def make_nystrom_evaluation(x_train, y_train, x_test, y_test, gamma, landmarks):
# verify sample size for evaluation
n_sample = paraman["--nystrom"]
if n_sample > x_train.shape[0]:
logger.warning("Batch size for nystrom evaluation is bigger than data size. {} > {}. Using "
"data size instead.".format(n_sample, x_train.shape[0]))
n_sample = x_train.shape[0]
paraman["--nystrom"] = n_sample
indexes_samples = np.random.permutation(x_train.shape[0])[:n_sample]
sample = x_train[indexes_samples]
samples_norm = None
# Make nystrom approximation
# nys_obj = Nystroem(gamma=gamma, n_components=landmarks.shape[0])
# nys_obj.fit(landmarks)
# nystrom_embedding = nys_obj.transform(sample)
landmarks_norm = get_squared_froebenius_norm_line_wise(landmarks)[:, np.newaxis]
metric = prepare_nystrom(landmarks, landmarks_norm, gamma=gamma)
nystrom_embedding = nystrom_transformation(sample, landmarks, metric, landmarks_norm, samples_norm, gamma=gamma)
nystrom_approx_kernel_value = nystrom_embedding @ nystrom_embedding.T
# Create real kernel matrix
real_kernel_special = special_rbf_kernel(sample, sample, gamma, norm_X=samples_norm, norm_Y=samples_norm)
# real_kernel = rbf_kernel(sample, sample, gamma)
real_kernel_norm = np.linalg.norm(real_kernel_special)
# evaluation reconstruction error
reconstruction_error_nystrom = np.linalg.norm(nystrom_approx_kernel_value - real_kernel_special) / real_kernel_norm
# start svm + nystrom classification
if x_test is not None:
logger.info("Start classification")
x_train_nystrom_embedding = nystrom_transformation(x_train, landmarks, metric, landmarks_norm, None, gamma=gamma)
x_test_nystrom_embedding = nystrom_transformation(x_test, landmarks, metric, landmarks_norm, None, gamma=gamma)
linear_svc_clf = LinearSVC(class_weight="balanced")
linear_svc_clf.fit(x_train_nystrom_embedding, y_train)
predictions = linear_svc_clf.predict(x_test_nystrom_embedding)
if paraman["--kddcup04"]:
# compute recall: nb_true_positive/real_nb_positive
recall = np.sum(predictions[y_test == 1])/np.sum(y_test[y_test == 1])
# compute precision: nb_true_positive/nb_positive
precision = np.sum(predictions[y_test == 1])/np.sum(predictions[predictions==1])
f1 = 2 * precision * recall / (precision + recall)
accuracy_nystrom_svm = f1
else:
accuracy_nystrom_svm = np.sum(predictions == y_test) / y_test.shape[0]
else:
accuracy_nystrom_svm = None
return reconstruction_error_nystrom, accuracy_nystrom_svm
def test_nystrom(self):
for name_pair, pair in self.pairs_data.items():
gamma = self.gamma_data[name_pair]
data_norm = self.norm_data[name_pair]
print(name_pair)
sklearn_nystrom = Nystroem(gamma=gamma, n_components=self.n_data)
sklearn_transformation = sklearn_nystrom.fit_transform(pair)
# sklearn_transformation_example = sklearn_nystrom.transform(example_data[name_pair])
special_metric = prepare_nystrom(pair, data_norm, gamma=gamma)
special_transformation = nystrom_transformation(
pair, pair, special_metric, data_norm, data_norm.T, gamma)
# special_transformation_example = nystrom_transformation(example_data[name_pair], pair, special_metric, data_norm, norm_example_data[name_pair], gamma)
sklearn_mat = sklearn_transformation @ sklearn_transformation.T
