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supervised_clustering.py
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supervised_clustering.py
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"""
=====================
Supervised clustering
=====================
An estimator that performs classification or regression,
using a given estimator
It performs feature agglomeration to reduce the number of features.
"""
# Licence : BSD
# Author: Jean Kossaifi <jean.kossaifi@gmail.com>
import numpy as np
from sklearn.utils.graph import cs_graph_components
from sklearn.cluster import ward_tree
from sklearn.externals.joblib import Parallel, delayed
from sklearn.base import BaseEstimator
from sklearn.linear_model import BayesianRidge
from sklearn.linear_model import SGDClassifier
from sklearn.cross_val import cross_val_score
###############################################################################
def tree_roots(children, n_components, n_leaves):
"""
Computes a list of all the roots of the tree.
Parameters
----------
children : [int, int] list
ward_tree, it's a binary tree
The element i represent the two children of the node (n_leaves + i)
n_components : int
number of connected components
n_leaves : int
number of leaves in the tree
Returns
-------
int list : list of the tree roots
Note
----
There are (2*n_leaves - n_components) nodes in a graph
"""
if n_components == 1:
#Only one component, the only root is the result of the last merge :
#2*n_leaves-n_components-1 becauses indices start up to zero
return [2 * n_leaves - 2]
else:
#A node is a root if it's not in the list of children
#(it's not merged with another one)
return list(set(range(2 * n_leaves - n_components))
.difference(set(np.array(children).flatten())))
###############################################################################
def average_signals(X, children, n_leaves):
"""
Computes a 2D-array of the average signal per node.
(ie per parcel since every node represents a possible parcel)
Parameters
----------
X : ndarray of shape = (n_samples, n_features)
children : [int, int] list
ward_tree
n_leaves : int
number of leaves in the tree
Returns
-------
ndarray of shape (n_samples, n_nodes)
(assuming a node may be a leaf)
It's column i represents the average signal for the parcel represented
by the node i
"""
if children == []:
return X
avg_signals = [] # average signal of the corresponding element in children
weigths = [] # number of voxels merged by the corresponding root
for l in children:
# children doesn't contain entries for leaves nodes. We'll append them
# at the end
node_signal = 0
node_weight = 0
for i in l:
if i < n_leaves: # if the element is a leave
node_signal += X[:, i] # the average is the value of the voxel
node_weight += 1 # he is the result of the merging of 1 voxel
else: # the element is a root
node_signal += avg_signals[i - n_leaves] * weigths[i - n_leaves]
node_weight += weigths[i - n_leaves]
avg_signals.append(node_signal / node_weight)
weigths.append(node_weight)
return np.concatenate((X, (np.array(avg_signals).T)), axis=1)
###############################################################################
def parcel_based_signals(X, labels):
"""
Computes a 2D-array of the average signal per parcel.
Parameters
----------
X : ndarray of shape = (n_samples, n_features)
labels : nparray, dtype=int, shape=n_features
Represents a parcellation
Array of the labels attributed to each feature
Returns
-------
ndarray of shape (n_samples, n_parcels)
where n_parcels = number of parcels in the parcellation
and column i represent the average signal for the parcel i
"""
avg_signals = []
for i in np.unique(labels):
avg_signals.append(X[:, labels == i].mean(axis=-1))
return np.array(avg_signals).T
###############################################################################
def split_parcellation(parcellation, children, n_leaves):
"""
Computes a list of all possible splited parcellations obtained
by splitting one and only one parcel of parcellation
Parameters
----------
parcellation : int list
parcellation
children : (int * int) list
ward_tree
n_leaves : int
number of leaves in the tree
Returns
-------
parcellations : (int list) list
A list of the parcellations obtained by splitting one and only one
of the current parcellation in two
(ie splitting each element of parcellation in two when it's possible)
"""
parcellations = []
for i in range(len(parcellation)):
if parcellation[i] >= n_leaves: # We can't cut the leaves
# l = list(p) gets a copy of p, not l = p !!!
l = list(parcellation)
l.remove(parcellation[i])
l.extend(children[parcellation[i] - n_leaves])
parcellations.append(l)
return parcellations
##############################################################################
def find_children(root, children, n_leaves):
"""
Find every children of root
Parameters
----------
root : int
children : (int* int) list
ward tree
n_leaves : int
number of leaves in the tree
Returns
-------
numpy array : a list of all the children of 'root'
"""
if root < n_leaves:
return [root]
else:
result = []
temp = children[root - n_leaves]
for node in temp:
if (node < n_leaves):
result.append(node)
else:
temp.extend(children[node - n_leaves])
return result
###############################################################################
def parcellation_to_label(parcellation, children, n_leaves):
"""
Computes a 2D array where every voxel in the same cluster
have the same number (label).
