/usr/lib/python2.7/dist-packages/mdp/nodes/classifier_nodes.py is in python-mdp 3.5-1.
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from builtins import zip
from builtins import range
from past.utils import old_div
__docformat__ = "restructuredtext en"
import mdp
from mdp import ClassifierNode, utils, numx, numx_rand, numx_linalg
# TODO: The GaussianClassifier and NearestMeanClassifier could be parallelized.
class SignumClassifier(ClassifierNode):
"""This classifier node classifies as ``1`` if the sum of the data points
is positive and as ``-1`` if the data point is negative"""
def _get_supported_dtypes(self):
"""Return the list of dtypes supported by this node."""
return (mdp.utils.get_dtypes('Float') +
mdp.utils.get_dtypes('Integer'))
@staticmethod
def is_trainable():
return False
def _label(self, x):
ret = [xi.sum() for xi in x]
return numx.sign(ret)
class PerceptronClassifier(ClassifierNode):
"""A simple perceptron with input_dim input nodes."""
def __init__(self, execute_method=None,
input_dim=None, output_dim=None, dtype=None):
super(PerceptronClassifier, self).__init__(
execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self.weights = []
self.offset_weight = 0
self.learning_rate = 0.1
def _check_train_args(self, x, labels):
if (isinstance(labels, (list, tuple, numx.ndarray)) and
len(labels) != x.shape[0]):
msg = ("The number of labels should be equal to the number of "
"datapoints (%d != %d)" % (len(labels), x.shape[0]))
raise mdp.TrainingException(msg)
if (not isinstance(labels, (list, tuple, numx.ndarray))):
labels = [labels]
if (not numx.all([abs(x) == 1 for x in labels])):
msg = "The labels must be either -1 or 1."
raise mdp.TrainingException(msg)
def _train(self, x, labels):
"""Update the internal structures according to the input data 'x'.
x -- a matrix having different variables on different columns
and observations on the rows.
labels -- can be a list, tuple or array of labels (one for each data point)
or a single label, in which case all input data is assigned to
the same class.
"""
# if weights are not yet initialised, initialise them
if not len(self.weights):
self.weights = numx.ones(self.input_dim)
for xi, labeli in mdp.utils.izip_stretched(x, labels):
new_weights = self.weights
new_offset = self.offset_weight
rate = self.learning_rate * (labeli - self._label(xi))
for j in range(self.input_dim):
new_weights[j] = self.weights[j] + rate * xi[j]
# the offset corresponds to a node with input 1 all the time
new_offset = self.offset_weight + rate * 1
self.weights = new_weights
self.offset_weight = new_offset
def _label(self, x):
"""Returns an array with class labels from the perceptron.
"""
return numx.sign(numx.dot(x, self.weights) + self.offset_weight)
class SimpleMarkovClassifier(ClassifierNode):
"""A simple version of a Markov classifier.
It can be trained on a vector of tuples the label being the next element
in the testing data.
"""
def __init__(self, execute_method=None,
input_dim=None, output_dim=None, dtype=None):
super(SimpleMarkovClassifier, self).__init__(
execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self.ntotal_connections = 0
self.features = {}
self.labels = {}
self.connections = {}
def _get_supported_dtypes(self):
"""Return the list of dtypes supported by this node."""
return (mdp.utils.get_dtypes('Float') +
mdp.utils.get_dtypes('AllInteger') +
mdp.utils.get_dtypes('Character'))
def _check_train_args(self, x, labels):
if (isinstance(labels, (list, tuple, numx.ndarray)) and
len(labels) != x.shape[0]):
msg = ("The number of labels should be equal to the number of "
"datapoints (%d != %d)" % (len(labels), x.shape[0]))
raise mdp.TrainingException(msg)
if (not isinstance(labels, (list, tuple, numx.ndarray))):
labels = [labels]
def _train(self, x, labels):
"""Update the internal structures according to the input data 'x'.
x -- a matrix having different variables on different columns
and observations on the rows.
labels -- can be a list, tuple or array of labels (one for each data point)
or a single label, in which case all input data is assigned to
the same class.
