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_PCA.py
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_PCA.py
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#
# BSD 3-Clause License
#
# Copyright (c) 2020, Jonathan Bac
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# 1. Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its
# contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
# DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
# FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#
import numpy as np
from sklearn.decomposition import PCA
from sklearn.utils.validation import check_array
from .._commonfuncs import GlobalEstimator
class lPCA(GlobalEstimator):
# SPDX-License-Identifier: MIT, 2017 Kerstin Johnsson [IDJohnsson]_
"""Intrinsic dimension estimation using the PCA algorithm. [Cangelosi2007]_ [Fan2010]_ [Fukunaga2010]_ [IDJohnsson]_
Version 'FO' (Fukunaga-Olsen) returns eigenvalues larger than alphaFO times the largest eigenvalue.\n
Version 'Fan' is the method by Fan et al.\n
Version 'maxgap' returns the position of the largest relative gap in the sequence of eigenvalues.\n
Version 'ratio' returns the number of eigenvalues needed to retain at least alphaRatio of the variance.\n
Version 'participation_ratio' returns the number of eigenvalues given by PR=sum(eigenvalues)^2/sum(eigenvalues^2)\n
Version 'Kaiser' returns the number of eigenvalues above average (the average eigenvalue is 1)\n
Version 'broken_stick' returns the number of eigenvalues above corresponding values of the broken stick distribution\n
Parameters
----------
ver: str, default='FO'
Version. Possible values: 'FO', 'Fan', 'maxgap','ratio', 'Kaiser', 'broken_stick'.
alphaRatio: float in (0,1)
Only for ver = 'ratio'. ID is estimated to be
the number of principal components needed to retain at least alphaRatio of the variance.
alphaFO: float in (0,1)
Only for ver = 'FO'. An eigenvalue is considered significant
if it is larger than alpha times the largest eigenvalue.
alphaFan: float
Only for ver = 'Fan'. The alpha parameter (large gap threshold).
betaFan: float
Only for ver = 'Fan'. The beta parameter (total covariance threshold).
PFan: float
Only for ver = 'Fan'. Total covariance in non-noise.
verbose: bool, default=False
explained_variance: bool, default=False
If True, lPCA.fit(X) expects as input
a precomputed explained_variance vector: X = sklearn.decomposition.PCA().fit(X).explained_variance_
Attributes
----------
gap_:
Ratio of each PC's explained variance (except the last)
with the following PC's explained variance
"""
def __init__(
self,
ver="FO",
alphaRatio=0.05,
alphaFO=0.05,
alphaFan=10,
betaFan=0.8,
PFan=0.95,
verbose=True,
fit_explained_variance=False,
):
self.ver = ver
self.alphaRatio = alphaRatio
self.alphaFO = alphaFO
self.alphaFan = alphaFan
self.betaFan = betaFan
self.PFan = PFan
self.verbose = verbose
self.fit_explained_variance = fit_explained_variance
def fit(self, X, y=None):
"""A reference implementation of a fitting function.
Parameters
----------
X : {array-like}, shape (n_samples, n_features)
A local dataset of training input samples.
y : dummy parameter to respect the sklearn API
Returns
-------
self : object
Returns self.
"""
if self.fit_explained_variance:
X = check_array(X, ensure_2d=False, ensure_min_samples=2)
else:
X = check_array(X, ensure_min_samples=2, ensure_min_features=2)
self.dimension_, self.gap_ = self._pcaLocalDimEst(X)
self.is_fitted_ = True
# `fit` should always return `self`
return self
def _fit_once(self, X, y=None):
"""A reference implementation of a fitting function.
Parameters
----------
X : {array-like}, shape (n_samples, n_features)
A local dataset of training input samples.
y : dummy parameter to respect the sklearn API
Returns
-------
self : object
Returns self.
