M. de Hoon et al. (2004) https://doi.org/10.1093/bioinformatics/bth078
"""
import numbers
try:
import numpy as np
except ImportError:
from Bio import MissingPythonDependencyError
raise MissingPythonDependencyError(
"Please install NumPy if you want to use Bio.Cluster. "
"See http://www.numpy.org/"
) from None
from . import _cluster # type: ignore
__all__ = (
"Node",
"Tree",
"kcluster",
"kmedoids",
"treecluster",
"somcluster",
"clusterdistance",
"clustercentroids",
"distancematrix",
"pca",
"Record",
"read",
)
__version__ = _cluster.version()
class Node(_cluster.Node):
"""Element of a hierarchical clustering tree.
A node contains items or other Nodes(sub-nodes).
"""
__doc__ = _cluster.Node.__doc__
class Tree(_cluster.Tree):
"""Hierarchical clustering tree.
A Tree consists of Nodes.
"""
def sort(self, order=None):
"""Sort the hierarchical clustering tree.
Sort the hierarchical clustering tree by switching the left and
right subnode of nodes such that the elements in the left-to-right
order of the tree tend to have increasing order values.
Return the indices of the elements in the left-to-right order in
the hierarchical clustering tree, such that the element with index
indices[i] occurs at position i in the dendrogram.
"""
n = len(self) + 1
indices = np.ones(n, dtype="intc")
if order is None:
order = np.ones(n, dtype="d")
elif isinstance(order, np.ndarray):
order = np.require(order, dtype="d", requirements="C")
else:
order = np.array(order, dtype="d")
_cluster.Tree.sort(self, indices, order)
return indices
def cut(self, nclusters=None):
"""Create clusters by cutting the hierarchical clustering tree.
Divide the elements in a hierarchical clustering result mytree
into clusters, and return an array with the number of the cluster
to which each element was assigned.
Keyword arguments:
- nclusters: The desired number of clusters.
"""
n = len(self) + 1
indices = np.ones(n, dtype="intc")
if nclusters is None:
nclusters = n
_cluster.Tree.cut(self, indices, nclusters)
return indices
def kcluster(
data,
nclusters=2,
mask=None,
weight=None,
transpose=False,
npass=1,
method="a",
dist="e",
initialid=None,
):
"""Perform k-means clustering.
This function performs k-means clustering on the values in data, and
returns the cluster assignments, the within-cluster sum of distances
of the optimal k-means clustering solution, and the number of times
the optimal solution was found.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
- nclusters: number of clusters (the 'k' in k-means).
- mask: nrows x ncolumns array of integers, showing which data
are missing. If mask[i,j]==0, then data[i,j] is missing.
- weight: the weights to be used when calculating distances
- transpose:
- if False: rows are clustered;
- if True: columns are clustered.
- npass: number of times the k-means clustering algorithm is
performed, each time with a different (random) initial
condition.
- method: specifies how the center of a cluster is found:
- method == 'a': arithmetic mean;
- method == 'm': median.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance;
- dist == 'b': City Block distance;
- dist == 'c': Pearson correlation;
- dist == 'a': absolute value of the correlation;
- dist == 'u': uncentered correlation;
- dist == 'x': absolute uncentered correlation;
- dist == 's': Spearman's rank correlation;
- dist == 'k': Kendall's tau.
- initialid: the initial clustering from which the algorithm
should start.
If initialid is None, the routine carries out npass
repetitions of the EM algorithm, each time starting from a
different random initial clustering. If initialid is given,
the routine carries out the EM algorithm only once, starting
from the given initial clustering and without randomizing the
order in which items are assigned to clusters (i.e., using
the same order as in the data matrix). In that case, the
k-means algorithm is fully deterministic.
Return values:
- clusterid: array containing the index of the cluster to which each
item was assigned in the best k-means clustering solution that was
found in the npass runs;
- error: the within-cluster sum of distances for the returned k-means
clustering solution;
- nfound: the number of times this solution was found.
"""
data = __check_data(data)
shape = data.shape
if transpose:
ndata, nitems = shape
else:
nitems, ndata = shape
mask = __check_mask(mask, shape)
weight = __check_weight(weight, ndata)
clusterid, npass = __check_initialid(initialid, npass, nitems)
error, nfound = _cluster.kcluster(
data, nclusters, mask, weight, transpose, npass, method, dist, clusterid
)
return clusterid, error, nfound
def kmedoids(distance, nclusters=2, npass=1, initialid=None):
"""Perform k-medoids clustering.
This function performs k-medoids clustering, and returns the cluster
assignments, the within-cluster sum of distances of the optimal
k-medoids clustering solution, and the number of times the optimal
solution was found.
