def evaluation_clustering_simple(n_data=100, sqrt_num_blobs=4, distance=5):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels, GaussianBlobsDataGenerator
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
# produce sone Gaussian blobs to cluster
ncenters = sqrt_num_blobs**2
stretch = 1
angle = 1
gen = GaussianBlobsDataGenerator(sqrt_num_blobs, distance, stretch, angle)
features = gen.get_streamed_features(n_data)
X = features.get_feature_matrix()
# compute approximate "ground truth" labels via taking the closest blob mean
coords = array(range(0, sqrt_num_blobs * distance, distance))
idx_0 = [abs(coords - x).argmin() for x in X[0]]
idx_1 = [abs(coords - x).argmin() for x in X[1]]
ground_truth = array(
[idx_0[i] * sqrt_num_blobs + idx_1[i] for i in range(n_data)],
dtype="float64")
#for label in unique(ground_truth):
# indices=ground_truth==label
# plot(X[0][indices], X[1][indices], 'o')
#show()
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
# in this case we know that the clustering has to be very good
#print(('Clustering accuracy = %.4f' % accuracy))
assert (accuracy > 0.8)
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO add multiclass labels and MI once the serialization works
#return gnd, accuracy, mutual_info
return accuracy
def evaluation_clustering_simple (n_data=100, sqrt_num_blobs=4, distance=5):
from shogun.Evaluation import ClusteringAccuracy, ClusteringMutualInformation
from shogun.Features import MulticlassLabels, GaussianBlobsDataGenerator
from shogun.Mathematics import Math
# reproducable results
Math.init_random(1)
# produce sone Gaussian blobs to cluster
ncenters=sqrt_num_blobs**2
stretch=1
angle=1
gen=GaussianBlobsDataGenerator(sqrt_num_blobs, distance, stretch, angle)
features=gen.get_streamed_features(n_data)
X=features.get_feature_matrix()
# compute approximate "ground truth" labels via taking the closest blob mean
coords=array(range(0,sqrt_num_blobs*distance,distance))
idx_0=[abs(coords -x).argmin() for x in X[0]]
idx_1=[abs(coords -x).argmin() for x in X[1]]
ground_truth=array([idx_0[i]*sqrt_num_blobs + idx_1[i] for i in range(n_data)], dtype="float64")
#for label in unique(ground_truth):
# indices=ground_truth==label
# plot(X[0][indices], X[1][indices], 'o')
#show()
centroids = run_clustering(features, ncenters)
gnd_hat = assign_labels(features, centroids, ncenters)
gnd = MulticlassLabels(ground_truth)
AccuracyEval = ClusteringAccuracy()
AccuracyEval.best_map(gnd_hat, gnd)
accuracy = AccuracyEval.evaluate(gnd_hat, gnd)
# in this case we know that the clustering has to be very good
#print(('Clustering accuracy = %.4f' % accuracy))
assert(accuracy>0.8)
MIEval = ClusteringMutualInformation()
mutual_info = MIEval.evaluate(gnd_hat, gnd)
#print(('Clustering mutual information = %.4f' % mutual_info))
# TODO add multiclass labels and MI once the serialization works
#return gnd, accuracy, mutual_info
return accuracy
def statistics_mmd_kernel_selection_single(m,distance,stretch,num_blobs,angle,selection_method):
from shogun.Features import RealFeatures
from shogun.Features import GaussianBlobsDataGenerator
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Statistics import LinearTimeMMD
from shogun.Statistics import MMDKernelSelectionMedian
from shogun.Statistics import MMDKernelSelectionMax
from shogun.Statistics import MMDKernelSelectionOpt
from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
from shogun.Distance import EuclideanDistance
from shogun.Mathematics import Statistics, Math
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# results for this low number will be bad (unstable, type I error wrong)
m=1000
distance=10
stretch=5
num_blobs=3
angle=pi/4
# streaming data generator
gen_p=GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
gen_q=GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
# stream some data and plot
num_plot=1000
features=gen_p.get_streamed_features(num_plot)
features=features.create_merged_copy(gen_q.get_streamed_features(num_plot))
data=features.get_feature_matrix()
#figure()
#subplot(2,2,1)
#grid(True)
#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
#title('$X\sim p$')
#subplot(2,2,2)
#grid(True)
#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
#title('$Y\sim q$')
# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
# different to the standard form, see documentation)
sigmas=[2**x for x in range(-3,10)]
widths=[x*x*2 for x in sigmas]
combined=CombinedKernel()
for i in range(len(sigmas)):
combined.append_kernel(GaussianKernel(10, widths[i]))
# mmd instance using streaming features, blocksize of 10000
block_size=1000
mmd=LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
# kernel selection instance (this can easily replaced by the other methods for selecting
# single kernels
if selection_method=="opt":
