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# Copyright 2020 Erik Härkönen. All rights reserved.
# This file is licensed to you under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License. You may obtain a copy
# of the License at http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software distributed under
# the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR REPRESENTATIONS
# OF ANY KIND, either express or implied. See the License for the specific language
# governing permissions and limitations under the License.
from sklearn.decomposition import FastICA, PCA, IncrementalPCA, MiniBatchSparsePCA, SparsePCA, KernelPCA
import fbpca
import numpy as np
import itertools
from types import SimpleNamespace
# ICA
class ICAEstimator():
def __init__(self, n_components):
self.n_components = n_components
self.maxiter = 10000
self.whiten = True # ICA: whitening is essential, should not be skipped
self.transformer = FastICA(n_components, random_state=0, whiten=self.whiten, max_iter=self.maxiter)
self.batch_support = False
self.stdev = np.zeros((n_components,))
self.total_var = 0.0
def get_param_str(self):
return "ica_c{}{}".format(self.n_components, '_w' if self.whiten else '')
def fit(self, X):
self.transformer.fit(X)
if self.transformer.n_iter_ >= self.maxiter:
raise RuntimeError(f'FastICA did not converge (N={X.shape[0]}, it={self.maxiter})')
# Normalize components
self.transformer.components_ /= np.sqrt(np.sum(self.transformer.components_**2, axis=-1, keepdims=True))
# Save variance for later
self.total_var = X.var(axis=0).sum()
# Compute projected standard deviations
self.stdev = np.dot(self.transformer.components_, X.T).std(axis=1)
# Sort components based on explained variance
idx = np.argsort(self.stdev)[::-1]
self.stdev = self.stdev[idx]
self.transformer.components_[:] = self.transformer.components_[idx]
def get_components(self):
var_ratio = self.stdev**2 / self.total_var
return self.transformer.components_, self.stdev, var_ratio # ICA outputs are not normalized
# Incremental PCA
class IPCAEstimator():
def __init__(self, n_components):
self.n_components = n_components
self.whiten = False
self.transformer = IncrementalPCA(n_components, whiten=self.whiten, batch_size=max(100, 2*n_components))
self.batch_support = True
def get_param_str(self):
return "ipca_c{}{}".format(self.n_components, '_w' if self.whiten else '')
def fit(self, X):
self.transformer.fit(X)
def fit_partial(self, X):
try:
self.transformer.partial_fit(X)
self.transformer.n_samples_seen_ = \
self.transformer.n_samples_seen_.astype(np.int64) # avoid overflow
return True
except ValueError as e:
print(f'\nIPCA error:', e)
return False
def get_components(self):
stdev = np.sqrt(self.transformer.explained_variance_) # already sorted
var_ratio = self.transformer.explained_variance_ratio_
return self.transformer.components_, stdev, var_ratio # PCA outputs are normalized
# Standard PCA
class PCAEstimator():
def __init__(self, n_components):
self.n_components = n_components
self.solver = 'full'
self.transformer = PCA(n_components, svd_solver=self.solver)
self.batch_support = False
def get_param_str(self):
return f"pca-{self.solver}_c{self.n_components}"
def fit(self, X):
self.transformer.fit(X)
# Save variance for later
self.total_var = X.var(axis=0).sum()
# Compute projected standard deviations
self.stdev = np.dot(self.transformer.components_, X.T).std(axis=1)
# Sort components based on explained variance
idx = np.argsort(self.stdev)[::-1]
self.stdev = self.stdev[idx]
self.transformer.components_[:] = self.transformer.components_[idx]
# Check orthogonality
dotps = [np.dot(*self.transformer.components_[[i, j]])
for (i, j) in itertools.combinations(range(self.n_components), 2)]
if not np.allclose(dotps, 0, atol=1e-4):
print('IPCA components not orghogonal, max dot', np.abs(dotps).max())
self.transformer.mean_ = X.mean(axis=0, keepdims=True)
def get_components(self):