Keyword arguments:
- distance: The distance matrix between the items. There are three
ways in which you can pass a distance matrix:
1. a 2D NumPy array (in which only the left-lower part of the array
will be accessed);
2. a 1D NumPy array containing the distances consecutively;
3. a list of rows containing the lower-triangular part of
the distance matrix.
Examples are:
>>> from numpy import array
>>> # option 1:
>>> distance = array([[0.0, 1.1, 2.3],
... [1.1, 0.0, 4.5],
... [2.3, 4.5, 0.0]])
>>> # option 2:
>>> distance = array([1.1, 2.3, 4.5])
>>> # option 3:
>>> distance = [array([]),
... array([1.1]),
... array([2.3, 4.5])]
These three correspond to the same distance matrix.
- nclusters: number of clusters (the 'k' in k-medoids)
- npass: the number of times the k-medoids clustering algorithm
is performed, each time with a different (random) initial
condition.
- initialid: the initial clustering from which the algorithm should start.
If initialid is not given, the routine carries out npass
repetitions of the EM algorithm, each time starting from a
different random initial clustering. If initialid is given,
the routine carries out the EM algorithm only once, starting
from the initial clustering specified by initialid and
without randomizing the order in which items are assigned to
clusters (i.e., using the same order as in the data matrix).
In that case, the k-medoids algorithm is fully deterministic.
Return values:
- clusterid: array containing the index of the cluster to which each
item was assigned in the best k-medoids clustering solution that was
found in the npass runs; note that the index of a cluster is the index
of the item that is the medoid of the cluster;
- error: the within-cluster sum of distances for the returned k-medoids
clustering solution;
- nfound: the number of times this solution was found.
"""
distance = __check_distancematrix(distance)
nitems = len(distance)
clusterid, npass = __check_initialid(initialid, npass, nitems)
error, nfound = _cluster.kmedoids(distance, nclusters, npass, clusterid)
return clusterid, error, nfound
[docs]def treecluster(
data,
mask=None,
weight=None,
transpose=False,
method="m",
dist="e",
distancematrix=None,
):
"""Perform hierarchical clustering, and return a Tree object.
This function implements the pairwise single, complete, centroid, and
average linkage hierarchical clustering methods.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
- mask: nrows x ncolumns array of integers, showing which data are
missing. If mask[i][j]==0, then data[i][j] is missing.
- weight: the weights to be used when calculating distances.
- transpose:
- if False, rows are clustered;
- if True, columns are clustered.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
- method: specifies which linkage method is used:
- method == 's': Single pairwise linkage
- method == 'm': Complete (maximum) pairwise linkage (default)
- method == 'c': Centroid linkage
- method == 'a': Average pairwise linkage
- distancematrix: The distance matrix between the items. There are
three ways in which you can pass a distance matrix:
1. a 2D NumPy array (in which only the left-lower part of the array
will be accessed);
2. a 1D NumPy array containing the distances consecutively;
3. a list of rows containing the lower-triangular part of
the distance matrix.
Examples are:
>>> from numpy import array
>>> # option 1:
>>> distance = array([[0.0, 1.1, 2.3],
... [1.1, 0.0, 4.5],
... [2.3, 4.5, 0.0]])
>>> # option 2:
>>> distance = array([1.1, 2.3, 4.5])
>>> # option 3:
>>> distance = [array([]),
... array([1.1]),
... array([2.3, 4.5])]
These three correspond to the same distance matrix.
PLEASE NOTE:
As the treecluster routine may shuffle the values in the
distance matrix as part of the clustering algorithm, be sure
to save this array in a different variable before calling
treecluster if you need it later.
Either data or distancematrix should be None. If distancematrix is None,
the hierarchical clustering solution is calculated from the values stored
in the argument data. If data is None, the hierarchical clustering solution
is instead calculated from the distance matrix. Pairwise centroid-linkage
clustering can be performed only from the data values and not from the
distance matrix. Pairwise single-, maximum-, and average-linkage clustering
can be calculated from the data values or from the distance matrix.
Return value:
treecluster returns a Tree object describing the hierarchical clustering
result. See the description of the Tree class for more information.
