def feature_function():
from modshogun import RealFeatures
from modshogun import CSVFile
import numpy as np
#3x3 random matrix
feat_arr = np.random.rand(3, 3)
#initialize RealFeatures from numpy array
features = RealFeatures(feat_arr)
#get matrix value function
print features.get_feature_matrix(features)
#get selected column of matrix
print features.get_feature_vector(1)
#get number of columns
print features.get_num_features()
#get number of rows
print features.get_num_vectors()
feats_from_csv = RealFeatures(CSVFile("csv/feature.csv"))
print "csv is ", feats_from_csv.get_feature_matrix()
def transfer_multitask_l12_logistic_regression (fm_train=traindat,fm_test=testdat,label_train=label_traindat):
from modshogun import BinaryLabels, RealFeatures, Task, TaskGroup
try:
from modshogun import MultitaskL12LogisticRegression
except ImportError:
print("MultitaskL12LogisticRegression not available")
exit(0)
features = RealFeatures(hstack((traindat,traindat)))
labels = BinaryLabels(hstack((label_train,label_train)))
n_vectors = features.get_num_vectors()
task_one = Task(0,n_vectors//2)
task_two = Task(n_vectors//2,n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
mtlr = MultitaskL12LogisticRegression(0.1,0.1,features,labels,task_group)
mtlr.set_tolerance(1e-2) # use 1e-2 tolerance
mtlr.set_max_iter(10)
mtlr.train()
mtlr.set_current_task(0)
out = mtlr.apply_regression().get_labels()
return out
def transfer_multitask_leastsquares_regression(fm_train=traindat,
fm_test=testdat,
label_train=label_traindat):
from modshogun import RegressionLabels, RealFeatures, Task, TaskGroup
try:
from modshogun import MultitaskLeastSquaresRegression
except ImportError:
print("MultitaskLeastSquaresRegression not available")
exit(0)
features = RealFeatures(traindat)
labels = RegressionLabels(label_train)
n_vectors = features.get_num_vectors()
task_one = Task(0, n_vectors // 2)
task_two = Task(n_vectors // 2, n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
mtlsr = MultitaskLeastSquaresRegression(0.1, features, labels, task_group)
mtlsr.set_regularization(1) # use regularization ratio
mtlsr.set_tolerance(1e-2) # use 1e-2 tolerance
mtlsr.train()
mtlsr.set_current_task(0)
out = mtlsr.apply_regression().get_labels()
return out
def transfer_multitask_leastsquares_regression (fm_train=traindat,fm_test=testdat,label_train=label_traindat):
from modshogun import RegressionLabels, RealFeatures, Task, TaskGroup
try:
from modshogun import MultitaskLeastSquaresRegression
except ImportError:
print("MultitaskLeastSquaresRegression not available")
exit(0)
features = RealFeatures(traindat)
labels = RegressionLabels(label_train)
n_vectors = features.get_num_vectors()
task_one = Task(0,n_vectors//2)
task_two = Task(n_vectors//2,n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
mtlsr = MultitaskLeastSquaresRegression(0.1,features,labels,task_group)
mtlsr.set_regularization(1) # use regularization ratio
mtlsr.set_tolerance(1e-2) # use 1e-2 tolerance
mtlsr.train()
mtlsr.set_current_task(0)
out = mtlsr.apply_regression().get_labels()
return out
def transfer_multitask_l12_logistic_regression(fm_train=traindat,
fm_test=testdat,
label_train=label_traindat):
from modshogun import BinaryLabels, RealFeatures, Task, TaskGroup
try:
from modshogun import MultitaskL12LogisticRegression
except ImportError:
print("MultitaskL12LogisticRegression not available")
exit(0)
features = RealFeatures(hstack((traindat, traindat)))
labels = BinaryLabels(hstack((label_train, label_train)))
n_vectors = features.get_num_vectors()
task_one = Task(0, n_vectors // 2)
task_two = Task(n_vectors // 2, n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
mtlr = MultitaskL12LogisticRegression(0.1, 0.1, features, labels,
task_group)
mtlr.set_tolerance(1e-2) # use 1e-2 tolerance
mtlr.set_max_iter(10)
mtlr.train()
mtlr.set_current_task(0)
out = mtlr.apply_regression().get_labels()
return out
def transfer_multitask_clustered_logistic_regression(fm_train=traindat,
fm_test=testdat,
label_train=label_traindat
):
from modshogun import BinaryLabels, RealFeatures, Task, TaskGroup, MultitaskClusteredLogisticRegression, MSG_DEBUG
features = RealFeatures(hstack((traindat, sin(traindat), cos(traindat))))
labels = BinaryLabels(hstack((label_train, label_train, label_train)))
n_vectors = features.get_num_vectors()
task_one = Task(0, n_vectors // 3)
task_two = Task(n_vectors // 3, 2 * n_vectors // 3)
task_three = Task(2 * n_vectors // 3, n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
task_group.append_task(task_three)
mtlr = MultitaskClusteredLogisticRegression(1.0, 100.0, features, labels,
task_group, 2)
#mtlr.io.set_loglevel(MSG_DEBUG)
mtlr.set_tolerance(1e-3) # use 1e-2 tolerance
mtlr.set_max_iter(100)
mtlr.train()
mtlr.set_current_task(0)
#print mtlr.get_w()
out = mtlr.apply_regression().get_labels()
return out
