def median_abs_dev(X, W=[], precision=1, c=1.0):
"""
Compute the (weighted) median absolute deviation.
mad = median(abs(x - median(x))) / c
Parameters
----------
X : numpy array of floats or integers
values
W : numpy array of floats or integers
weights
precision : integer
number of decimal places to consider weights
c : float
constant used as divisor for mad computation;
c = 0.6745 is used to convert from mad to standard deviation
Returns
-------
mad : float
(weighted) median absolute deviation
Examples
--------
>>> import numpy as np
>>> from mindboggle.guts.compute import median_abs_dev
>>> X = np.array([1,2,4,7,8])
>>> W = np.array([.1,.1,.3,.2,.3])
>>> precision = 1
>>> # [1, 2, 4, 4, 4, 7, 7, 8, 8, 8]
>>> median_abs_dev(X, W, precision)
2.0
"""
import numpy as np
from mindboggle.guts.compute import weighted_to_repeated_values
# Make sure arguments have the correct type:
if not isinstance(X, np.ndarray):
X = np.array(X)
if not isinstance(W, np.ndarray):
W = np.array(W)
if not isinstance(precision, int):
precision = int(precision)
if np.size(W):
X = weighted_to_repeated_values(X, W, precision)
mad = np.median(np.abs(X - np.median(X))) / c
return mad
def median_abs_dev(X, W=[], precision=1, c=1.0):
"""
Compute the (weighted) median absolute deviation.
mad = median(abs(x - median(x))) / c
Parameters
----------
X : numpy array of floats or integers
values
W : numpy array of floats or integers
weights
precision : integer
number of decimal places to consider weights
c : float
constant used as divisor for mad computation;
c = 0.6745 is used to convert from mad to standard deviation
Returns
-------
mad : float
(weighted) median absolute deviation
Examples
--------
>>> import numpy as np
>>> from mindboggle.guts.compute import median_abs_dev
>>> X = np.array([1,2,4,7,8])
>>> W = np.array([.1,.1,.3,.2,.3])
>>> precision = 1
>>> # [1, 2, 4, 4, 4, 7, 7, 8, 8, 8]
>>> median_abs_dev(X, W, precision)
2.0
"""
import numpy as np
from mindboggle.guts.compute import weighted_to_repeated_values
# Make sure arguments have the correct type:
if not isinstance(X, np.ndarray):
X = np.array(X)
if not isinstance(W, np.ndarray):
W = np.array(W)
if not isinstance(precision, int):
precision = int(precision)
if np.size(W):
X = weighted_to_repeated_values(X, W, precision)
mad = np.median(np.abs(X - np.median(X))) / c
return mad
def weighted_median(X, W=[], precision=1):
"""
Compute a weighted median.
Parameters
----------
X : numpy array of floats or integers
values
W : numpy array of floats or integers
weights
precision : integer
number of decimal places to consider weights
Returns
-------
wmedian : float
weighted median
Examples
--------
>>> import numpy as np
>>> from mindboggle.guts.compute import weighted_median
>>> X = np.array([1,2,4,7,8])
>>> W = np.array([.1,.1,.3,.2,.3])
>>> precision = 1
>>> # [1, 2, 4, 4, 4, 7, 7, 8, 8, 8]
>>> weighted_median(X, W, precision)
5.5
"""
import numpy as np
from mindboggle.guts.compute import weighted_to_repeated_values
# Make sure arguments have the correct type:
if not isinstance(X, np.ndarray):
X = np.array(X)
if not isinstance(W, np.ndarray):
W = np.array(W)
if not isinstance(precision, int):
precision = int(precision)
wmedian = np.median(weighted_to_repeated_values(X, W, precision))
return wmedian
def weighted_median(X, W=[], precision=1):
"""
Compute a weighted median.