"""
# if labels is a number, all x's belong to the same class
for xi, labeli in mdp.utils.izip_stretched(x, labels):
self._learn(xi, labeli)
def _learn(self, feature, label):
feature = tuple(feature)
self.ntotal_connections += 1
if label in self.labels:
self.labels[label] += 1
else:
self.labels[label] = 1
if feature in self.features:
self.features[feature] += 1
else:
self.features[feature] = 1
connection = (feature, label)
if connection in self.connections:
self.connections[connection] += 1
else:
self.connections[connection] = 1
def _prob(self, features):
return [self._prob_one(feature) for feature in features]
def _prob_one(self, feature):
feature = tuple(feature)
probabilities = {}
try:
n_feature_connections = self.features[feature]
except KeyError:
n_feature_connections = 0
# if n_feature_connections == 0, we get a division by zero
# we could throw here, but maybe it's best to simply return
# an empty dict object
return {}
for label in self.labels:
conn = (feature, label)
try:
n_conn = self.connections[conn]
except KeyError:
n_conn = 0
try:
n_label_connections = self.labels[label]
except KeyError:
n_label_connections = 0
p_feature_given_label = 1.0 * n_conn / n_label_connections
p_label = 1.0 * n_label_connections / self.ntotal_connections
p_feature = 1.0 * n_feature_connections / self.ntotal_connections
prob = 1.0 * p_feature_given_label * p_label / p_feature
probabilities[label] = prob
return probabilities
class DiscreteHopfieldClassifier(ClassifierNode):
"""Node for simulating a simple discrete Hopfield model"""
# TODO: It is unclear if this belongs to classifiers or is a general node
# because label space is a subset of feature space
def __init__(self, execute_method=None,
input_dim=None, output_dim=None, dtype='b'):
super(DiscreteHopfieldClassifier, self).__init__(
execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self._weight_matrix = 0 # assigning zero to ease addition
self._num_patterns = 0
self._shuffled_update = True
def _get_supported_dtypes(self):
return ['b']
def _train(self, x):
"""Provide the hopfield net with the possible states.
x -- a matrix having different variables on different columns
and observations on rows.
"""
for pattern in x:
self._train_one(pattern)
def _train_one(self, pattern):
pattern = mdp.utils.bool_to_sign(pattern)
weights = numx.outer(pattern, pattern)
self._weight_matrix += old_div(weights, float(self.input_dim))
self._num_patterns += 1
@property
def memory_size(self):
"""Returns the Hopfield net's memory size"""
return self.input_dim
@property
def load_parameter(self):
"""Returns the load parameter of the Hopfield net.
The quality of memory recall for a Hopfield net breaks down when the
load parameter is larger than 0.14."""
return old_div(self._num_patterns, float(self.input_dim))
def _stop_training(self):
# remove self-feedback
# we could use numx.fill_diagonal, but thats numpy 1.4 only
for i in range(self.input_dim):
self._weight_matrix[i][i] = 0
def _label(self, x, threshold = 0):
"""Retrieves patterns from the associative memory.
"""
threshold = numx.zeros(self.input_dim) + threshold
return numx.array([self._label_one(pattern, threshold) for pattern in x])
def _label_one(self, pattern, threshold):
pattern = mdp.utils.bool_to_sign(pattern)
has_converged = False
while not has_converged:
has_converged = True
iter_order = list(range(len(self._weight_matrix)))
if self._shuffled_update:
numx_rand.shuffle(iter_order)
for row in iter_order:
w_row = self._weight_matrix[row]
thresh_row = threshold[row]
new_pattern_row = numx.sign(numx.dot(w_row, pattern) - thresh_row)
if new_pattern_row == 0:
# Following McKay, Neural Networks, we do nothing
# when the new pattern is zero
pass
elif pattern[row] != new_pattern_row:
has_converged = False
pattern[row] = new_pattern_row
return mdp.utils.sign_to_bool(pattern)
# TODO: Make it more efficient
class KMeansClassifier(ClassifierNode):
"""Employs K-Means Clustering for a given number of centroids."""