"""
if data is None and distancematrix is None:
raise ValueError("use either data or distancematrix")
if data is not None and distancematrix is not None:
raise ValueError("use either data or distancematrix; do not use both")
if data is not None:
data = __check_data(data)
shape = data.shape
ndata = shape[0] if transpose else shape[1]
mask = __check_mask(mask, shape)
weight = __check_weight(weight, ndata)
if distancematrix is not None:
distancematrix = __check_distancematrix(distancematrix)
if mask is not None:
raise ValueError("mask is ignored if distancematrix is used")
if weight is not None:
raise ValueError("weight is ignored if distancematrix is used")
tree = Tree()
_cluster.treecluster(
tree, data, mask, weight, transpose, method, dist, distancematrix
)
return tree
def somcluster(
data,
mask=None,
weight=None,
transpose=False,
nxgrid=2,
nygrid=1,
inittau=0.02,
niter=1,
dist="e",
):
"""Calculate a Self-Organizing Map.
This function implements a Self-Organizing Map on a rectangular grid.
Keyword arguments:
- data: nrows x ncolumns array containing the data values;
- mask: nrows x ncolumns array of integers, showing which data are
missing. If mask[i][j]==0, then data[i][j] is missing.
- weight: the weights to be used when calculating distances
- transpose:
- if False: rows are clustered;
- if True: columns are clustered.
- nxgrid: the horizontal dimension of the rectangular SOM map
- nygrid: the vertical dimension of the rectangular SOM map
- inittau: the initial value of tau (the neighborbood function)
- niter: the number of iterations
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
Return values:
- clusterid: array with two columns, with the number of rows equal to
the items that are being clustered. Each row in the array contains
the x and y coordinates of the cell in the rectangular SOM grid to
which the item was assigned.
- celldata: an array with dimensions [nxgrid, nygrid, number of columns]
if rows are being clustered, or [nxgrid, nygrid, number of rows) if
columns are being clustered.
Each element [ix, iy] of this array is a 1D vector containing the
data values for the centroid of the cluster in the SOM grid cell
with coordinates [ix, iy].
"""
if transpose:
ndata, nitems = data.shape
else:
nitems, ndata = data.shape
data = __check_data(data)
shape = data.shape
mask = __check_mask(mask, shape)
weight = __check_weight(weight, ndata)
if nxgrid < 1:
raise ValueError("nxgrid should be a positive integer (default is 2)")
if nygrid < 1:
raise ValueError("nygrid should be a positive integer (default is 1)")
clusterids = np.ones((nitems, 2), dtype="intc")
celldata = np.empty((nxgrid, nygrid, ndata), dtype="d")
_cluster.somcluster(
clusterids, celldata, data, mask, weight, transpose, inittau, niter, dist
)
return clusterids, celldata
def clusterdistance(
data,
mask=None,
weight=None,
index1=None,
index2=None,
method="a",
dist="e",
transpose=False,
):
"""Calculate and return the distance between two clusters.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
- mask: nrows x ncolumns array of integers, showing which data are
missing. If mask[i, j]==0, then data[i, j] is missing.
- weight: the weights to be used when calculating distances
- index1: 1D array identifying which items belong to the
first cluster. If the cluster contains only one item, then
index1 can also be written as a single integer.
- index2: 1D array identifying which items belong to the
second cluster. If the cluster contains only one item, then
index2 can also be written as a single integer.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
- method: specifies how the distance between two clusters is defined:
- method == 'a': the distance between the arithmetic means
of the two clusters
- method == 'm': the distance between the medians of the two clusters
- method == 's': the smallest pairwise distance between members
of the two clusters
- method == 'x': the largest pairwise distance between members
of the two clusters
- method == 'v': average of the pairwise distances between members
of the two clusters
- transpose:
- if False: clusters of rows are considered;
- if True: clusters of columns are considered.
"""
data = __check_data(data)
shape = data.shape
ndata = shape[0] if transpose else shape[1]
mask = __check_mask(mask, shape)
weight = __check_weight(weight, ndata)
index1 = __check_index(index1)
index2 = __check_index(index2)
return _cluster.clusterdistance(
data, mask, weight, index1, index2, method, dist, transpose
)
def clustercentroids(data, mask=None, clusterid=None, method="a", transpose=False):
"""Calculate and return the centroid of each cluster.
The clustercentroids routine calculates the cluster centroids, given to
which cluster each item belongs. The centroid is defined as either
the mean or the median over all items for each dimension.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
- mask: nrows x ncolumns array of integers, showing which data are
missing. If mask[i, j]==0, then data[i, j] is missing.
- clusterid: array containing the cluster number for each item.
The cluster number should be non-negative.
- method: specifies whether the centroid is calculated from the
arithmetic mean (method == 'a', default) or the median (method == 'm')
over each dimension.
- transpose: if False, each row contains the data for one item;
if True, each column contains the data for one item.
Return values:
- cdata: 2D array containing the cluster centroids.
If transpose is False, then the dimensions of cdata are
nclusters x ncolumns.