"""
if self.fit_explained_variance:
X = check_array(X, ensure_2d=False, ensure_min_samples=2)
else:
X = check_array(X, ensure_min_samples=2, ensure_min_features=2)
self.dimension_, self.gap_ = self._pcaLocalDimEst(X)
self.is_fitted_ = True
# `fit` should always return `self`
return self
def _pcaLocalDimEst(self, X):
if self.fit_explained_variance:
explained_var = X
else:
pca = PCA().fit(X)
self.explained_var_ = explained_var = pca.explained_variance_
if self.ver == "FO":
return self._FO(explained_var)
elif self.ver == "Fan":
return self._fan(explained_var)
elif self.ver == "maxgap":
return self._maxgap(explained_var)
elif self.ver == "ratio":
return self._ratio(explained_var)
elif self.ver == "participation_ratio":
return self._participation_ratio(explained_var)
elif self.ver == "Kaiser":
return self._Kaiser(explained_var)
elif self.ver == "broken_stick":
return self._broken_stick(explained_var)
def _FO(self, explained_var):
de = sum(explained_var > (self.alphaFO * explained_var[0]))
gaps = explained_var[:-1] / explained_var[1:]
return de, gaps
@staticmethod
def _maxgap(explained_var):
gaps = explained_var[:-1] / explained_var[1:]
de = np.nanargmax(gaps) + 1
return de, gaps
def _ratio(self, explained_var):
sumexp = np.cumsum(explained_var)
sumexp_norm = sumexp / np.max(sumexp)
de = sum(sumexp_norm < self.alphaRatio) + 1
gaps = explained_var[:-1] / explained_var[1:]
return de, gaps
def _participation_ratio(self, explained_var):
PR = sum(explained_var) ** 2 / sum(explained_var ** 2)
de = PR
gaps = explained_var[:-1] / explained_var[1:]
return de, gaps
def _fan(self, explained_var):
r = np.where(np.cumsum(explained_var) / sum(explained_var) > self.PFan)[0][0]
sigma = np.mean(explained_var[r:])
explained_var -= sigma
gaps = explained_var[:-1] / explained_var[1:]
de = 1 + np.min(
np.concatenate(
(
np.where(gaps > self.alphaFan)[0],
np.where(
(np.cumsum(explained_var) / sum(explained_var)) > self.betaFan
)[0],
)
)
)
return de, gaps
def _Kaiser(self, explained_var):
de = sum(explained_var > np.mean(explained_var))
gaps = explained_var[:-1] / explained_var[1:]
return de, gaps
@staticmethod
def _brokenstick_distribution(dim):
distr = np.zeros(dim)
for i in range(dim):
for j in range(i, dim):
distr[i] = distr[i] + 1 / (j + 1)
distr[i] = distr[i] / dim
return distr
def _broken_stick(self, explained_var):
bs = self._brokenstick_distribution(dim=len(explained_var))
gaps = explained_var[:-1] / explained_var[1:]
de = 0
explained_var_norm = explained_var / np.sum(explained_var)
for i in range(len(explained_var)):
if bs[i] > explained_var_norm[i]:
de = i + 1
break
return de, gaps
##### dev in progress
# from sklearn.cluster import KMeans
# def pcaOtpmPointwiseDimEst(data, N, alpha = 0.05):
# km = KMeans(n_clusters=N)
# km.fit(data)
# pt = km.cluster_centers_
# pt_bm = km.labels_
# pt_sm = np.repeat(np.nan, len(pt_bm))
#
# for k in range(len(data)):
# pt_sm[k] = np.argmin(lens(pt[[i for i in range(N) if i!=pt_bm[k]],:] - data[k,:]))
# if (pt_sm[k] >= pt_bm[k]):
# pt_sm[k] += 1
#
# de_c = np.repeat(np.nan, N)
# nbr_nb_c = np.repeat(np.nan, N)
# for k in range(N):
# nb = np.unique(np.concatenate((pt_sm[pt_bm == k], pt_bm[pt_sm == k]))).astype(int)
# nbr_nb_c[k] = len(nb)
# loc_dat = pt[nb,:] - pt[k,:]
# if len(loc_dat) == 1:
# continue
# de_c[k] = lPCA().fit(loc_dat).dimension_ #pcaLocalDimEst(loc_dat, ver = "FO", alphaFO = alpha)
#
# de = de_c[pt_bm]
# nbr_nb = nbr_nb_c[pt_bm]
# return de, nbr_nb