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import numpy as np
from scipy.spatial.distance import pdist, squareform
from sklearn.utils.validation import check_array
from .._commonfuncs import GlobalEstimator
[docs]class KNN(GlobalEstimator):
# SPDX-License-Identifier: MIT, 2017 Kerstin Johnsson [IDJohnsson]_
"""Intrinsic dimension estimation using the kNN algorithm. [Carter2010]_ [IDJohnsson]_
This is a simplified version of the kNN dimension estimation method described by Carter et al. (2010),
the difference being that block bootstrapping is not used.
Parameters
----------
X: 2D numeric array
A 2D data set with each row describing a data point.
k: int
Number of distances to neighbors used at a time.
ps: 1D numeric array
Vector with sample sizes; each sample size has to be larger than k and smaller than nrow(data).
M: int, default=1
Number of bootstrap samples for each sample size.
gamma: int, default=2
Weighting constant.
"""
def __init__(self, k=None, ps=None, M=1, gamma=2):
self.k = k
self.ps = ps
self.M = M
self.gamma = gamma
[docs] def fit(self, X, y=None):
"""A reference implementation of a fitting function.
Parameters
----------
X : {array-like}, shape (n_samples, n_features)
The training input samples.
y : dummy parameter to respect the sklearn API
Returns
-------
self: object
Returns self.
self.dimension_: float
The estimated intrinsic dimension
self.residual_: float
Residuals
"""
self._k = 2 if self.k is None else self.k
self._ps = np.arange(self._k + 1, self._k + 5) if self.ps is None else self.ps
X = check_array(X, ensure_min_samples=self._k + 1, ensure_min_features=2)
self.dimension_, self.residual_ = self._knnDimEst(X)
self.is_fitted_ = True
# `fit` should always return `self`
return self
def _knnDimEst(self, X):
n = len(X)
Q = len(self._ps)
if min(self._ps) <= self._k or max(self._ps) > n:
raise ValueError("ps must satisfy k<ps<len(X)")
# Compute the distance between any two points in the X set
dist = squareform(pdist(X))
# Compute weighted graph length for each sample
L = np.zeros((Q, self.M))
for i in range(Q):
for j in range(self.M):
samp_ind = np.random.randint(0, n, self._ps[i])
for l in samp_ind:
L[i, j] += np.sum(
np.sort(dist[l, samp_ind])[1 : (self._k + 1)] ** self.gamma
)
# Add the weighted sum of the distances to the k nearest neighbors.
# We should not include the sample itself, to which the distance is
# zero.
# Least squares solution for m
d = X.shape[1]
epsilon = np.repeat(np.nan, d)
for m0, m in enumerate(np.arange(1, d + 1)):
alpha = (m - self.gamma) / m
ps_alpha = self._ps ** alpha
hat_c = np.sum(ps_alpha * np.sum(L, axis=1)) / (
np.sum(ps_alpha ** 2) * self.M
)
epsilon[m0] = np.sum(
(L - np.tile((hat_c * ps_alpha)[:, None], self.M)) ** 2
)
# matrix(vec, nrow = length(vec), ncol = b) is a matrix with b
# identical columns equal to vec
# sum(matr) is the sum of all elements in the matrix matr
de = np.argmin(epsilon) + 1 # Missing values are discarded
return de, epsilon[de - 1]