If transpose is True, then the dimensions of cdata are
nrows x nclusters.
- cmask: 2D array of integers describing which items in cdata,
if any, are missing.
"""
data = __check_data(data)
mask = __check_mask(mask, data.shape)
nrows, ncolumns = data.shape
if clusterid is None:
n = ncolumns if transpose else nrows
clusterid = np.zeros(n, dtype="intc")
nclusters = 1
else:
clusterid = np.require(clusterid, dtype="intc", requirements="C")
nclusters = max(clusterid + 1)
if transpose:
shape = (nrows, nclusters)
else:
shape = (nclusters, ncolumns)
cdata = np.zeros(shape, dtype="d")
cmask = np.zeros(shape, dtype="intc")
_cluster.clustercentroids(data, mask, clusterid, method, transpose, cdata, cmask)
return cdata, cmask
def distancematrix(data, mask=None, weight=None, transpose=False, dist="e"):
"""Calculate and return a distance matrix from the data.
This function returns the distance matrix calculated from the data.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
- mask: nrows x ncolumns array of integers, showing which data are
missing. If mask[i, j]==0, then data[i, j] is missing.
- weight: the weights to be used when calculating distances.
- transpose: if False: the distances between rows are calculated;
if True: the distances between columns are calculated.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
Return value:
The distance matrix is returned as a list of 1D arrays containing the
distance matrix calculated from the data. The number of columns in eac
row is equal to the row number. Hence, the first row has zero length.
For example:
>>> from numpy import array
>>> from Bio.Cluster import distancematrix
>>> data = array([[0, 1, 2, 3],
... [4, 5, 6, 7],
... [8, 9, 10, 11],
... [1, 2, 3, 4]])
>>> distances = distancematrix(data, dist='e')
>>> distances
[array([], dtype=float64), array([16.]), array([64., 16.]), array([ 1., 9., 49.])]
which can be rewritten as::
distances = [array([], dtype=float64),
array([ 16.]),
array([ 64., 16.]),
array([ 1., 9., 49.])]
This corresponds to the distance matrix::
[ 0., 16., 64., 1.]
[16., 0., 16., 9.]
[64., 16., 0., 49.]
[ 1., 9., 49., 0.]
"""
data = __check_data(data)
shape = data.shape
mask = __check_mask(mask, shape)
if transpose:
ndata, nitems = shape
else:
nitems, ndata = shape
weight = __check_weight(weight, ndata)
matrix = [np.empty(i, dtype="d") for i in range(nitems)]
_cluster.distancematrix(data, mask, weight, transpose, dist, matrix)
return matrix
def pca(data):
"""Perform principal component analysis.
Keyword arguments:
- data: nrows x ncolumns array containing the data values.
Return value:
This function returns an array containing the mean of each column, the
principal components as an nmin x ncolumns array, as well as the
coordinates (an nrows x nmin array) of the data along the principal
components, and the associated eigenvalues. The principal components, the
coordinates, and the eigenvalues are sorted by the magnitude of the
eigenvalue, with the largest eigenvalues appearing first. Here, nmin is
the smaller of nrows and ncolumns.
Adding the column means to the dot product of the coordinates and the
principal components recreates the data matrix:
>>> from numpy import array, dot, amax, amin
>>> from Bio.Cluster import pca
>>> matrix = array([[ 0., 0., 0.],
... [ 1., 0., 0.],
... [ 7., 3., 0.],
... [ 4., 2., 6.]])
>>> columnmean, coordinates, pc, _ = pca(matrix)
>>> m = matrix - (columnmean + dot(coordinates, pc))
>>> amax(m) < 1e-12 and amin(m) > -1e-12
True
"""
data = __check_data(data)
nrows, ncols = data.shape
nmin = min(nrows, ncols)
columnmean = np.empty(ncols, dtype="d")
pc = np.empty((nmin, ncols), dtype="d")
coordinates = np.empty((nrows, nmin), dtype="d")
eigenvalues = np.empty(nmin, dtype="d")
_cluster.pca(data, columnmean, coordinates, pc, eigenvalues)
return columnmean, coordinates, pc, eigenvalues
class Record:
"""Store gene expression data.
A Record stores the gene expression data and related information contained
in a data file following the file format defined for Michael Eisen's
Cluster/TreeView program.
Attributes:
- data: a matrix containing the gene expression data
- mask: a matrix containing only 1's and 0's, denoting which values
are present (1) or missing (0). If all items of mask are
one (no missing data), then mask is set to None.
- geneid: a list containing a unique identifier for each gene
(e.g., ORF name)
- genename: a list containing an additional description for each gene
(e.g., gene name)
- gweight: the weight to be used for each gene when calculating the
distance
- gorder: an array of real numbers indicating the preferred order of the
genes in the output file
- expid: a list containing a unique identifier for each sample.