Parameters
----------
X : numpy array of floats or integers
values
W : numpy array of floats or integers
weights
precision : integer
number of decimal places to consider weights
Returns
-------
wmedian : float
weighted median
Examples
--------
>>> import numpy as np
>>> from mindboggle.guts.compute import weighted_median
>>> X = np.array([1,2,4,7,8])
>>> W = np.array([.1,.1,.3,.2,.3])
>>> precision = 1
>>> # [1, 2, 4, 4, 4, 7, 7, 8, 8, 8]
>>> weighted_median(X, W, precision)
5.5
"""
import numpy as np
from mindboggle.guts.compute import weighted_to_repeated_values
# Make sure arguments have the correct type:
if not isinstance(X, np.ndarray):
X = np.array(X)
if not isinstance(W, np.ndarray):
W = np.array(W)
if not isinstance(precision, int):
precision = int(precision)
wmedian = np.median(weighted_to_repeated_values(X, W, precision))
return wmedian
def stats_per_label(values,
labels,
include_labels=[],
exclude_labels=[],
weights=[],
precision=1):
"""
Compute various statistical measures across vertices per label,
optionally using weights (such as surface area per vertex).
Example (area-weighted mean):
average value = sum(a_i * v_i) / total_surface_area,
where *a_i* and *v_i* are the area and value for each vertex *i*.
Note ::
This function is different than means_per_label() in two ways:
1. It computes more than simply the (weighted) mean and sdev.
2. It only accepts 1-D arrays of values.
Reference
---------
Weighted skewness and kurtosis unbiased by sample size
Lorenzo Rimoldini, arXiv:1304.6564 (2013)
http://arxiv.org/abs/1304.6564
Parameters
----------
values : numpy array of individual or lists of integers or floats
values for all vertices
labels : list or array of integers
label for each value
include_labels : list of integers
labels to include
exclude_labels : list of integers
labels to be excluded
weights : numpy array of floats
weights to compute weighted statistical measures
precision : integer
number of decimal places to consider weights
Returns
-------
medians : list of floats
median for each label
mads : list of floats
median absolute deviation for each label
means : list of floats
mean for each label
sdevs : list of floats
standard deviation for each label
skews : list of floats
skew for each label
kurts : list of floats
kurtosis value for each label
lower_quarts : list of floats
lower quartile for each label
upper_quarts : list of floats
upper quartile for each label
label_list : list of integers
list of unique labels
Examples
--------
>>> import os
>>> from mindboggle.mio.vtks import read_scalars
>>> from mindboggle.guts.compute import stats_per_label
>>> data_path = os.environ['MINDBOGGLE_DATA']
>>> values_file = os.path.join(data_path, 'arno', 'shapes', 'lh.pial.mean_curvature.vtk')
>>> area_file = os.path.join(data_path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> labels_file = os.path.join(data_path, 'arno', 'labels', 'lh.labels.DKT25.manual.vtk')
>>> values, name = read_scalars(values_file, True, True)
>>> areas, name = read_scalars(area_file, True, True)
>>> labels, name = read_scalars(labels_file)
>>> include_labels = []
>>> exclude_labels = [-1]
>>> weights = areas
>>> precision = 1
>>> stats_per_label(values, labels, include_labels, exclude_labels, weights, precision)
"""
import numpy as np
from scipy.stats import skew, kurtosis, scoreatpercentile
from mindboggle.guts.compute import weighted_to_repeated_values, median_abs_dev
# Make sure arguments are numpy arrays:
if not isinstance(values, np.ndarray):
values = np.asarray(values)
if not isinstance(weights, np.ndarray):
weights = np.asarray(weights)
# Initialize all statistical lists:
if include_labels:
label_list = include_labels
else:
label_list = np.unique(labels)
label_list = [int(x) for x in label_list if int(x) not in exclude_labels]
medians = []