Parameters
----------
parcellation : int list
children : (int * int) list
ward tree
n_features :
number of features of the clustered data
n_leaves :
number of leaves in the ward tree
Returns
-------
a numpy array, shape=n_features, dtype=1,
where every voxel in the same parcel
have the same number/label (ie, labels[i]==labels[j] if
X[i] and X[j] are in the same parcel in parcellation
"""
labels = np.empty(n_leaves, dtype=np.int)
for i, root in enumerate(parcellation):
labels[find_children(root, children, n_leaves)] = (i + 1)
return labels
###############################################################################
# Class for using hierarchical clustering
class BaseSupervisedClustering(BaseEstimator):
"""
A classifier using hierarchical clustering to reduce features number
Parameters
----------
estimator : estimator, with methods fit and predict
n_iterations : int
default : 50
number of iterations = max number of parcel we want
connectivity : sparse matrix, optionnal
connectivity matrix
cv : scikits cross_validation model OR integer, optional
the type of cross validation to use
If integer, the number of folds to use during internal cross validation
copy : bool, optional
true if you want to use a copy of connectivity
default is true
n_jobs : int, optional
number of cpu to use
default is 1
verbose : int, optional
level of verbosity (0, 1 or 2)
Default is 0
Returns
-------
self
Attributes
----------
scores : float list
the score of the best parcellation of each iteration
the element i correspond to the score of the best parcellation
at iteration i
coef_ : the coefficients of the classifier fitted to the data
(using the hierarchical clustering)
labels_ : ndarray of shape (n_features)
the parcellation chosen
Two features have the same label if they are in the same parcel.
The smaller label correspond to the smaller parcel
Notes
-----
1) Firstly, ward tree is computed. Its a binary tree.
The ward tree is represented by a list of pairsi
Thus, the element i of this list represent the two children
of the node i.
/!\ The leaves are NOT represented in this list.
2) Every cut of this tree gives a possible parcellation.
Thus, we set the first parcellation as the root(s) of the tree, and,
at each iteration, we construct a list of all the parcellations obtainable
by cutting one of the parcels of the current parcellation in two.
(we replace the parcel by its two children)
3)We select the best parcellation of this list by cross validation
This is the iteration parcellation.
4)Finally, we obtain a list of al the parcellations choosen at
each iteration.
We choose the best by- selecting the best delta, ie the
parcellation i+1, where
score_of_parcellation[i+1] - score_of_parcellation[i] is max.
5)We then compute a list wich associate to each voxel the label of its
parcellation.
Lastly, we fit the given estimator with this parcel-based signal.
Comments
--------
After n iterations we have (n+1) parcellations
(n choosen, plus the root(s)).
The selected parcellation of the iteration i has n_components+n parcels.
The root n is the element (n - n_leaves) of the ward tree
(we assume that the features are referenced by integers from 0 to n_leaves,
and the ward tree, an (int * int) list represent the roots of the tree by
its two children)
Reference
---------
http://hal.inria.fr/docs/00/58/92/01/PDF/supervised_clustering_vm_review.pdf
"""
def __init__(self, estimator, n_iterations=50, connectivity=None,
copy=True, cv=None, n_jobs=1, verbose=0):
if copy and connectivity is not None:
self.connectivity = connectivity.copy()
else:
self.connectivity = connectivity
self.estimator = estimator
self.cv = cv
self.n_iterations = n_iterations
self.n_jobs = n_jobs
self.verbose = verbose
self.copy = copy
def fit(self, X, y):
"""
Fits Supervised Clustering.