- eweight: the weight to be used for each sample when calculating the
distance
- eorder: an array of real numbers indication the preferred order of the
samples in the output file
- uniqid: the string that was used instead of UNIQID in the input file.
"""
def __init__(self, handle=None):
"""Read gene expression data from the file handle and return a Record.
The file should be in the format defined for Michael Eisen's
Cluster/TreeView program.
"""
self.data = None
self.mask = None
self.geneid = None
self.genename = None
self.gweight = None
self.gorder = None
self.expid = None
self.eweight = None
self.eorder = None
self.uniqid = None
if not handle:
return
line = handle.readline().strip("\r\n").split("\t")
n = len(line)
self.uniqid = line[0]
self.expid = []
cols = {0: "GENEID"}
for word in line[1:]:
if word == "NAME":
cols[line.index(word)] = word
self.genename = []
elif word == "GWEIGHT":
cols[line.index(word)] = word
self.gweight = []
elif word == "GORDER":
cols[line.index(word)] = word
self.gorder = []
else:
self.expid.append(word)
self.geneid = []
self.data = []
self.mask = []
needmask = 0
for line in handle:
line = line.strip("\r\n").split("\t")
if len(line) != n:
raise ValueError(
"Line with %d columns found (expected %d)" % (len(line), n)
)
if line[0] == "EWEIGHT":
i = max(cols) + 1
self.eweight = np.array(line[i:], float)
continue
if line[0] == "EORDER":
i = max(cols) + 1
self.eorder = np.array(line[i:], float)
continue
rowdata = []
rowmask = []
n = len(line)
for i in range(n):
word = line[i]
if i in cols:
if cols[i] == "GENEID":
self.geneid.append(word)
if cols[i] == "NAME":
self.genename.append(word)
if cols[i] == "GWEIGHT":
self.gweight.append(float(word))
if cols[i] == "GORDER":
self.gorder.append(float(word))
continue
if not word:
rowdata.append(0.0)
rowmask.append(0)
needmask = 1
else:
rowdata.append(float(word))
rowmask.append(1)
self.data.append(rowdata)
self.mask.append(rowmask)
self.data = np.array(self.data)
if needmask:
self.mask = np.array(self.mask, int)
else:
self.mask = None
if self.gweight:
self.gweight = np.array(self.gweight)
if self.gorder:
self.gorder = np.array(self.gorder)
def treecluster(self, transpose=False, method="m", dist="e"):
"""Apply hierarchical clustering and return a Tree object.
The pairwise single, complete, centroid, and average linkage
hierarchical clustering methods are available.
Keyword arguments:
- transpose: if False: rows are clustered;
if True: columns are clustered.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
- method: specifies which linkage method is used:
- method == 's': Single pairwise linkage
- method == 'm': Complete (maximum) pairwise linkage (default)
- method == 'c': Centroid linkage
- method == 'a': Average pairwise linkage
See the description of the Tree class for more information about
the Tree object returned by this method.
"""
if transpose:
weight = self.gweight
else:
weight = self.eweight
return treecluster(self.data, self.mask, weight, transpose, method, dist)
def kcluster(
self,
nclusters=2,
transpose=False,
npass=1,
method="a",
dist="e",
initialid=None,
):
"""Apply k-means or k-median clustering.
This method returns a tuple (clusterid, error, nfound).
Keyword arguments:
- nclusters: number of clusters (the 'k' in k-means)
- transpose: if False, genes (rows) are clustered;
if True, samples (columns) are clustered.
- npass: number of times the k-means clustering algorithm is
performed, each time with a different (random) initial condition.
- method: specifies how the center of a cluster is found:
- method == 'a': arithmetic mean
- method == 'm': median
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
- initialid: the initial clustering from which the algorithm should
start. If initialid is None, the routine carries out npass
repetitions of the EM algorithm, each time starting from a different
random initial clustering. If initialid is given, the routine
carries out the EM algorithm only once, starting from the given
initial clustering and without randomizing the order in which items
are assigned to clusters (i.e., using the same order as in the data
matrix). In that case, the k-means algorithm is fully deterministic.
Return values:
- clusterid: array containing the number of the cluster to which each
gene/sample was assigned in the best k-means clustering
solution that was found in the npass runs;
- error: the within-cluster sum of distances for the returned
k-means clustering solution;
- nfound: the number of times this solution was found.