special_mat = special_transformation @ special_transformation.T
equality = np.allclose(sklearn_mat, special_mat)
try:
self.assertTrue(
equality,
msg="Sklearn nystrom approximatio is different for data {}"
.format(name_pair))
except Exception as e:
real_matrix = rbf_kernel(pair, gamma=gamma)
delta_sk_real = np.linalg.norm(sklearn_mat - real_matrix)
delta_spec_real = np.linalg.norm(special_mat - real_matrix)
if not np.allclose(delta_sk_real, delta_spec_real):
raise Exception(
"Exception 1: {}. Exception 2: They are not even equally distant from real matrix"
.format(str(e)))
raise e
uop = UfastOperator(seeds, FWHT)
uop_arr = uop.toarray()
uniform_sample = data[np.random.permutation(
data.shape[0])[:uop_arr.shape[0]]]
uop_arr_norm = np.linalg.norm(uop_arr, axis=1)[:, np.newaxis]
plt.scatter(seeds[:, 0], seeds[:, 1], marker="x", s=200, color='r')
plt.scatter(uop_arr[:, 0], uop_arr[:, 1], color='g')
# plt.show()
real_kernel_value = rbf_kernel(x, gamma=gamma)
# nystrom with uop
metric = prepare_nystrom(uop_arr, None, gamma=gamma)
nystrom_embedding = nystrom_transformation(x,
uop_arr,
metric,
None,
None,
gamma=gamma)
nystrom_approx_kernel_value = nystrom_embedding @ nystrom_embedding.T
print(
"uop",
np.linalg.norm(nystrom_approx_kernel_value - real_kernel_value) /
np.linalg.norm(real_kernel_value))
# nystrom with uniform sample
metric = prepare_nystrom(uniform_sample, None, gamma=gamma)
nystrom_embedding = nystrom_transformation(x,
uniform_sample,
metric,
None,
None,
def make_nystrom_evaluation(x_train, y_train, x_test, y_test, U_centroids):
"""
Evaluation Nystrom construction time and approximation precision.
The approximation is based on a subsample of size n_sample of the input data set.
:param x_train: Input dataset as ndarray.
:param U_centroids: The matrix of centroids as ndarray or SparseFactor object
:param n_sample: The number of sample to take into account in the reconstruction (can't be too large)
:return:
"""
n_sample = paraman["--nystrom"]
if n_sample > x_train.shape[0]:
logger.warning("Batch size for nystrom evaluation is bigger than data size. {} > {}. Using "
"data size instead.".format(n_sample, x_train.shape[0]))
n_sample = x_train.shape[0]
paraman["--nystrom"] = n_sample
# Compute euristic gamma as the mean of euclidian distance between example
gamma = compute_euristic_gamma(x_train)
log_memory_usage("Memory after euristic gamma computation in make_nystrom_evaluation")
# precompute the centroids norm for later use (optimization)
centroids_norm = get_squared_froebenius_norm_line_wise(U_centroids)[:, np.newaxis]
# centroids_norm = None
indexes_samples = np.random.permutation(x_train.shape[0])[:n_sample]
sample = x_train[indexes_samples]
samples_norm = None
log_memory_usage("Memory after sample selection in make_nystrom_evaluation")
########################
# Nystrom on centroids #
########################
logger.info("Build Nystrom on centroids")
## TIME: nystrom build time
# nystrom build time is Nystrom preparation time for later use.
## START
nystrom_build_start_time = time.process_time()
metric = prepare_nystrom(U_centroids, centroids_norm, gamma=gamma)
nystrom_build_stop_time = time.process_time()
log_memory_usage("Memory after SVD computation in make_nystrom_evaluation")