def transfer_multitask_clustered_logistic_regression (fm_train=traindat,fm_test=testdat,label_train=label_traindat):
from modshogun import BinaryLabels, RealFeatures, Task, TaskGroup, MSG_DEBUG
try:
from modshogun import MultitaskClusteredLogisticRegression
except ImportError:
print("MultitaskClusteredLogisticRegression not available")
exit()
features = RealFeatures(hstack((traindat,sin(traindat),cos(traindat))))
labels = BinaryLabels(hstack((label_train,label_train,label_train)))
n_vectors = features.get_num_vectors()
task_one = Task(0,n_vectors//3)
task_two = Task(n_vectors//3,2*n_vectors//3)
task_three = Task(2*n_vectors//3,n_vectors)
task_group = TaskGroup()
task_group.append_task(task_one)
task_group.append_task(task_two)
task_group.append_task(task_three)
mtlr = MultitaskClusteredLogisticRegression(1.0,100.0,features,labels,task_group,2)
#mtlr.io.set_loglevel(MSG_DEBUG)
mtlr.set_tolerance(1e-3) # use 1e-2 tolerance
mtlr.set_max_iter(100)
mtlr.train()
mtlr.set_current_task(0)
#print mtlr.get_w()
out = mtlr.apply_regression().get_labels()
return out
def load_data(num_train_samples=7291, m_data_dict=data_dict):
from modshogun import RealFeatures, MulticlassLabels
import numpy
train_vec = m_data_dict['yTr'][0][:num_train_samples].astype(numpy.float64)
train_labels = MulticlassLabels(train_vec)
test_vec = m_data_dict['yTe'][0].astype(numpy.float64)
test_labels = MulticlassLabels(test_vec)
print "#train_labels = " + str(train_labels.get_num_labels())
print "#test_labels = " + str(test_labels.get_num_labels())
train_mat = m_data_dict['xTr'][:, :num_train_samples].astype(numpy.float64)
train_features = RealFeatures(train_mat)
test_mat = m_data_dict['xTe'].astype(numpy.float64)
test_features = RealFeatures(test_mat)
print "#train_vectors = " + str(train_features.get_num_vectors())
print "#test_vectors = " + str(test_features.get_num_vectors())
print "data dimension = " + str(test_features.get_num_features())
return train_features, train_labels, test_features, test_labels
def load_data(num_train_samples=7291, m_data_dict=data_dict): from modshogun import RealFeatures, MulticlassLabels import numpy train_vec = m_data_dict['yTr'][0][:num_train_samples].astype(numpy.float64) train_labels = MulticlassLabels(train_vec) test_vec = m_data_dict['yTe'][0].astype(numpy.float64) test_labels = MulticlassLabels(test_vec) print "#train_labels = " + str(train_labels.get_num_labels()) print "#test_labels = " + str(test_labels.get_num_labels()) train_mat = m_data_dict['xTr'][:,:num_train_samples].astype(numpy.float64) train_features = RealFeatures(train_mat) test_mat = m_data_dict['xTe'].astype(numpy.float64) test_features = RealFeatures(test_mat) print "#train_vectors = " + str(train_features.get_num_vectors()) print "#test_vectors = " + str(test_features.get_num_vectors()) print "data dimension = " + str(test_features.get_num_features()) return train_features, train_labels, test_features, test_labels
def multiclass_c45classifiertree_modular(train=traindat,
test=testdat,
labels=label_traindat,
ft=feattypes):
try:
from modshogun import RealFeatures, MulticlassLabels, CSVFile, C45ClassifierTree
from numpy import random, int32
except ImportError:
print("Could not import Shogun and/or numpy modules")
return
# wrap features and labels into Shogun objects
feats_train = RealFeatures(CSVFile(train))
feats_test = RealFeatures(CSVFile(test))
train_labels = MulticlassLabels(CSVFile(labels))
# divide train dataset into training and validation subsets in the ratio 2/3 to 1/3
subset = int32(random.permutation(feats_train.get_num_vectors()))
vsubset = subset[1:subset.size / 3]
trsubset = subset[1 + subset.size / 3:subset.size]
# C4.5 Tree formation using training subset
train_labels.add_subset(trsubset)
feats_train.add_subset(trsubset)
c = C45ClassifierTree()
c.set_labels(train_labels)
c.set_feature_types(ft)
c.train(feats_train)
train_labels.remove_subset()
feats_train.remove_subset()
# prune tree using validation subset
train_labels.add_subset(vsubset)
feats_train.add_subset(vsubset)
c.prune_tree(feats_train, train_labels)
train_labels.remove_subset()
feats_train.remove_subset()
# Classify test data
output = c.apply_multiclass(feats_test).get_labels()
output_certainty = c.get_certainty_vector()
return c, output, output_certainty
def multiclass_c45classifiertree_modular(train=traindat,test=testdat,labels=label_traindat,ft=feattypes):
try:
from modshogun import RealFeatures, MulticlassLabels, CSVFile, C45ClassifierTree
from numpy import random, int32
except ImportError:
print("Could not import Shogun and/or numpy modules")
return
# wrap features and labels into Shogun objects
feats_train=RealFeatures(CSVFile(train))
feats_test=RealFeatures(CSVFile(test))
train_labels=MulticlassLabels(CSVFile(labels))
# divide train dataset into training and validation subsets in the ratio 2/3 to 1/3
subset=int32(random.permutation(feats_train.get_num_vectors()))