mads = []
means = []
sdevs = []
skews = []
kurts = []
lower_quarts = []
upper_quarts = []
# Extract all vertex indices for each label:
for label in label_list:
I = [i for i, x in enumerate(labels) if x == label]
if I:
# Get the vertex values:
X = values[I]
if len([x for x in X if x != 0]):
# If there are as many weights as values, apply the weights to the values:
if np.size(weights) == np.size(values):
W = weights[I]
sumW = np.sum(W)
# If the sum of the weights and the standard deviation is non-zero,
# compute all statistics of the weighted values:
if sumW > 0:
Xdiff = X - np.mean(X)
Xstd = np.sqrt(np.sum(W * Xdiff**2) / sumW)
means.append(np.sum(W * X) / sumW)
sdevs.append(Xstd)
if Xstd > 0:
skews.append(
(np.sum(W * Xdiff**3) / sumW) / Xstd**3)
kurts.append((np.sum(W * Xdiff**4) / sumW) /
Xstd**4 - 3)
else:
skews.append(skew(X))
kurts.append(kurtosis(X))
X = weighted_to_repeated_values(X, W, precision)
# If the sum of the weights equals zero, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# If there are no (or not enough) weights, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# Compute median, median absolute deviation, and lower and upper quartiles:
if np.size(X):
medians.append(np.median(X))
mads.append(median_abs_dev(X))
lower_quarts.append(scoreatpercentile(X, 25))
upper_quarts.append(scoreatpercentile(X, 75))
# If the weights are all smaller than the precision, then X will disappear,
# so set the above statistics (in the 'if' block) to zero:
else:
medians.append(0)
mads.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If all values are equal to zero, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If there are no vertices for the label, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
return medians, mads, means, sdevs, skews, kurts, \
lower_quarts, upper_quarts, label_list
def stats_per_label(values, labels, include_labels=[], exclude_labels=[],
weights=[], precision=1):
"""
Compute various statistical measures across vertices per label,
optionally using weights (such as surface area per vertex).
Example (area-weighted mean):
average value = sum(a_i * v_i) / total_surface_area,
where *a_i* and *v_i* are the area and value for each vertex *i*.
Reference:
Weighted skewness and kurtosis unbiased by sample size
Lorenzo Rimoldini, arXiv:1304.6564 (2013)
http://arxiv.org/abs/1304.6564
Note ::
This function is different than means_per_label() in two ways:
1. It computes more than simply the (weighted) mean and sdev.
2. It only accepts 1-D arrays of values.
Parameters
----------
values : numpy array of individual or lists of integers or floats
values for all vertices
labels : list or array of integers
label for each value
include_labels : list of integers
labels to include
exclude_labels : list of integers
labels to be excluded
weights : numpy array of floats
weights to compute weighted statistical measures
precision : integer
number of decimal places to consider weights
Returns
-------
medians : list of floats
median for each label
mads : list of floats
median absolute deviation for each label
means : list of floats
mean for each label
sdevs : list of floats
standard deviation for each label
skews : list of floats
skew for each label
kurts : list of floats
kurtosis value for each label
lower_quarts : list of floats
lower quartile for each label
upper_quarts : list of floats
upper quartile for each label
label_list : list of integers
list of unique labels
Examples
--------
>>> import numpy as np
>>> from mindboggle.mio.vtks import read_scalars
>>> from mindboggle.guts.compute import stats_per_label
>>> from mindboggle.mio.fetch_data import prep_tests
>>> urls, fetch_data = prep_tests()
>>> values_file = fetch_data(urls['left_mean_curvature'])
>>> labels_file = fetch_data(urls['left_freesurfer_labels'])