def __init__(self, num_clusters, max_iter=10000, execute_method=None,
input_dim=None, output_dim=None, dtype=None):
"""
:Arguments:
num_clusters
number of centroids to use = number of clusters
max_iter
if the algorithm does not reach convergence (for some
numerical reason), stop after ``max_iter`` iterations
"""
super(KMeansClassifier, self).__init__(execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self._num_clusters = num_clusters
self.data = []
self.tlen = 0
self._centroids = None
self.max_iter = max_iter
def _train(self, x):
# append all data
# we could use a Cumulator class here
self.tlen += x.shape[0]
self.data.extend(x.ravel().tolist())
def _stop_training(self):
self.data = numx.array(self.data, dtype=self.dtype)
self.data.shape = (self.tlen, self.input_dim)
# choose initial centroids unless they are already given
if not self._centroids:
import random
centr_idx = random.sample(range(self.tlen), self._num_clusters)
#numx_rand.permutation(self.tlen)[:self._num_clusters]
centroids = self.data[centr_idx]
else:
centroids = self._centroids
for step in range(self.max_iter):
# list of (sum_position, num_clusters)
new_centroids = [(0., 0.)] * len(centroids)
# cluster
for x in self.data:
idx = self._nearest_centroid_idx(x, centroids)
# update position and count
pos_count = (new_centroids[idx][0] + x,
new_centroids[idx][1] + 1.)
new_centroids[idx] = pos_count
# get new centroid position
new_centroids = numx.array([old_div(c[0], c[1]) if c[1]>0. else centroids[idx]
for idx, c in enumerate(new_centroids)])
# check if we are stable
if numx.all(new_centroids == centroids):
self._centroids = centroids
return
centroids = new_centroids
def _nearest_centroid_idx(self, data, centroids):
dists = numx.array([numx.linalg.norm(data - c) for c in centroids])
return dists.argmin()
def _label(self, x):
"""For a set of feature vectors x, this classifier returns
a list of centroids.
"""
return [self._nearest_centroid_idx(xi, self._centroids) for xi in x]
class GaussianClassifier(ClassifierNode):
"""Perform a supervised Gaussian classification.
Given a set of labelled data, the node fits a gaussian distribution
to each class.
"""
def __init__(self, execute_method=False,
input_dim=None, output_dim=None, dtype=None):
super(GaussianClassifier, self).__init__(execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self._cov_objs = {} # only stored during training
# this list contains the square root of the determinant of the
# corresponding covariance matrix
self._sqrt_def_covs = []
# we are going to store the inverse of the covariance matrices
# since only those are useful to compute the probabilities
self.inv_covs = []
self.means = []
self.p = [] # number of observations
self.labels = None
@staticmethod
def is_invertible():
return False
def _check_train_args(self, x, labels):
if isinstance(labels, (list, tuple, numx.ndarray)) and (
len(labels) != x.shape[0]):
msg = ("The number of labels should be equal to the number of "
"datapoints (%d != %d)" % (len(labels), x.shape[0]))
raise mdp.TrainingException(msg)
def _update_covs(self, x, lbl):
if lbl not in self._cov_objs:
self._cov_objs[lbl] = utils.CovarianceMatrix(dtype=self.dtype)
self._cov_objs[lbl].update(x)
def _train(self, x, labels):
"""
:Arguments:
x
data
labels
Can be a list, tuple or array of labels (one for each data point)
or a single label, in which case all input data is assigned to
the same class.