vsubset=subset[1:subset.size/3]
trsubset=subset[1+subset.size/3:subset.size]
# C4.5 Tree formation using training subset
train_labels.add_subset(trsubset)
feats_train.add_subset(trsubset)
c=C45ClassifierTree()
c.set_labels(train_labels)
c.set_feature_types(ft)
c.train(feats_train)
train_labels.remove_subset()
feats_train.remove_subset()
# prune tree using validation subset
train_labels.add_subset(vsubset)
feats_train.add_subset(vsubset)
c.prune_tree(feats_train,train_labels)
train_labels.remove_subset()
feats_train.remove_subset()
# Classify test data
output=c.apply_multiclass(feats_test).get_labels()
output_certainty=c.get_certainty_vector()
return c,output,output_certainty
def transfer_multitask_group_regression(fm_train=traindat,fm_test=testdat,label_train=label_traindat): from modshogun import RegressionLabels, RealFeatures, Task, TaskGroup, MultitaskLSRegression features = RealFeatures(traindat) labels = RegressionLabels(label_train) n_vectors = features.get_num_vectors() task_one = Task(0,n_vectors/2) task_two = Task(n_vectors/2,n_vectors) task_group = TaskGroup() task_group.add_task(task_one) task_group.add_task(task_two) mtlsr = MultitaskLSRegression(0.1,features,labels,task_group) mtlsr.train() mtlsr.set_current_task(0) out = mtlsr.apply_regression().get_labels() return out
def transfer_multitask_group_regression(fm_train=traindat,
fm_test=testdat,
label_train=label_traindat):
from modshogun import RegressionLabels, RealFeatures, Task, TaskGroup, MultitaskLSRegression
features = RealFeatures(traindat)
labels = RegressionLabels(label_train)
n_vectors = features.get_num_vectors()
task_one = Task(0, n_vectors / 2)
task_two = Task(n_vectors / 2, n_vectors)
task_group = TaskGroup()
task_group.add_task(task_one)
task_group.add_task(task_two)
mtlsr = MultitaskLSRegression(0.1, features, labels, task_group)
mtlsr.train()
mtlsr.set_current_task(0)
out = mtlsr.apply_regression().get_labels()
return out
def transfer_multitask_logistic_regression (fm_train=traindat,fm_test=testdat,label_train=label_traindat): from modshogun import BinaryLabels, RealFeatures, Task, TaskGroup, MultitaskLogisticRegression features = RealFeatures(hstack((traindat,traindat))) labels = BinaryLabels(hstack((label_train,label_train))) n_vectors = features.get_num_vectors() task_one = Task(0,n_vectors/2) task_two = Task(n_vectors/2,n_vectors) task_group = TaskGroup() task_group.append_task(task_one) task_group.append_task(task_two) mtlr = MultitaskLogisticRegression(0.1,features,labels,task_group) mtlr.set_regularization(1) # use regularization ratio mtlr.set_tolerance(1e-2) # use 1e-2 tolerance mtlr.train() mtlr.set_current_task(0) out = mtlr.apply().get_labels() return out
def metric_lmnn_statistics(
k=3,
fname_features='../../data/fm_train_multiclass_digits.dat.gz',
fname_labels='../../data/label_train_multiclass_digits.dat'):
try:
from modshogun import LMNN, CSVFile, RealFeatures, MulticlassLabels, MSG_DEBUG
import matplotlib.pyplot as pyplot
except ImportError:
print 'Error importing modshogun or other required modules. Please, verify their installation.'
return
features = RealFeatures(load_compressed_features(fname_features).T)
labels = MulticlassLabels(CSVFile(fname_labels))
# print 'number of examples = %d' % features.get_num_vectors()
# print 'number of features = %d' % features.get_num_features()
assert (features.get_num_vectors() == labels.get_num_labels())
# train LMNN
lmnn = LMNN(features, labels, k)
lmnn.set_correction(100)
# lmnn.io.set_loglevel(MSG_DEBUG)
print 'Training LMNN, this will take about two minutes...'
lmnn.train()
print 'Training done!'
# plot objective obtained during training
statistics = lmnn.get_statistics()
pyplot.plot(statistics.obj.get())
pyplot.grid(True)
pyplot.xlabel('Iterations')
pyplot.ylabel('LMNN objective')
pyplot.title(
'LMNN objective during training for the multiclass digits data set')
pyplot.show()
def metric_lmnn_statistics(
k=3,
fname_features="../../data/fm_train_multiclass_digits.dat.gz",
fname_labels="../../data/label_train_multiclass_digits.dat",
):
try:
from modshogun import LMNN, CSVFile, RealFeatures, MulticlassLabels, MSG_DEBUG
import matplotlib.pyplot as pyplot
except ImportError:
print "Error importing modshogun or other required modules. Please, verify their installation."
return
features = RealFeatures(load_compressed_features(fname_features).T)
labels = MulticlassLabels(CSVFile(fname_labels))
# print 'number of examples = %d' % features.get_num_vectors()
# print 'number of features = %d' % features.get_num_features()
assert features.get_num_vectors() == labels.get_num_labels()
# train LMNN
lmnn = LMNN(features, labels, k)
lmnn.set_correction(100)
# lmnn.io.set_loglevel(MSG_DEBUG)
print "Training LMNN, this will take about two minutes..."
lmnn.train()
print "Training done!"