"""
if transpose:
weight = self.gweight
else:
weight = self.eweight
return kcluster(
self.data,
nclusters,
self.mask,
weight,
transpose,
npass,
method,
dist,
initialid,
)
def somcluster(
self, transpose=False, nxgrid=2, nygrid=1, inittau=0.02, niter=1, dist="e"
):
"""Calculate a self-organizing map on a rectangular grid.
The somcluster method returns a tuple (clusterid, celldata).
Keyword arguments:
- transpose: if False, genes (rows) are clustered;
if True, samples (columns) are clustered.
- nxgrid: the horizontal dimension of the rectangular SOM map
- nygrid: the vertical dimension of the rectangular SOM map
- inittau: the initial value of tau (the neighborbood function)
- niter: the number of iterations
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
Return values:
- clusterid: array with two columns, while the number of rows is equal
to the number of genes or the number of samples depending on
whether genes or samples are being clustered. Each row in
the array contains the x and y coordinates of the cell in the
rectangular SOM grid to which the gene or samples was assigned.
- celldata: an array with dimensions (nxgrid, nygrid, number of
samples) if genes are being clustered, or (nxgrid, nygrid,
number of genes) if samples are being clustered. Each item
[ix, iy] of this array is a 1D vector containing the gene
expression data for the centroid of the cluster in the SOM grid
cell with coordinates [ix, iy].
"""
if transpose:
weight = self.gweight
else:
weight = self.eweight
return somcluster(
self.data,
self.mask,
weight,
transpose,
nxgrid,
nygrid,
inittau,
niter,
dist,
)
def clustercentroids(self, clusterid=None, method="a", transpose=False):
"""Calculate the cluster centroids and return a tuple (cdata, cmask).
The centroid is defined as either the mean or the median over all
items for each dimension.
Keyword arguments:
- data: nrows x ncolumns array containing the expression data
- mask: nrows x ncolumns array of integers, showing which data
are missing. If mask[i, j]==0, then data[i, j] is missing.
- transpose: if False, gene (row) clusters are considered;
if True, sample (column) clusters are considered.
- clusterid: array containing the cluster number for each gene or
sample. The cluster number should be non-negative.
- method: specifies how the centroid is calculated:
- method == 'a': arithmetic mean over each dimension. (default)
- method == 'm': median over each dimension.
Return values:
- cdata: 2D array containing the cluster centroids. If transpose
is False, then the dimensions of cdata are nclusters x ncolumns.
If transpose is True, then the dimensions of cdata are nrows x
nclusters.
- cmask: 2D array of integers describing which items in cdata,
if any, are missing.
"""
return clustercentroids(self.data, self.mask, clusterid, method, transpose)
def clusterdistance(
self, index1=0, index2=0, method="a", dist="e", transpose=False
):
"""Calculate the distance between two clusters.
Keyword arguments:
- index1: 1D array identifying which genes/samples belong to the
first cluster. If the cluster contains only one gene, then
index1 can also be written as a single integer.
- index2: 1D array identifying which genes/samples belong to the
second cluster. If the cluster contains only one gene, then
index2 can also be written as a single integer.
- transpose: if False, genes (rows) are clustered;
if True, samples (columns) are clustered.
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
- method: specifies how the distance between two clusters is defined:
- method == 'a': the distance between the arithmetic means
of the two clusters
- method == 'm': the distance between the medians of the
two clusters
- method == 's': the smallest pairwise distance between members
of the two clusters
- method == 'x': the largest pairwise distance between members
of the two clusters
- method == 'v': average of the pairwise distances between members
of the two clusters
- transpose: if False: clusters of rows are considered;
if True: clusters of columns are considered.
"""
if transpose:
weight = self.gweight
else:
weight = self.eweight
return clusterdistance(
self.data, self.mask, weight, index1, index2, method, dist, transpose
)
def distancematrix(self, transpose=False, dist="e"):
"""Calculate the distance matrix and return it as a list of arrays.
Keyword arguments:
- transpose:
if False: calculate the distances between genes (rows);
if True: calculate the distances between samples (columns).
- dist: specifies the distance function to be used:
- dist == 'e': Euclidean distance
- dist == 'b': City Block distance
- dist == 'c': Pearson correlation
- dist == 'a': absolute value of the correlation
- dist == 'u': uncentered correlation
- dist == 'x': absolute uncentered correlation
- dist == 's': Spearman's rank correlation
- dist == 'k': Kendall's tau
Return value:
The distance matrix is returned as a list of 1D arrays containing the
distance matrix between the gene expression data. The number of columns
in each row is equal to the row number. Hence, the first row has zero
length. An example of the return value is:
matrix = [[],
array([1.]),
array([7., 3.]),
array([4., 2., 6.])]