var_ratio = self.stdev**2 / self.total_var
return self.transformer.components_, self.stdev, var_ratio
# Facebook's PCA
# Good default choice: very fast and accurate.
# Very high sample counts won't fit into RAM,
# in which case IncrementalPCA must be used.
class FacebookPCAEstimator():
def __init__(self, n_components):
self.n_components = n_components
self.transformer = SimpleNamespace()
self.batch_support = False
self.n_iter = 2
self.l = 2*self.n_components
def get_param_str(self):
return "fbpca_c{}_it{}_l{}".format(self.n_components, self.n_iter, self.l)
def fit(self, X):
U, s, Va = fbpca.pca(X, k=self.n_components, n_iter=self.n_iter, raw=True, l=self.l)
self.transformer.components_ = Va
# Save variance for later
self.total_var = X.var(axis=0).sum()
# Compute projected standard deviations
self.stdev = np.dot(self.transformer.components_, X.T).std(axis=1)
# Sort components based on explained variance
idx = np.argsort(self.stdev)[::-1]
self.stdev = self.stdev[idx]
self.transformer.components_[:] = self.transformer.components_[idx]
# Check orthogonality
dotps = [np.dot(*self.transformer.components_[[i, j]])
for (i, j) in itertools.combinations(range(self.n_components), 2)]
if not np.allclose(dotps, 0, atol=1e-4):
print('FBPCA components not orghogonal, max dot', np.abs(dotps).max())
self.transformer.mean_ = X.mean(axis=0, keepdims=True)
def get_components(self):
var_ratio = self.stdev**2 / self.total_var
return self.transformer.components_, self.stdev, var_ratio
# Sparse PCA
# The algorithm is online along the features direction, not the samples direction
# => no partial_fit
class SPCAEstimator():
def __init__(self, n_components, alpha=10.0):
self.n_components = n_components
self.whiten = False
self.alpha = alpha # higher alpha => sparser components
#self.transformer = MiniBatchSparsePCA(n_components, alpha=alpha, n_iter=100,
# batch_size=max(20, n_components//5), random_state=0, normalize_components=True)
self.transformer = SparsePCA(n_components, alpha=alpha, ridge_alpha=0.01,
max_iter=100, random_state=0, n_jobs=-1, normalize_components=True) # TODO: warm start using PCA result?
self.batch_support = False # maybe through memmap and HDD-stored tensor
self.stdev = np.zeros((n_components,))
self.total_var = 0.0
def get_param_str(self):
return "spca_c{}_a{}{}".format(self.n_components, self.alpha, '_w' if self.whiten else '')
def fit(self, X):
self.transformer.fit(X)
# Save variance for later
self.total_var = X.var(axis=0).sum()
# Compute projected standard deviations
# NB: cannot simply project with dot product!
self.stdev = self.transformer.transform(X).std(axis=0) # X = (n_samples, n_features)
# Sort components based on explained variance
idx = np.argsort(self.stdev)[::-1]
self.stdev = self.stdev[idx]
self.transformer.components_[:] = self.transformer.components_[idx]
# Check orthogonality
dotps = [np.dot(*self.transformer.components_[[i, j]])
for (i, j) in itertools.combinations(range(self.n_components), 2)]
if not np.allclose(dotps, 0, atol=1e-4):
print('SPCA components not orghogonal, max dot', np.abs(dotps).max())
def get_components(self):
var_ratio = self.stdev**2 / self.total_var
return self.transformer.components_, self.stdev, var_ratio # SPCA outputs are normalized
def get_estimator(name, n_components, alpha):
if name == 'pca':
return PCAEstimator(n_components)
if name == 'ipca':
return IPCAEstimator(n_components)
elif name == 'fbpca':
return FacebookPCAEstimator(n_components)
elif name == 'ica':
return ICAEstimator(n_components)
elif name == 'spca':
return SPCAEstimator(n_components, alpha)
else:
raise RuntimeError('Unknown estimator') |