# plot objective obtained during training
statistics = lmnn.get_statistics()
pyplot.plot(statistics.obj.get())
pyplot.grid(True)
pyplot.xlabel("Iterations")
pyplot.ylabel("LMNN objective")
pyplot.title("LMNN objective during training for the multiclass digits data set")
pyplot.show()
def train(self, images, labels):
"""
Train eigenfaces
"""
print "Train...",
#copy labels
self._labels = labels;
#transform the numpe vector to shogun structure
features = RealFeatures(images)
#PCA
self.pca = PCA()
#set dimension
self.pca.set_target_dim(self._num_components);
#compute PCA
self.pca.init(features)
for sampleIdx in range(features.get_num_vectors()):
v = features.get_feature_vector(sampleIdx);
p = self.pca.apply_to_feature_vector(v);
self._projections.insert(sampleIdx, p);
print "ok!"
def train(self, images, labels):
"""
Train eigenfaces
"""
print "Train..."
#copy labels
self._labels = labels
#transform the numpe vector to shogun structure
features = RealFeatures(images)
#PCA
self.pca = PCA()
#set dimension
self.pca.set_target_dim(self._num_components)
#compute PCA
self.pca.init(features)
for sampleIdx in range(features.get_num_vectors()):
v = features.get_feature_vector(sampleIdx)
p = self.pca.apply_to_feature_vector(v)
self._projections.insert(sampleIdx, p)
print "Train ok!"
def statistics_hsic(n, difference, angle):
from modshogun import RealFeatures
from modshogun import DataGenerator
from modshogun import GaussianKernel
from modshogun import HSIC
from modshogun import PERMUTATION, HSIC_GAMMA
from modshogun import EuclideanDistance
from modshogun import Statistics, Math
# for reproducable results (the numpy one might not be reproducible across
# different OS/Python-distributions
Math.init_random(1)
np.random.seed(1)
# note that the HSIC has to store kernel matrices
# which upper bounds the sample size
# use data generator class to produce example data
data = DataGenerator.generate_sym_mix_gauss(n, difference, angle)
#plot(data[0], data[1], 'x');show()
# create shogun feature representation
features_x = RealFeatures(np.array([data[0]]))
features_y = RealFeatures(np.array([data[1]]))
# compute median data distance in order to use for Gaussian kernel width
# 0.5*median_distance normally (factor two in Gaussian kernel)
# However, shoguns kernel width is different to usual parametrization
# Therefore 0.5*2*median_distance^2
# Use a subset of data for that, only 200 elements. Median is stable
subset = np.random.permutation(features_x.get_num_vectors()).astype(
np.int32)
subset = subset[0:200]
features_x.add_subset(subset)
dist = EuclideanDistance(features_x, features_x)
distances = dist.get_distance_matrix()
features_x.remove_subset()
median_distance = np.median(distances)
sigma_x = median_distance**2
features_y.add_subset(subset)
dist = EuclideanDistance(features_y, features_y)
distances = dist.get_distance_matrix()
features_y.remove_subset()
median_distance = np.median(distances)
sigma_y = median_distance**2
#print "median distance for Gaussian kernel on x:", sigma_x
#print "median distance for Gaussian kernel on y:", sigma_y
kernel_x = GaussianKernel(10, sigma_x)
kernel_y = GaussianKernel(10, sigma_y)
hsic = HSIC(kernel_x, kernel_y, features_x, features_y)
# perform test: compute p-value and test if null-hypothesis is rejected for
# a test level of 0.05 using different methods to approximate
# null-distribution
statistic = hsic.compute_statistic()
#print "HSIC:", statistic
alpha = 0.05
#print "computing p-value using sampling null"
hsic.set_null_approximation_method(PERMUTATION)
# normally, at least 250 iterations should be done, but that takes long
hsic.set_num_null_samples(100)
# sampling null allows usage of unbiased or biased statistic
p_value_boot = hsic.compute_p_value(statistic)
thresh_boot = hsic.compute_threshold(alpha)
#print "p_value:", p_value_boot
#print "threshold for 0.05 alpha:", thresh_boot
#print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_boot<alpha
#print "computing p-value using gamma method"
hsic.set_null_approximation_method(HSIC_GAMMA)
p_value_gamma = hsic.compute_p_value(statistic)
thresh_gamma = hsic.compute_threshold(alpha)
#print "p_value:", p_value_gamma
#print "threshold for 0.05 alpha:", thresh_gamma
#print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_gamma<alpha
# sample from null distribution (these may be plotted or whatsoever)
# mean should be close to zero, variance stronly depends on data/kernel
# sampling null, biased statistic
#print "sampling null distribution using sample_null"
hsic.set_null_approximation_method(PERMUTATION)
hsic.set_num_null_samples(100)
null_samples = hsic.sample_null()
#print "null mean:", np.mean(null_samples)
#print "null variance:", np.var(null_samples)
#hist(null_samples, 100); show()