This corresponds to the distance matrix:
[0., 1., 7., 4.]
[1., 0., 3., 2.]
[7., 3., 0., 6.]
[4., 2., 6., 0.]
"""
if transpose:
weight = self.gweight
else:
weight = self.eweight
return distancematrix(self.data, self.mask, weight, transpose, dist)
def save(self, jobname, geneclusters=None, expclusters=None):
"""Save the clustering results.
The saved files follow the convention for the Java TreeView program,
which can therefore be used to view the clustering result.
Keyword arguments:
- jobname: The base name of the files to be saved. The filenames
are jobname.cdt, jobname.gtr, and jobname.atr for hierarchical
clustering, and jobname-K*.cdt, jobname-K*.kgg, jobname-K*.kag
for k-means clustering results.
- geneclusters: For hierarchical clustering results, geneclusters
is a Tree object as returned by the treecluster method. For k-means
clustering results, geneclusters is a vector containing ngenes
integers, describing to which cluster a given gene belongs. This
vector can be calculated by kcluster.
- expclusters: For hierarchical clustering results, expclusters
is a Tree object as returned by the treecluster method. For k-means
clustering results, expclusters is a vector containing nexps
integers, describing to which cluster a given sample belongs. This
vector can be calculated by kcluster.
"""
(ngenes, nexps) = np.shape(self.data)
if self.gorder is None:
gorder = np.arange(ngenes)
else:
gorder = self.gorder
if self.eorder is None:
eorder = np.arange(nexps)
else:
eorder = self.eorder
if (
geneclusters is not None
and expclusters is not None
and type(geneclusters) != type(expclusters) # noqa: E721
):
raise ValueError(
"found one k-means and one hierarchical "
"clustering solution in geneclusters and "
"expclusters"
)
gid = 0
aid = 0
filename = jobname
postfix = ""
if isinstance(geneclusters, Tree):
# This is a hierarchical clustering result.
geneindex = self._savetree(jobname, geneclusters, gorder, False)
gid = 1
elif geneclusters is not None:
# This is a k-means clustering result.
filename = jobname + "_K"
k = max(geneclusters) + 1
kggfilename = "%s_K_G%d.kgg" % (jobname, k)
geneindex = self._savekmeans(kggfilename, geneclusters, gorder, False)
postfix = "_G%d" % k
else:
geneindex = np.argsort(gorder)
if isinstance(expclusters, Tree):
# This is a hierarchical clustering result.
expindex = self._savetree(jobname, expclusters, eorder, True)
aid = 1
elif expclusters is not None:
# This is a k-means clustering result.
filename = jobname + "_K"
k = max(expclusters) + 1
kagfilename = "%s_K_A%d.kag" % (jobname, k)
expindex = self._savekmeans(kagfilename, expclusters, eorder, True)
postfix += "_A%d" % k
else:
expindex = np.argsort(eorder)
filename = filename + postfix
self._savedata(filename, gid, aid, geneindex, expindex)
def _savetree(self, jobname, tree, order, transpose):
"""Save the hierarchical clustering solution (PRIVATE)."""
if transpose:
extension = ".atr"
keyword = "ARRY"
else:
extension = ".gtr"
keyword = "GENE"
index = tree.sort(order)
nnodes = len(tree)
with open(jobname + extension, "w") as outputfile:
nodeID = [""] * nnodes
nodedist = np.array([node.distance for node in tree[:]])
for nodeindex in range(nnodes):
min1 = tree[nodeindex].left
min2 = tree[nodeindex].right
nodeID[nodeindex] = "NODE%dX" % (nodeindex + 1)
outputfile.write(nodeID[nodeindex])
outputfile.write("\t")
if min1 < 0:
index1 = -min1 - 1
outputfile.write(nodeID[index1] + "\t")
nodedist[nodeindex] = max(nodedist[nodeindex], nodedist[index1])
else:
outputfile.write("%s%dX\t" % (keyword, min1))
if min2 < 0:
index2 = -min2 - 1
outputfile.write(nodeID[index2] + "\t")
nodedist[nodeindex] = max(nodedist[nodeindex], nodedist[index2])
else:
outputfile.write("%s%dX\t" % (keyword, min2))
outputfile.write(str(1.0 - nodedist[nodeindex]))
outputfile.write("\n")
return index
def _savekmeans(self, filename, clusterids, order, transpose):
"""Save the k-means clustering solution (PRIVATE)."""