"""
# if labels is a number, all x's belong to the same class
if isinstance(labels, (list, tuple, numx.ndarray)):
labels_ = numx.asarray(labels)
# get all classes from cl
for lbl in set(labels_):
x_lbl = numx.compress(labels_==lbl, x, axis=0)
self._update_covs(x_lbl, lbl)
else:
self._update_covs(x, labels)
def _stop_training(self):
self.labels = list(self._cov_objs.keys())
self.labels.sort()
nitems = 0
for lbl in self.labels:
cov, mean, p = self._cov_objs[lbl].fix()
nitems += p
self._sqrt_def_covs.append(numx.sqrt(numx_linalg.det(cov)))
if self._sqrt_def_covs[-1] == 0.0:
err = ("The covariance matrix is singular for at least "
"one class.")
raise mdp.NodeException(err)
self.means.append(mean)
self.p.append(p)
self.inv_covs.append(utils.inv(cov))
for i in range(len(self.p)):
self.p[i] /= float(nitems)
del self._cov_objs
def _gaussian_prob(self, x, lbl_idx):
"""Return the probability of the data points x with respect to a
gaussian.
Input arguments:
x -- Input data
S -- Covariance matrix
mn -- Mean
"""
x = self._refcast(x)
dim = self.input_dim
sqrt_detS = self._sqrt_def_covs[lbl_idx]
invS = self.inv_covs[lbl_idx]
# subtract the mean
x_mn = x - self.means[lbl_idx][numx.newaxis, :]
# exponent
exponent = -0.5 * (utils.mult(x_mn, invS)*x_mn).sum(axis=1)
# constant
constant = old_div((2.*numx.pi)**(old_div(-dim,2.)), sqrt_detS)
# probability
return constant * numx.exp(exponent)
def class_probabilities(self, x):
"""Return the posterior probability of each class given the input."""
self._pre_execution_checks(x)
# compute the probability for each class
tmp_prob = numx.zeros((x.shape[0], len(self.labels)),
dtype=self.dtype)
for i in range(len(self.labels)):
tmp_prob[:, i] = self._gaussian_prob(x, i)
tmp_prob[:, i] *= self.p[i]
# normalize to probability 1
# (not necessary, but sometimes useful)
tmp_tot = tmp_prob.sum(axis=1)
tmp_tot = tmp_tot[:, numx.newaxis]
return old_div(tmp_prob, tmp_tot)
def _prob(self, x):
"""Return the posterior probability of each class given the input in a dict."""
class_prob = self.class_probabilities(x)
return [dict(list(zip(self.labels, prob))) for prob in class_prob]
def _label(self, x):
"""Classify the input data using Maximum A-Posteriori."""
class_prob = self.class_probabilities(x)
winner = class_prob.argmax(axis=-1)
return [self.labels[winner[i]] for i in range(len(winner))]
# TODO: Maybe extract some common elements form this class and
# GaussianClassifier, like in _train.
class NearestMeanClassifier(ClassifierNode):
"""Nearest-Mean classifier."""
def __init__(self, execute_method=None,
input_dim=None, output_dim=None, dtype=None):
super(NearestMeanClassifier, self).__init__(
execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self.label_means = {} # not normalized during training
self.n_label_samples = {}
# initialized after training, used for vectorized execution:
self.ordered_labels = []
self.ordered_means = None # will be array
def _train(self, x, labels):
"""Update the mean information for the different classes.
labels -- Can be a list, tuple or array of labels (one for each data
point) or a single label, in which case all input data is assigned
to the same class (computationally this is more efficient).