return p_value_boot, thresh_boot, p_value_gamma, thresh_gamma, statistic, null_samples
def hsic_graphical():
# parameters, change to get different results
m=250
difference=3
# setting the angle lower makes a harder test
angle=pi/30
# number of samples taken from null and alternative distribution
num_null_samples=500
# use data generator class to produce example data
data=DataGenerator.generate_sym_mix_gauss(m,difference,angle)
# create shogun feature representation
features_x=RealFeatures(array([data[0]]))
features_y=RealFeatures(array([data[1]]))
# compute median data distance in order to use for Gaussian kernel width
# 0.5*median_distance normally (factor two in Gaussian kernel)
# However, shoguns kernel width is different to usual parametrization
# Therefore 0.5*2*median_distance^2
# Use a subset of data for that, only 200 elements. Median is stable
subset=int32(array([x for x in range(features_x.get_num_vectors())])) # numpy
subset=random.permutation(subset) # numpy permutation
subset=subset[0:200]
features_x.add_subset(subset)
dist=EuclideanDistance(features_x, features_x)
distances=dist.get_distance_matrix()
features_x.remove_subset()
median_distance=np.median(distances)
sigma_x=median_distance**2
features_y.add_subset(subset)
dist=EuclideanDistance(features_y, features_y)
distances=dist.get_distance_matrix()
features_y.remove_subset()
median_distance=np.median(distances)
sigma_y=median_distance**2
print "median distance for Gaussian kernel on x:", sigma_x
print "median distance for Gaussian kernel on y:", sigma_y
kernel_x=GaussianKernel(10,sigma_x)
kernel_y=GaussianKernel(10,sigma_y)
# create hsic instance. Note that this is a convienience constructor which copies
# feature data. features_x and features_y are not these used in hsic.
# This is only for user-friendlyness. Usually, its ok to do this.
# Below, the alternative distribution is sampled, which means
# that new feature objects have to be created in each iteration (slow)
# However, normally, the alternative distribution is not sampled
hsic=HSIC(kernel_x,kernel_y,features_x,features_y)
# sample alternative distribution
alt_samples=zeros(num_null_samples)
for i in range(len(alt_samples)):
data=DataGenerator.generate_sym_mix_gauss(m,difference,angle)
features_x.set_feature_matrix(array([data[0]]))
features_y.set_feature_matrix(array([data[1]]))
# re-create hsic instance everytime since feature objects are copied due to
# useage of convienience constructor
hsic=HSIC(kernel_x,kernel_y,features_x,features_y)
alt_samples[i]=hsic.compute_statistic()
# sample from null distribution
# permutation, biased statistic
hsic.set_null_approximation_method(PERMUTATION)
hsic.set_num_null_samples(num_null_samples)
null_samples_boot=hsic.sample_null()
# fit gamma distribution, biased statistic
hsic.set_null_approximation_method(HSIC_GAMMA)
gamma_params=hsic.fit_null_gamma()
# sample gamma with parameters
null_samples_gamma=array([gamma(gamma_params[0], gamma_params[1]) for _ in range(num_null_samples)])
# plot
figure()
# plot data x and y
subplot(2,2,1)
gca().xaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
gca().yaxis.set_major_locator( MaxNLocator(nbins = 4) ) # reduce number of x-ticks
grid(True)
plot(data[0], data[1], 'o')
title('Data, rotation=$\pi$/'+str(1/angle*pi)+'\nm='+str(m))
xlabel('$x$')
ylabel('$y$')
# compute threshold for test level
alpha=0.05
null_samples_boot.sort()
null_samples_gamma.sort()
thresh_boot=null_samples_boot[floor(len(null_samples_boot)*(1-alpha))];
thresh_gamma=null_samples_gamma[floor(len(null_samples_gamma)*(1-alpha))];
type_one_error_boot=sum(null_samples_boot<thresh_boot)/float(num_null_samples)
type_one_error_gamma=sum(null_samples_gamma<thresh_boot)/float(num_null_samples)
# plot alternative distribution with threshold
subplot(2,2,2)
gca().xaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
gca().yaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
grid(True)
hist(alt_samples, 20, normed=True);
axvline(thresh_boot, 0, 1, linewidth=2, color='red')
type_two_error=sum(alt_samples<thresh_boot)/float(num_null_samples)
title('Alternative Dist.\n' + 'Type II error is ' + str(type_two_error))
# compute range for all null distribution histograms
hist_range=[min([min(null_samples_boot), min(null_samples_gamma)]), max([max(null_samples_boot), max(null_samples_gamma)])]
# plot null distribution with threshold
subplot(2,2,3)
gca().xaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
gca().yaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
grid(True)
hist(null_samples_boot, 20, range=hist_range, normed=True);
axvline(thresh_boot, 0, 1, linewidth=2, color='red')
title('Sampled Null Dist.\n' + 'Type I error is ' + str(type_one_error_boot))
# plot null distribution gamma
subplot(2,2,4)