if transpose:
label = "ARRAY"
names = self.expid
else:
label = self.uniqid
names = self.geneid
with open(filename, "w") as outputfile:
outputfile.write(label + "\tGROUP\n")
index = np.argsort(order)
n = len(names)
sortedindex = np.zeros(n, int)
counter = 0
cluster = 0
while counter < n:
for j in index:
if clusterids[j] == cluster:
outputfile.write(f"{names[j]}\t{cluster}\n")
sortedindex[counter] = j
counter += 1
cluster += 1
return sortedindex
def _savedata(self, jobname, gid, aid, geneindex, expindex):
"""Save the clustered data (PRIVATE)."""
if self.genename is None:
genename = self.geneid
else:
genename = self.genename
(ngenes, nexps) = np.shape(self.data)
with open(jobname + ".cdt", "w") as outputfile:
if self.mask is not None:
mask = self.mask
else:
mask = np.ones((ngenes, nexps), int)
if self.gweight is not None:
gweight = self.gweight
else:
gweight = np.ones(ngenes)
if self.eweight is not None:
eweight = self.eweight
else:
eweight = np.ones(nexps)
if gid:
outputfile.write("GID\t")
outputfile.write(self.uniqid)
outputfile.write("\tNAME\tGWEIGHT")
# Now add headers for data columns.
for j in expindex:
outputfile.write(f"\t{self.expid[j]}")
outputfile.write("\n")
if aid:
outputfile.write("AID")
if gid:
outputfile.write("\t")
outputfile.write("\t\t")
for j in expindex:
outputfile.write("\tARRY%dX" % j)
outputfile.write("\n")
outputfile.write("EWEIGHT")
if gid:
outputfile.write("\t")
outputfile.write("\t\t")
for j in expindex:
outputfile.write(f"\t{eweight[j]:f}")
outputfile.write("\n")
for i in geneindex:
if gid:
outputfile.write("GENE%dX\t" % i)
outputfile.write(f"{self.geneid[i]}\t{genename[i]}\t{gweight[i]:f}")
for j in expindex:
outputfile.write("\t")
if mask[i, j]:
outputfile.write(str(self.data[i, j]))
outputfile.write("\n")
def read(handle):
"""Read gene expression data from the file handle and return a Record.
The file should be in the file format defined for Michael Eisen's
Cluster/TreeView program.
"""
return Record(handle)
# Everything below is private
#
def __check_data(data):
if isinstance(data, np.ndarray):
data = np.require(data, dtype="d", requirements="C")
else:
data = np.array(data, dtype="d")
if data.ndim != 2:
raise ValueError("data should be 2-dimensional")
if np.isnan(data).any():
raise ValueError("data contains NaN values")
return data
def __check_mask(mask, shape):
if mask is None:
return np.ones(shape, dtype="intc")
elif isinstance(mask, np.ndarray):
return np.require(mask, dtype="intc", requirements="C")
else:
return np.array(mask, dtype="intc")
def __check_weight(weight, ndata):
if weight is None:
return np.ones(ndata, dtype="d")
if isinstance(weight, np.ndarray):
weight = np.require(weight, dtype="d", requirements="C")
else:
weight = np.array(weight, dtype="d")
if np.isnan(weight).any():
raise ValueError("weight contains NaN values")
return weight
def __check_initialid(initialid, npass, nitems):
if initialid is None:
if npass <= 0:
raise ValueError("npass should be a positive integer")
clusterid = np.empty(nitems, dtype="intc")
else:
npass = 0
clusterid = np.array(initialid, dtype="intc")
return clusterid, npass
def __check_index(index):
if index is None:
return np.zeros(1, dtype="intc")
elif isinstance(index, numbers.Integral):
return np.array([index], dtype="intc")
elif isinstance(index, np.ndarray):
return np.require(index, dtype="intc", requirements="C")
else:
return np.array(index, dtype="intc")
def __check_distancematrix(distancematrix):
if distancematrix is None:
return distancematrix
if isinstance(distancematrix, np.ndarray):
distancematrix = np.require(distancematrix, dtype="d", requirements="C")
else:
try:
distancematrix = np.array(distancematrix, dtype="d")
except ValueError:
n = len(distancematrix)
d = [None] * n
for i, row in enumerate(distancematrix):
if isinstance(row, np.ndarray):
row = np.require(row, dtype="d", requirements="C")
else:
row = np.array(row, dtype="d")
if row.ndim != 1:
raise ValueError("row %d is not one-dimensional" % i) from None
m = len(row)
if m != i:
raise ValueError(
"row %d has incorrect size (%d, expected %d)" % (i, m, i)
) from None
if np.isnan(row).any():
raise ValueError("distancematrix contains NaN values") from None
d[i] = row
return d
if np.isnan(distancematrix).any():
raise ValueError("distancematrix contains NaN values")
return distancematrix