>>> area_file = fetch_data(urls['left_area'])
>>> values, name = read_scalars(values_file, True, True)
>>> areas, name = read_scalars(area_file, True, True)
>>> labels, name = read_scalars(labels_file)
>>> include_labels = []
>>> exclude_labels = [-1]
>>> weights = areas
>>> precision = 1
>>> medians, mads, means, sdevs, skews, kurts, lower_quarts, upper_quarts, label_list = stats_per_label(values,
... labels, include_labels, exclude_labels, weights, precision)
>>> print(np.array_str(np.array(medians[0:5]),
... precision=5, suppress_small=True))
[-1.13602 -1.22961 -2.49665 -3.80782 -3.37309]
>>> print(np.array_str(np.array(mads[0:5]),
... precision=5, suppress_small=True))
[ 1.17026 1.5045 1.28234 2.11515 1.69333]
>>> print(np.array_str(np.array(means[0:5]),
... precision=5, suppress_small=True))
[-1.1793 -1.21405 -2.49318 -3.58116 -3.34987]
>>> print(np.array_str(np.array(kurts[0:5]),
... precision=5, suppress_small=True))
[ 2.34118 -0.3969 -0.55787 -0.73993 0.3807 ]
"""
import numpy as np
from scipy.stats import skew, kurtosis, scoreatpercentile
from mindboggle.guts.compute import weighted_to_repeated_values, median_abs_dev
# Make sure arguments are numpy arrays:
if not isinstance(values, np.ndarray):
values = np.asarray(values)
if not isinstance(weights, np.ndarray):
weights = np.asarray(weights)
# Initialize all statistical lists:
if include_labels:
label_list = include_labels
else:
label_list = np.unique(labels)
label_list = [int(x) for x in label_list if int(x) not in exclude_labels]
medians = []
mads = []
means = []
sdevs = []
skews = []
kurts = []
lower_quarts = []
upper_quarts = []
# Extract all vertex indices for each label:
for label in label_list:
I = [i for i,x in enumerate(labels) if x == label]
if I:
# Get the vertex values:
X = values[I]
if len([x for x in X if x != 0]):
# If there are as many weights as values, apply the weights to the values:
if np.size(weights) == np.size(values):
W = weights[I]
sumW = np.sum(W)
# If the sum of the weights and the standard deviation is non-zero,
# compute all statistics of the weighted values:
if sumW > 0:
Xdiff = X - np.mean(X)
Xstd = np.sqrt(np.sum(W * Xdiff**2) / sumW)
means.append(np.sum(W * X) / sumW)
sdevs.append(Xstd)
if Xstd > 0:
skews.append((np.sum(W * Xdiff**3) / sumW) / Xstd**3)
kurts.append((np.sum(W * Xdiff**4) / sumW) / Xstd**4 - 3)
else:
skews.append(skew(X))
kurts.append(kurtosis(X))
X = weighted_to_repeated_values(X, W, precision)
# If the sum of the weights equals zero, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# If there are no (or not enough) weights, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# Compute median, median absolute deviation, and lower and upper quartiles:
if np.size(X):
medians.append(np.median(X))
mads.append(median_abs_dev(X))
lower_quarts.append(scoreatpercentile(X, 25))
upper_quarts.append(scoreatpercentile(X, 75))
# If the weights are all smaller than the precision, then X will disappear,
# so set the above statistics (in the 'if' block) to zero:
else:
medians.append(0)
mads.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If all values are equal to zero, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If there are no vertices for the label, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
return medians, mads, means, sdevs, skews, kurts, \
lower_quarts, upper_quarts, label_list
def stats_per_label(values, labels, include_labels=[], exclude_labels=[], weights=[], precision=1):
"""
Compute various statistical measures across vertices per label,
optionally using weights (such as surface area per vertex).
Example (area-weighted mean):
average value = sum(a_i * v_i) / total_surface_area,
where *a_i* and *v_i* are the area and value for each vertex *i*.
Note ::
This function is different than means_per_label() in two ways:
1. It computes more than simply the (weighted) mean and sdev.
2. It only accepts 1-D arrays of values.
Reference
---------
Weighted skewness and kurtosis unbiased by sample size
Lorenzo Rimoldini, arXiv:1304.6564 (2013)
http://arxiv.org/abs/1304.6564
Parameters
----------
values : numpy array of individual or lists of integers or floats
values for all vertices
labels : list or array of integers
label for each value
include_labels : list of integers
labels to include
exclude_labels : list of integers
labels to be excluded
weights : numpy array of floats
weights to compute weighted statistical measures
precision : integer
number of decimal places to consider weights
Returns
-------
medians : list of floats
median for each label
mads : list of floats
median absolute deviation for each label
means : list of floats
mean for each label
sdevs : list of floats
standard deviation for each label
skews : list of floats
skew for each label
kurts : list of floats
kurtosis value for each label
lower_quarts : list of floats
lower quartile for each label
upper_quarts : list of floats
upper quartile for each label
label_list : list of integers
list of unique labels
Examples
--------
>>> import os
>>> from mindboggle.mio.vtks import read_scalars
>>> from mindboggle.guts.compute import stats_per_label
>>> data_path = os.environ['MINDBOGGLE_DATA']
>>> values_file = os.path.join(data_path, 'arno', 'shapes', 'lh.pial.mean_curvature.vtk')
>>> area_file = os.path.join(data_path, 'arno', 'shapes', 'lh.pial.area.vtk')
>>> labels_file = os.path.join(data_path, 'arno', 'labels', 'lh.labels.DKT25.manual.vtk')
>>> values, name = read_scalars(values_file, True, True)
>>> areas, name = read_scalars(area_file, True, True)
>>> labels, name = read_scalars(labels_file)
>>> include_labels = []
>>> exclude_labels = [-1]
>>> weights = areas
>>> precision = 1
>>> stats_per_label(values, labels, include_labels, exclude_labels, weights, precision)
"""
import numpy as np
from scipy.stats import skew, kurtosis, scoreatpercentile
from mindboggle.guts.compute import weighted_to_repeated_values, median_abs_dev
# Make sure arguments are numpy arrays:
if not isinstance(values, np.ndarray):
values = np.asarray(values)
if not isinstance(weights, np.ndarray):
weights = np.asarray(weights)
# Initialize all statistical lists:
if include_labels:
label_list = include_labels
else:
label_list = np.unique(labels)
label_list = [int(x) for x in label_list if int(x) not in exclude_labels]
medians = []
mads = []
means = []
sdevs = []
skews = []
kurts = []
lower_quarts = []
upper_quarts = []
# Extract all vertex indices for each label:
for label in label_list:
I = [i for i, x in enumerate(labels) if x == label]
if I:
# Get the vertex values:
X = values[I]
if len([x for x in X if x != 0]):
# If there are as many weights as values, apply the weights to the values:
if np.size(weights) == np.size(values):
W = weights[I]
sumW = np.sum(W)
# If the sum of the weights and the standard deviation is non-zero,
# compute all statistics of the weighted values:
if sumW > 0:
Xdiff = X - np.mean(X)
Xstd = np.sqrt(np.sum(W * Xdiff ** 2) / sumW)
means.append(np.sum(W * X) / sumW)
sdevs.append(Xstd)
if Xstd > 0:
skews.append((np.sum(W * Xdiff ** 3) / sumW) / Xstd ** 3)
kurts.append((np.sum(W * Xdiff ** 4) / sumW) / Xstd ** 4 - 3)
else:
skews.append(skew(X))
kurts.append(kurtosis(X))
X = weighted_to_repeated_values(X, W, precision)
# If the sum of the weights equals zero, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# If there are no (or not enough) weights, simply compute the statistics:
else:
means.append(np.mean(X))
sdevs.append(np.std(X))
skews.append(skew(X))
kurts.append(kurtosis(X))
# Compute median, median absolute deviation, and lower and upper quartiles:
if np.size(X):
medians.append(np.median(X))
mads.append(median_abs_dev(X))
lower_quarts.append(scoreatpercentile(X, 25))
upper_quarts.append(scoreatpercentile(X, 75))
# If the weights are all smaller than the precision, then X will disappear,
# so set the above statistics (in the 'if' block) to zero:
else:
medians.append(0)
mads.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If all values are equal to zero, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
# If there are no vertices for the label, set all statistics to zero:
else:
medians.append(0)
mads.append(0)
means.append(0)
sdevs.append(0)
skews.append(0)
kurts.append(0)
lower_quarts.append(0)
upper_quarts.append(0)
return medians, mads, means, sdevs, skews, kurts, lower_quarts, upper_quarts, label_list