gca().xaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
gca().yaxis.set_major_locator( MaxNLocator(nbins = 3) ) # reduce number of x-ticks
grid(True)
hist(null_samples_gamma, 20, range=hist_range, normed=True);
axvline(thresh_gamma, 0, 1, linewidth=2, color='red')
title('Null Dist. Gamma\nType I error is ' + str(type_one_error_gamma))
grid(True)
# pull plots a bit apart
subplots_adjust(hspace=0.5)
subplots_adjust(wspace=0.5)
acc = evaluator.evaluate(predicted_labels, test_labels)
err = 1-acc
return err
features_file = '../data/fm_ape_gut.txt'
labels_file = '../data/label_ape_gut.txt'
features = RealFeatures(CSVFile(features_file))
labels = MulticlassLabels(CSVFile(labels_file))
# reduce the number of features to use so that the training is faster but still
# the results of feature selection are significant
fm = features.get_feature_matrix()
features = RealFeatures(fm[:500, :])
assert(features.get_num_vectors() == labels.get_num_labels())
print('Number of examples = %d, number of features = %d.' % (features.get_num_vectors(), features.get_num_features()))
visualize_tdsne(features, labels)
lmnn = diagonal_lmnn(features, labels, max_iter=1200)
diagonal_transform = lmnn.get_linear_transform()
diagonal = numpy.diag(diagonal_transform)
print('%d out of %d elements are non-zero' % (numpy.sum(diagonal != 0), diagonal.shape[0]))
statistics = lmnn.get_statistics()
pyplot.plot(statistics.obj.get())
pyplot.show()
#!/usr/bin/python
from modshogun import CSVFile, RealFeatures, RescaleFeatures
from scipy.linalg import solve_triangular, cholesky, sqrtm, inv
import matplotlib.pyplot as pyplot
import numpy
# load wine features
features = RealFeatures(CSVFile('../data/fm_wine.dat'))
print('%d vectors with %d features.' %
(features.get_num_vectors(), features.get_num_features()))
print('original features mean = ' + str(numpy.mean(features, axis=1)))
# rescale the features to [0,1]
feature_rescaling = RescaleFeatures()
feature_rescaling.init(features)
features.add_preprocessor(feature_rescaling)
features.apply_preprocessor()
print('mean after rescaling = ' + str(numpy.mean(features, axis=1)))
# remove mean from data
data = features.get_feature_matrix()
data = data.T
data -= numpy.mean(data, axis=0)
print numpy.mean(data, axis=0)
fig, axarr = pyplot.subplots(1, 2)
axarr[0].matshow(numpy.cov(data.T))
def plot_neighborhood_graph(x, nn, axis):
for i in xrange(x.shape[0]):
xs = [x[i, 0], x[nn[1, i], 0]]
ys = [x[i, 1], x[nn[1, i], 1]]
axis.plot(xs, ys, COLS[int(y[i])])
figure, axarr = pyplot.subplots(3, 1)
x, y = sandwich_data()
features = RealFeatures(x.T)
labels = MulticlassLabels(y)
print('%d vectors with %d features' %
(features.get_num_vectors(), features.get_num_features()))
assert (features.get_num_vectors() == labels.get_num_labels())
distance = EuclideanDistance(features, features)
k = 2
knn = KNN(k, distance, labels)
plot_data(x, y, axarr[0])
plot_neighborhood_graph(x, knn.nearest_neighbors(), axarr[0])
axarr[0].set_aspect('equal')
axarr[0].set_xlim(-6, 4)
axarr[0].set_ylim(-3, 2)
lmnn = LMNN(features, labels, k)
lmnn.set_maxiter(10000)
lmnn.train()
def statistics_hsic (n, difference, angle): from modshogun import RealFeatures from modshogun import DataGenerator from modshogun import GaussianKernel from modshogun import HSIC from modshogun import BOOTSTRAP, HSIC_GAMMA from modshogun import EuclideanDistance from modshogun import Math, Statistics, IntVector # init seed for reproducability Math.init_random(1) # note that the HSIC has to store kernel matrices # which upper bounds the sample size # use data generator class to produce example data data=DataGenerator.generate_sym_mix_gauss(n,difference,angle) #plot(data[0], data[1], 'x');show() # create shogun feature representation features_x=RealFeatures(array([data[0]])) features_y=RealFeatures(array([data[1]])) # compute median data distance in order to use for Gaussian kernel width # 0.5*median_distance normally (factor two in Gaussian kernel) # However, shoguns kernel width is different to usual parametrization # Therefore 0.5*2*median_distance^2 # Use a subset of data for that, only 200 elements. Median is stable subset=IntVector.randperm_vec(features_x.get_num_vectors()) subset=subset[0:200] features_x.add_subset(subset) dist=EuclideanDistance(features_x, features_x) distances=dist.get_distance_matrix() features_x.remove_subset() median_distance=Statistics.matrix_median(distances, True) sigma_x=median_distance**2 features_y.add_subset(subset) dist=EuclideanDistance(features_y, features_y) distances=dist.get_distance_matrix() features_y.remove_subset() median_distance=Statistics.matrix_median(distances, True) sigma_y=median_distance**2 #print "median distance for Gaussian kernel on x:", sigma_x #print "median distance for Gaussian kernel on y:", sigma_y