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import numpy as np
from sklearn.decomposition import PCA
from sklearn.utils.validation import check_array
from .._commonfuncs import GlobalEstimator
[docs]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
[docs] 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