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from sklearn.utils.validation import check_array
import numpy as np
from sklearn.metrics.pairwise import pairwise_distances_chunked
from sklearn.linear_model import LinearRegression
from .._commonfuncs import get_nn, GlobalEstimator
[docs]class TwoNN(GlobalEstimator):
# SPDX-License-Identifier: MIT, 2019 Francesco Mottes [IDMottes]_
"""Intrinsic dimension estimation using the TwoNN algorithm. [Facco2019]_ [IDFacco]_ [IDMottes]_
Parameters
----------
discard_fraction: float
Fraction (between 0 and 1) of largest distances to discard (heuristic from the paper)
dist: bool
Whether data is a precomputed distance matrix
Attributes
----------
x_: 1d array
np.array with the -log(mu) values.
y_: 1d array
np.array with the -log(F(mu_{sigma(i)})) values.
"""
def __init__(self, discard_fraction: float = 0.1, dist: bool = False):
self.discard_fraction = discard_fraction
self.dist = dist
[docs] def fit(self, X, y=None):
"""A reference implementation of a fitting function.
Parameters
----------
X : {array-like}, shape (n_samples, n_features)
A data set for which the intrinsic dimension is estimated.
y : dummy parameter to respect the sklearn API
Returns
-------
self : object
Returns self.
"""
X = check_array(X, ensure_min_samples=2, ensure_min_features=2)
self.dimension_, self.x_, self.y_ = self._twonn(X)
self.is_fitted_ = True
# `fit` should always return `self`
return self
def _twonn(self, X):
"""
Calculates intrinsic dimension of the provided data points with the TWO-NN algorithm.
-----------
Parameters:
X : 2d array-like
2d data matrix. Samples on rows and features on columns.
return_xy : bool (default=False)
Whether to return also the coordinate vectors used for the linear fit.
discard_fraction : float between 0 and 1
Fraction of largest distances to discard (heuristic from the paper)
dist : bool (default=False)
Whether data is a precomputed distance matrix
-----------
Returns:
d : float
Intrinsic dimension of the dataset according to TWO-NN.
x : 1d np.array (optional)
Array with the -log(mu) values.
y : 1d np.array (optional)
Array with the -log(F(mu_{sigma(i)})) values.
-----------
References:
E. Facco, M. d’Errico, A. Rodriguez & A. Laio
Estimating the intrinsic dimension of datasets by a minimal neighborhood information (https://doi.org/10.1038/s41598-017-11873-y)
"""
N = len(X)
if self.dist:
r1, r2 = X[:, 0], X[:, 1]
_mu = r2 / r1
# discard the largest distances
mu = _mu[np.argsort(_mu)[: int(N * (1 - self.discard_fraction))]]
else:
# mu = r2/r1 for each data point
# relatively high dimensional data, use distance matrix generator
if X.shape[1] > 25:
distmat_chunks = pairwise_distances_chunked(X)
_mu = np.zeros((len(X)))
i = 0
for x in distmat_chunks:
x = np.sort(x, axis=1)
r1, r2 = x[:, 1], x[:, 2]
_mu[i : i + len(x)] = r2 / r1
i += len(x)
# discard the largest distances
mu = _mu[np.argsort(_mu)[: int(N * (1 - self.discard_fraction))]]
else: # relatively low dimensional data, search nearest neighbors directly
dists, _ = get_nn(X, k=2)
r1, r2 = dists[:, 0], dists[:, 1]
_mu = r2 / r1
# discard the largest distances
mu = _mu[np.argsort(_mu)[: int(N * (1 - self.discard_fraction))]]
# Empirical cumulate
Femp = np.arange(int(N * (1 - self.discard_fraction))) / N
# Fit line
lr = LinearRegression(fit_intercept=False)
lr.fit(np.log(mu).reshape(-1, 1), -np.log(1 - Femp).reshape(-1, 1))
d = lr.coef_[0][0] # extract slope
return (
d,
np.log(mu).reshape(-1, 1),
-np.log(1 - Femp).reshape(-1, 1),
)