Parameters
----------
X : ndarray of shape = (n_samples, n_features)
Y : ndarray of shape = (n_samples)
Returns
-------
self
"""
# n_components computed here because the user can change connectivity
if self.connectivity is not None:
self.n_components = cs_graph_components(self.connectivity)[0]
else:
self.n_components = 1
children, n_components, n_leaves = ward_tree(X.T,
connectivity=self.connectivity, n_components=self.n_components)
children = children.tolist() # Faster with a list
avg_signals = average_signals(X, children, n_leaves)
# The first parcellations is the list of the tree roots
parcellation = tree_roots(children, n_components, n_leaves)
parcellations = [] # List of the best parcellations
self.scores_ = []
if self.verbose >= 2:
print "\n# First parcellation (=tree roots) : %s" % parcellations
## EXPLORATION LOOP
for i in range(1, self.n_iterations+1): # for verbose mode
if self.verbose:
print "# Iteration %d" % i
iteration_parcellations = split_parcellation(parcellation,
children, n_leaves)
if (len(iteration_parcellations) == 0):
# No parcellation can be splitted
print " UserWARNING : n_iterations is too big :"
print " Ending function at iteration %d." % i
break
# Selecting the best parcellation for current iteration
scores = Parallel(n_jobs=self.n_jobs)(delayed(cross_val_score)
(estimator=self.estimator, X=avg_signals[:, j], y=y,
cv=self.cv, n_jobs=1, verbose=0)
for j in iteration_parcellations)
scores = np.mean(scores, axis=1)
indice = np.argmax(scores)
parcellation = np.copy(iteration_parcellations[indice])
parcellations.append(np.copy(parcellation))
self.scores_.append(np.copy(scores[indice]))
## SELECTION LOOP
# We select the parcellation for wich the variation of score is
# the bigger, only if it score is > score_max / 2
# Furthermore we select only parcellations obtained after 20 iterations
indice_min = 20
self.score_min_ = 7 * (np.max(self.scores_) / 10)
max = 0
indice = 0
self.delta_scores_ = [0]
for i in range(indice_min):
self.delta_scores.append(0)
for i in range(indice_min, len(self.scores_)-1):
if self.scores_[i+1] >= self.score_min_:
current_delta = self.scores_[i+1] - self.scores_[i]
if current_delta > max:
max = current_delta
indice = i
self.delta_scores_.append(current_delta)
else:
self.delta_scores_.append(0)
parcellation = parcellations[indice]
# Computing the corresponding labels array
self.labels_ = parcellation_to_label(parcellation, children, n_leaves)
self.estimator.fit(avg_signals[:, parcellation], y)
if hasattr(self.estimator, 'coef_'):
if len(self.estimator.coef_.shape) == 1:
self.coef_ = self.estimator.coef_
else:
self.coef_ = self.estimator.coef_[-1]
return self
def inverse_transform(self):
"""
Returns a numpy array of shape n_features where the element i
correspond to the coefficient attributed to the feature i
by the supervised clustering
"""
if self.coef_ is None:
return None
coefs = np.empty(len(self.labels_))
for i, label in enumerate(np.unique(self.labels_)):
coefs[self.labels_ == label] =\
self.coef_[i] / np.sum(self.labels_ == label)
return coefs
def transform(self, X):
"""
Returns the average signal on the selected parcels.
Parameters
----------
X : ndarray of shape = (n_samples, n_features)
Returns
-------
ndarray of shape = (n_samples, len(np.unique(self.labels_)))
The parcel based-signal.
"""
return parcel_based_signals(X, self.labels_)
def predict(self, X):
"""
Predicts target values according to the fitted model
Parameters
----------
X : ndarray of shape = (n_samples, n_features)
Returns
-------
The return type is the result of the estimator predict function applied
to the previously computed parcellation based signal.
"""
avg_signals = self.transform(X)
return self.estimator.predict(avg_signals)
def score(self, X, y):
"""
Returns the error of the classifier self.estimator,
using the parcel_based_signals constructed with X
Parameters
----------
X : array_like, shape = [n_samples, n_features]
Training set.
y : array_like, shape = [n_samples]
Labels for X.
Returns
-------
z : float
Note
----
See the estimator score function for more details
"""
avg_signals = self.transform(X)
return self.estimator.score(avg_signals, y)
def SupervisedClusteringClassifier(
estimator=SGDClassifier(loss="hinge", penalty="l1"),
n_iterations=50, connectivity=None, copy=True,
cv=None, n_jobs=1, verbose=0):
"""
A classifier using hierarchical clustering to reduce features number
Parameters
----------
estimator : estimator, with methods fit and predict
n_iterations : int
default : 50
number of iterations = max number of parcel we want
connectivity : sparse matrix, optionnal
connectivity matrix
cv : scikits cross_validation model OR integer, optional
the type of cross validation to use
If integer, the number of folds to use during internal cross validation
copy : bool, optional
true if you want to use a copy of connectivity
default is true
n_jobs : int, optional
number of cpu to use
default is 1
verbose : int, optional
level of verbosity (0, 1 or 2)
Default is 0
Returns
-------
self
Attributes
----------
scores : float list
the score of the best parcellation of each iteration
the element i correspond to the score of the best parcellation
at iteration i
coef_ : the coefficients of the classifier fitted to the data
(using the hierarchical clustering)
labels_ : ndarray of shape (n_features)
the parcellation chosen
Two features have the same label if they are in the same parcel.