# STOP
nystrom_build_time = nystrom_build_stop_time - nystrom_build_start_time
## TIME: nystrom inference time
# Nystrom inference time is the time for Nystrom transformation for all the samples.
## START
nystrom_inference_time_start = time.process_time()
nystrom_embedding = nystrom_transformation(sample, U_centroids, metric, centroids_norm, samples_norm, gamma=gamma)
nystrom_approx_kernel_value = nystrom_embedding @ nystrom_embedding.T
nystrom_inference_time_stop = time.process_time()
log_memory_usage("Memory after kernel matrix approximation in make_nystrom_evaluation")
## STOP
nystrom_inference_time = (nystrom_inference_time_stop - nystrom_inference_time_start) / n_sample
################################################################
######################
# Nystrom on uniform #
######################
logger.info("Build Nystrom on uniform sampling")
indexes_uniform_samples = np.random.permutation(x_train.shape[0])[:U_centroids.shape[0]]
uniform_sample = x_train[indexes_uniform_samples]
uniform_sample_norm = get_squared_froebenius_norm_line_wise(uniform_sample)[:, np.newaxis]
log_memory_usage("Memory after uniform sample selection in make_nystrom_evaluation")
metric_uniform = prepare_nystrom(uniform_sample, uniform_sample_norm, gamma=gamma)
log_memory_usage("Memory after SVD computation in uniform part of make_nystrom_evaluation")
nystrom_embedding_uniform = nystrom_transformation(sample, uniform_sample, metric_uniform, uniform_sample_norm, samples_norm, gamma=gamma)
nystrom_approx_kernel_value_uniform = nystrom_embedding_uniform @ nystrom_embedding_uniform.T
#################################################################
###############
# Real Kernel #
###############
logger.info("Compute real kernel matrix")
real_kernel_special = special_rbf_kernel(sample, sample, gamma, norm_X=samples_norm, norm_Y=samples_norm)
# real_kernel = rbf_kernel(sample, sample, gamma)
real_kernel_norm = np.linalg.norm(real_kernel_special)
log_memory_usage("Memory after real kernel computation in make_nystrom_evaluation")
#################################
# Sklearn based Nystrom uniform #
#################################
# sklearn_nystrom = Nystroem(gamma=gamma, n_components=uniform_sample.shape[0])
# sklearn_nystrom = sklearn_nystrom.fit(uniform_sample)
# sklearn_transfo = sklearn_nystrom.transform(sample)
# kernel_sklearn_nys = sklearn_transfo @ sklearn_transfo.T
################################################################
####################
# Error evaluation #
####################
sampled_froebenius_norm = np.linalg.norm(nystrom_approx_kernel_value - real_kernel_special) / real_kernel_norm
sampled_froebenius_norm_uniform = np.linalg.norm(nystrom_approx_kernel_value_uniform - real_kernel_special) / real_kernel_norm
# svm evaluation
if x_test is not None:
logger.info("Start classification")
time_classification_start = time.process_time()
x_train_nystrom_embedding = nystrom_transformation(x_train, U_centroids, metric, centroids_norm, None, gamma=gamma)
x_test_nystrom_embedding = nystrom_transformation(x_test, U_centroids, metric, centroids_norm, None, gamma=gamma)
linear_svc_clf = LinearSVC(class_weight="balanced")
linear_svc_clf.fit(x_train_nystrom_embedding, y_train)
predictions = linear_svc_clf.predict(x_test_nystrom_embedding)
time_classification_stop = time.process_time()
if paraman["--kddcup04"]:
# compute recall: nb_true_positive/real_nb_positive
recall = np.sum(predictions[y_test == 1])/np.sum(y_test[y_test == 1])
# compute precision: nb_true_positive/nb_positive
precision = np.sum(predictions[y_test == 1])/np.sum(predictions[predictions==1])
f1 = 2 * precision * recall / (precision + recall)
accuracy_nystrom_svm = f1
else:
accuracy_nystrom_svm = np.sum(predictions == y_test) / y_test.shape[0]
delta_time_classification = time_classification_stop - time_classification_start
else:
accuracy_nystrom_svm = None
delta_time_classification = None
nystrom_results = {
"nystrom_build_time": nystrom_build_time,
"nystrom_inference_time": nystrom_inference_time,
"nystrom_sampled_error_reconstruction": sampled_froebenius_norm,
"nystrom_sampled_error_reconstruction_uniform": sampled_froebenius_norm_uniform,
"nystrom_svm_accuracy": accuracy_nystrom_svm,
"nystrom_svm_time": delta_time_classification
}
resprinter.add(nystrom_results)