selection=MMDKernelSelectionOpt(mmd)
elif selection_method=="max":
selection=MMDKernelSelectionMax(mmd)
elif selection_method=="median":
selection=MMDKernelSelectionMedian(mmd)
# print measures (just for information)
# in case Opt: ratios of MMD and standard deviation
# in case Max: MMDs for each kernel
# Does not work for median method
if selection_method!="median":
ratios=selection.compute_measures()
#print "Measures:", ratios
#subplot(2,2,3)
#plot(ratios)
#title('Measures')
# perform kernel selection
kernel=selection.select_kernel()
kernel=GaussianKernel.obtain_from_generic(kernel)
#print "selected kernel width:", kernel.get_width()
# compute tpye I and II error (use many more trials). Type I error is only
# estimated to check MMD1_GAUSSIAN method for estimating the null
# distribution. Note that testing has to happen on difference data than
# kernel selecting, but the linear time mmd does this implicitly
mmd.set_kernel(kernel)
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
# number of trials should be larger to compute tight confidence bounds
num_trials=5;
alpha=0.05 # test power
typeIerrors=[0 for x in range(num_trials)]
typeIIerrors=[0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i]=mmd.perform_test()>alpha
mmd.set_simulate_h0(False)
typeIIerrors[i]=mmd.perform_test()>alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return kernel,typeIerrors,typeIIerrors
def statistics_mmd_kernel_selection_combined(m, distance, stretch, num_blobs,
angle, selection_method):
from shogun.Features import RealFeatures
from shogun.Features import GaussianBlobsDataGenerator
from shogun.Kernel import GaussianKernel, CombinedKernel
from shogun.Statistics import LinearTimeMMD
from shogun.Statistics import MMDKernelSelectionCombMaxL2
from shogun.Statistics import MMDKernelSelectionCombOpt
from shogun.Statistics import BOOTSTRAP, MMD1_GAUSSIAN
from shogun.Distance import EuclideanDistance
from shogun.Mathematics import Statistics, Math
# init seed for reproducability
Math.init_random(1)
# note that the linear time statistic is designed for much larger datasets
# results for this low number will be bad (unstable, type I error wrong)
# streaming data generator
gen_p = GaussianBlobsDataGenerator(num_blobs, distance, 1, 0)
gen_q = GaussianBlobsDataGenerator(num_blobs, distance, stretch, angle)
# stream some data and plot
num_plot = 1000
features = gen_p.get_streamed_features(num_plot)
features = features.create_merged_copy(
gen_q.get_streamed_features(num_plot))
data = features.get_feature_matrix()
#figure()
#subplot(2,2,1)
#grid(True)
#plot(data[0][0:num_plot], data[1][0:num_plot], 'r.', label='$x$')
#title('$X\sim p$')
#subplot(2,2,2)
#grid(True)
#plot(data[0][num_plot+1:2*num_plot], data[1][num_plot+1:2*num_plot], 'b.', label='$x$', alpha=0.5)
#title('$Y\sim q$')
# create combined kernel with Gaussian kernels inside (shoguns Gaussian kernel is
# different to the standard form, see documentation)
sigmas = [2**x for x in range(-3, 10)]
widths = [x * x * 2 for x in sigmas]
combined = CombinedKernel()
for i in range(len(sigmas)):
combined.append_kernel(GaussianKernel(10, widths[i]))
# mmd instance using streaming features, blocksize of 10000
block_size = 10000
mmd = LinearTimeMMD(combined, gen_p, gen_q, m, block_size)
# kernel selection instance (this can easily replaced by the other methods for selecting
# combined kernels
if selection_method == "opt":
selection = MMDKernelSelectionCombOpt(mmd)
elif selection_method == "l2":
selection = MMDKernelSelectionCombMaxL2(mmd)
# perform kernel selection (kernel is automatically set)
kernel = selection.select_kernel()
kernel = CombinedKernel.obtain_from_generic(kernel)
#print "selected kernel weights:", kernel.get_subkernel_weights()
#subplot(2,2,3)
#plot(kernel.get_subkernel_weights())
#title("Kernel weights")
# compute tpye I and II error (use many more trials). Type I error is only
# estimated to check MMD1_GAUSSIAN method for estimating the null
# distribution. Note that testing has to happen on difference data than
# kernel selecting, but the linear time mmd does this implicitly
mmd.set_null_approximation_method(MMD1_GAUSSIAN)
# number of trials should be larger to compute tight confidence bounds
num_trials = 5
alpha = 0.05 # test power
typeIerrors = [0 for x in range(num_trials)]
typeIIerrors = [0 for x in range(num_trials)]
for i in range(num_trials):
# this effectively means that p=q - rejecting is tpye I error
mmd.set_simulate_h0(True)
typeIerrors[i] = mmd.perform_test() > alpha
mmd.set_simulate_h0(False)
typeIIerrors[i] = mmd.perform_test() > alpha
#print "type I error:", mean(typeIerrors), ", type II error:", mean(typeIIerrors)
return kernel, typeIerrors, typeIIerrors