The smaller label correspond to the smaller parcel
Notes
-----
1) Firstly, ward tree is computed. Its a binary tree.
The ward tree is represented by a list of pairsi
Thus, the element i of this list represent the two children
of the node i.
/!\ The leaves are NOT represented in this list.
2) Every cut of this tree gives a possible parcellation.
Thus, we set the first parcellation as the root(s) of the tree, and,
at each iteration, we construct a list of all the parcellations obtainable
by cutting one of the parcels of the current parcellation in two.
(we replace the parcel by its two children)
3)We select the best parcellation of this list by cross validation
This is the iteration parcellation.
4)Finally, we obtain a list of al the parcellations choosen at
each iteration.
We choose the best by- selecting the best delta, ie the
parcellation i+1, where
score_of_parcellation[i+1] - score_of_parcellation[i] is max.
5)We then compute a list wich associate to each voxel the label of its
parcellation.
Lastly, we fit the given estimator with this parcel-based signal.
Comments
--------
After n iterations we have (n+1) parcellations
(n choosen, plus the root(s)).
The selected parcellation of the iteration i has n_components+n parcels.
The root n is the element (n - n_leaves) of the ward tree
(we assume that the features are referenced by integers from 0 to n_leaves,
and the ward tree, an (int * int) list represent the roots of the tree by
its two children)
Reference
---------
http://hal.inria.fr/docs/00/58/92/01/PDF/supervised_clustering_vm_review.pdf
"""
return BaseSupervisedClustering(estimator, n_iterations=n_iterations,
connectivity=connectivity, copy=copy, cv=cv, n_jobs=n_jobs,
verbose=verbose)
def SupervisedClusteringRegressor(
estimator=BayesianRidge(fit_intercept=True, normalize=True),
n_iterations=50, connectivity=None, copy=False,
cv=None, n_jobs=1, verbose=0):
"""
A regressor using hierarchical clustering to reduce features number
Parameters
----------
estimator : estimator, with methods fit and predict, optional
default is BayesanRidge(fit_intercept=True, normalize=True)
n_iterations : int
default : 50
number of iterations = max number of parcel we want
connectivity : sparse matrix, optionnal
connectivity matrix
cv : scikits cross_validation model OR integer, optional
the type of cross validation to use
If integer, the number of folds to use during internal cross validation
copy : bool, optional
true if you want to use a copy of connectivity
default is true
n_jobs : int, optional
number of cpu to use
default is 1
verbose : int, optional
level of verbosity (0, 1 or 2)
Default is 0
Returns
-------
self
Attributes
----------
scores : float list
the score of the best parcellation of each iteration
the element i correspond to the score of the best parcellation
at iteration i
coef_ : the coefficients of the classifier fitted to the data
(using the hierarchical clustering)
labels_ : ndarray of shape (n_features)
the parcellation chosen
Two features have the same label if they are in the same parcel.
The smaller label correspond to the smaller parcel
Notes
-----
1) Firstly, ward tree is computed. Its a binary tree.
The ward tree is represented by a list of pairsi
Thus, the element i of this list represent the two children
of the node i.
/!\ The leaves are NOT represented in this list.
2) Every cut of this tree gives a possible parcellation.
Thus, we set the first parcellation as the root(s) of the tree, and,
at each iteration, we construct a list of all the parcellations obtainable
by cutting one of the parcels of the current parcellation in two.
(we replace the parcel by its two children)
3)We select the best parcellation of this list by cross validation
This is the iteration parcellation.
4)Finally, we obtain a list of al the parcellations choosen at
each iteration.
We choose the best by- selecting the best delta, ie the
parcellation i+1, where
score_of_parcellation[i+1] - score_of_parcellation[i] is max.
5)We then compute a list wich associate to each voxel the label of its
parcellation.
Lastly, we fit the given estimator with this parcel-based signal.
Comments
--------
After n iterations we have (n+1) parcellations
(n choosen, plus the root(s)).
The selected parcellation of the iteration i has n_components+n parcels.
The root n is the element (n - n_leaves) of the ward tree
(we assume that the features are referenced by integers from 0 to n_leaves,
and the ward tree, an (int * int) list represent the roots of the tree by
its two children)
Reference
---------
http://hal.inria.fr/docs/00/58/92/01/PDF/supervised_clustering_vm_review.pdf
"""
return BaseSupervisedClustering(estimator, n_iterations=n_iterations,
connectivity=connectivity, copy=copy, cv=cv, n_jobs=n_jobs,
verbose=verbose)