"""
if isinstance(labels, (list, tuple, numx.ndarray)):
labels = numx.asarray(labels)
for label in set(labels):
x_label = numx.compress(labels==label, x, axis=0)
self._update_mean(x_label, label)
else:
self._update_mean(x, labels)
def _update_mean(self, x, label):
"""Update the mean with data for a single label."""
if label not in self.label_means:
self.label_means[label] = numx.zeros(self.input_dim)
self.n_label_samples[label] = 0
# TODO: use smarter summing to avoid rounding errors
self.label_means[label] += numx.sum(x, axis=0)
self.n_label_samples[label] += len(x)
def _check_train_args(self, x, labels):
if isinstance(labels, (list, tuple, numx.ndarray)) and (
len(labels) != x.shape[0]):
msg = ("The number of labels should be equal to the number of "
"datapoints (%d != %d)" % (len(labels), x.shape[0]))
raise mdp.TrainingException(msg)
def _stop_training(self):
"""Calculate the class means."""
ordered_means = []
for label in self.label_means:
self.label_means[label] /= self.n_label_samples[label]
self.ordered_labels.append(label)
ordered_means.append(self.label_means[label])
self.ordered_means = numx.vstack(ordered_means)
def _label(self, x):
"""Classify the data based on minimal distance to mean."""
n_labels = len(self.ordered_labels)
differences = x[:,:,numx.newaxis].repeat(n_labels, 2). \
swapaxes(1,2) - self.ordered_means
square_distances = (differences**2).sum(2)
label_indices = square_distances.argmin(1)
labels = [self.ordered_labels[i] for i in label_indices]
return labels
class KNNClassifier(ClassifierNode):
"""K-Nearest-Neighbour Classifier."""
def __init__(self, k=1, execute_method=None,
input_dim=None, output_dim=None, dtype=None):
"""Initialize classifier.
k -- Number of closest sample points that are taken into account.
"""
super(KNNClassifier, self).__init__(execute_method=execute_method,
input_dim=input_dim,
output_dim=output_dim,
dtype=dtype)
self.k = k
self._label_samples = {} # temporary variable during training
self.n_samples = None
# initialized after training:
self.samples = None # 2d array with all samples
self.sample_label_indices = None # 1d array for label indices
self.ordered_labels = []
def _train(self, x, labels):
"""Add the sampel points to the classes.
labels -- Can be a list, tuple or array of labels (one for each data
point) or a single label, in which case all input data is assigned
to the same class (computationally this is more efficient).
"""
if isinstance(labels, (list, tuple, numx.ndarray)):
labels = numx.asarray(labels)
for label in set(labels):
x_label = numx.compress(labels==label, x, axis=0)
self._add_samples(x_label, label)
else:
self._add_samples(x, labels)
def _add_samples(self, x, label):
"""Store x set for later neirest-neighbour calculation."""
if label not in self._label_samples:
self._label_samples[label] = []
self._label_samples[label].append(x)
def _check_train_args(self, x, labels):
if isinstance(labels, (list, tuple, numx.ndarray)) and (
len(labels) != x.shape[0]):
msg = ("The number of labels should be equal to the number of "
"datapoints (%d != %d)" % (len(labels), x.shape[0]))
raise mdp.TrainingException(msg)
def _stop_training(self):
"""Organize the sample data."""
ordered_samples = []
for label in self._label_samples:
ordered_samples.append(
numx.concatenate(self._label_samples[label]))
self.ordered_labels.append(label)
del self._label_samples
self.samples = numx.concatenate(ordered_samples)
self.n_samples = len(self.samples)
self.sample_label_indices = numx.concatenate(
[numx.ones(len(ordered_samples[i]),
dtype="int32") * i
for i in range(len(self.ordered_labels))])
def _label(self, x):
"""Label the data by comparison with the reference points."""
square_distances = (x*x).sum(1)[:, numx.newaxis] \
+ (self.samples*self.samples).sum(1)
square_distances -= 2 * numx.dot(x, self.samples.T)
min_inds = square_distances.argsort()
win_inds = [numx.bincount(self.sample_label_indices[indices[0:self.k]]).
argmax(0) for indices in min_inds]
labels = [self.ordered_labels[i] for i in win_inds]
return labels
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