kernel_x=GaussianKernel(10,sigma_x) kernel_y=GaussianKernel(10,sigma_y) hsic=HSIC(kernel_x,kernel_y,features_x,features_y) # perform test: compute p-value and test if null-hypothesis is rejected for # a test level of 0.05 using different methods to approximate # null-distribution statistic=hsic.compute_statistic() #print "HSIC:", statistic alpha=0.05 #print "computing p-value using bootstrapping" hsic.set_null_approximation_method(BOOTSTRAP) # normally, at least 250 iterations should be done, but that takes long hsic.set_bootstrap_iterations(100) # bootstrapping allows usage of unbiased or biased statistic p_value_boot=hsic.compute_p_value(statistic) thresh_boot=hsic.compute_threshold(alpha) #print "p_value:", p_value_boot #print "threshold for 0.05 alpha:", thresh_boot #print "p_value <", alpha, ", i.e. test sais p and q are dependend:", p_value_boot<alpha #print "computing p-value using gamma method" hsic.set_null_approximation_method(HSIC_GAMMA) p_value_gamma=hsic.compute_p_value(statistic) thresh_gamma=hsic.compute_threshold(alpha) #print "p_value:", p_value_gamma #print "threshold for 0.05 alpha:", thresh_gamma #print "p_value <", alpha, ", i.e. test sais p and q are dependend::", p_value_gamma<alpha # sample from null distribution (these may be plotted or whatsoever) # mean should be close to zero, variance stronly depends on data/kernel # bootstrapping, biased statistic #print "sampling null distribution using bootstrapping" hsic.set_null_approximation_method(BOOTSTRAP) hsic.set_bootstrap_iterations(100) null_samples=hsic.bootstrap_null() #print "null mean:", mean(null_samples) #print "null variance:", var(null_samples) #hist(null_samples, 100); show() return p_value_boot, thresh_boot, p_value_gamma, thresh_gamma, statistic, null_samples
xi = x[y==val]
axis.scatter(xi[:,0], xi[:,1], s=50, facecolors='none', edgecolors=COLS[idx])
def plot_neighborhood_graph(x, nn, axis):
for i in xrange(x.shape[0]):
xs = [x[i,0], x[nn[1,i], 0]]
ys = [x[i,1], x[nn[1,i], 1]]
axis.plot(xs, ys, COLS[int(y[i])])
figure, axarr = pyplot.subplots(3, 1)
x, y = sandwich_data()
features = RealFeatures(x.T)
labels = MulticlassLabels(y)
print('%d vectors with %d features' % (features.get_num_vectors(), features.get_num_features()))
assert(features.get_num_vectors() == labels.get_num_labels())
distance = EuclideanDistance(features, features)
k = 2
knn = KNN(k, distance, labels)
plot_data(x, y, axarr[0])
plot_neighborhood_graph(x, knn.nearest_neighbors(), axarr[0])
axarr[0].set_aspect('equal')
axarr[0].set_xlim(-6, 4)
axarr[0].set_ylim(-3, 2)
lmnn = LMNN(features, labels, k)
lmnn.set_maxiter(10000)
lmnn.train()
#!/usr/bin/env python2.7 # # This software is distributed under BSD 3-clause license (see LICENSE file). # # Copyright (C) 2014 Thoralf Klein # from modshogun import RealFeatures, BinaryLabels, LibLinear from numpy import random, mean X_train = RealFeatures(random.randn(30, 100)) Y_train = BinaryLabels(random.randn(X_train.get_num_vectors())) svm = LibLinear(1.0, X_train, Y_train) svm.train() Y_pred = svm.apply_binary(X_train) Y_train.get_labels() == Y_pred.get_labels() print "accuracy:", mean(Y_train.get_labels() == Y_pred.get_labels())
def hsic_graphical():
# parameters, change to get different results
m = 250
difference = 3
# setting the angle lower makes a harder test
angle = pi / 30
# number of samples taken from null and alternative distribution
num_null_samples = 500
# use data generator class to produce example data
data = DataGenerator.generate_sym_mix_gauss(m, difference, angle)
# create shogun feature representation
features_x = RealFeatures(array([data[0]]))
features_y = RealFeatures(array([data[1]]))
# compute median data distance in order to use for Gaussian kernel width
# 0.5*median_distance normally (factor two in Gaussian kernel)
# However, shoguns kernel width is different to usual parametrization
# Therefore 0.5*2*median_distance^2
# Use a subset of data for that, only 200 elements. Median is stable
subset = int32(array([x for x in range(features_x.get_num_vectors())
])) # numpy
subset = random.permutation(subset) # numpy permutation
subset = subset[0:200]
features_x.add_subset(subset)
dist = EuclideanDistance(features_x, features_x)
distances = dist.get_distance_matrix()
features_x.remove_subset()
median_distance = np.median(distances)
sigma_x = median_distance**2
features_y.add_subset(subset)
dist = EuclideanDistance(features_y, features_y)
distances = dist.get_distance_matrix()
features_y.remove_subset()
median_distance = np.median(distances)
sigma_y = median_distance**2
print "median distance for Gaussian kernel on x:", sigma_x
print "median distance for Gaussian kernel on y:", sigma_y
kernel_x = GaussianKernel(10, sigma_x)
kernel_y = GaussianKernel(10, sigma_y)
# create hsic instance. Note that this is a convienience constructor which copies
# feature data. features_x and features_y are not these used in hsic.
# This is only for user-friendlyness. Usually, its ok to do this.
# Below, the alternative distribution is sampled, which means
# that new feature objects have to be created in each iteration (slow)
# However, normally, the alternative distribution is not sampled
hsic = HSIC(kernel_x, kernel_y, features_x, features_y)
# sample alternative distribution
alt_samples = zeros(num_null_samples)
for i in range(len(alt_samples)):
data = DataGenerator.generate_sym_mix_gauss(m, difference, angle)
features_x.set_feature_matrix(array([data[0]]))
features_y.set_feature_matrix(array([data[1]]))
# re-create hsic instance everytime since feature objects are copied due to
# useage of convienience constructor
hsic = HSIC(kernel_x, kernel_y, features_x, features_y)
alt_samples[i] = hsic.compute_statistic()
# sample from null distribution
# permutation, biased statistic
hsic.set_null_approximation_method(PERMUTATION)
hsic.set_num_null_samples(num_null_samples)
null_samples_boot = hsic.sample_null()
# fit gamma distribution, biased statistic
hsic.set_null_approximation_method(HSIC_GAMMA)
gamma_params = hsic.fit_null_gamma()
# sample gamma with parameters
null_samples_gamma = array([
gamma(gamma_params[0], gamma_params[1])
for _ in range(num_null_samples)
])
# plot
figure()
# plot data x and y
subplot(2, 2, 1)
gca().xaxis.set_major_locator(
MaxNLocator(nbins=4)) # reduce number of x-ticks
gca().yaxis.set_major_locator(
MaxNLocator(nbins=4)) # reduce number of x-ticks
grid(True)
plot(data[0], data[1], 'o')
title('Data, rotation=$\pi$/' + str(1 / angle * pi) + '\nm=' + str(m))
xlabel('$x$')
ylabel('$y$')
# compute threshold for test level
alpha = 0.05
null_samples_boot.sort()
null_samples_gamma.sort()
thresh_boot = null_samples_boot[floor(
len(null_samples_boot) * (1 - alpha))]
thresh_gamma = null_samples_gamma[floor(
len(null_samples_gamma) * (1 - alpha))]
type_one_error_boot = sum(
null_samples_boot < thresh_boot) / float(num_null_samples)
type_one_error_gamma = sum(
null_samples_gamma < thresh_boot) / float(num_null_samples)
# plot alternative distribution with threshold
subplot(2, 2, 2)
gca().xaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
gca().yaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
grid(True)
hist(alt_samples, 20, normed=True)
axvline(thresh_boot, 0, 1, linewidth=2, color='red')
type_two_error = sum(alt_samples < thresh_boot) / float(num_null_samples)
title('Alternative Dist.\n' + 'Type II error is ' + str(type_two_error))
# compute range for all null distribution histograms
hist_range = [
min([min(null_samples_boot),
min(null_samples_gamma)]),
max([max(null_samples_boot),
max(null_samples_gamma)])
]
# plot null distribution with threshold
subplot(2, 2, 3)
gca().xaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
gca().yaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
grid(True)
hist(null_samples_boot, 20, range=hist_range, normed=True)
axvline(thresh_boot, 0, 1, linewidth=2, color='red')
title('Sampled Null Dist.\n' + 'Type I error is ' +
str(type_one_error_boot))
# plot null distribution gamma
subplot(2, 2, 4)
gca().xaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
gca().yaxis.set_major_locator(
MaxNLocator(nbins=3)) # reduce number of x-ticks
grid(True)
hist(null_samples_gamma, 20, range=hist_range, normed=True)
axvline(thresh_gamma, 0, 1, linewidth=2, color='red')
title('Null Dist. Gamma\nType I error is ' + str(type_one_error_gamma))
grid(True)
# pull plots a bit apart
subplots_adjust(hspace=0.5)
subplots_adjust(wspace=0.5)
#!/usr/bin/python
from modshogun import CSVFile, RealFeatures, RescaleFeatures
from scipy.linalg import solve_triangular, cholesky, sqrtm, inv
import matplotlib.pyplot as pyplot
import numpy
# load wine features
features = RealFeatures(CSVFile('../data/fm_wine.dat'))
print('%d vectors with %d features.' % (features.get_num_vectors(), features.get_num_features()))
print('original features mean = ' + str(numpy.mean(features, axis=1)))
# rescale the features to [0,1]
feature_rescaling = RescaleFeatures()
feature_rescaling.init(features)
features.add_preprocessor(feature_rescaling)
features.apply_preprocessor()
print('mean after rescaling = ' + str(numpy.mean(features, axis=1)))
# remove mean from data
data = features.get_feature_matrix()
data = data.T
data-= numpy.mean(data, axis=0)
print numpy.mean(data, axis=0)
fig, axarr = pyplot.subplots(1,2)
axarr[0].matshow(numpy.cov(data.T))
#### whiten data