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from audioop import mul
import numpy as np
from pynndescent import NNDescent
from sklearn.linear_model import LinearRegression
from tqdm import tqdm
class IntrinsicDim:
def __init__(self, data, metric="euclidean"):
# normalize and if redundant
self.data = np.unique(data.reshape(len(data), -1), axis=0)
self.metric = metric
self.name = "Intrinsic Dimension"
def find_mu(self):
# number of trees in random projection forest
n_trees = min(64, 5 + int(round((self.data.shape[0]) ** 0.5 / 20.0)))
# max number of nearest neighbor iters to perform
n_iters = max(5, int(round(np.log2(self.data.shape[0]))))
# distance metric
# get nearest neighbors
nnd = NNDescent(
self.data,
n_neighbors=3,
metric=self.metric,
n_trees=n_trees,
n_iters=n_iters,
max_candidates=10,
verbose=False
)
_, knn_dists = nnd.neighbor_graph
mu = knn_dists[:, 2] / knn_dists[:, 1]
return mu
def estimate_id_fast(self):
mu = self.find_mu()
N = self.data.shape[0]
sort_idx = np.argsort(mu)
Femp = np.arange(N)/N
lr = LinearRegression(fit_intercept=False)
lr.fit(np.log(mu[sort_idx]).reshape(-1,1), -np.log(1-Femp).reshape(-1,1))
d = lr.coef_[0][0]
return d
def estimate_id(self):
N = self.data.shape[0]
mu = np.zeros(N)
for i in tqdm(range(N)):
dist = np.sort(np.sqrt(np.sum((self.data[i]-self.data)**2, axis=1)))
r1, r2 = dist[dist>0][:2]
mu[i]=r2/r1
sort_idx = np.argsort(mu)
Femp = np.arange(N)/N
lr = LinearRegression(fit_intercept=False)
lr.fit(np.log(mu[sort_idx]).reshape(-1,1), -np.log(1-Femp).reshape(-1,1))
d = lr.coef_[0][0]
return d
def twonn_dimension(self, return_xy=False):
N = len(self.data)
mu = []
for i in tqdm(range(N)):
dist = np.sort(np.sqrt(np.sum((self.data[i]-self.data)**2, axis=1)))
r1, r2 = dist[dist>0][:2]
mu.append((i+1,r2/r1))
sigma_i = dict(zip(range(1,len(mu)+1), np.array(sorted(mu, key=lambda x: x[1]))[:,0].astype(int)))
mu = dict(mu)
F_i = {}
for i in mu:
F_i[sigma_i[i]] = i/N
x = np.log([mu[i] for i in sorted(mu.keys())])
y = np.array([1-F_i[i] for i in sorted(mu.keys())])
x = x[y>0]
y = y[y>0]
y = -1*np.log(y)
d = np.linalg.lstsq(np.vstack([x, np.zeros(len(x))]).T, y, rcond=None)[0][0]
if return_xy:
return d, x, y
else:
return d
def twonn_dimension_fast(self):
N = len(self.data)
mu = self.find_mu().tolist()
mu = list(enumerate(mu, start=1))
sigma_i = dict(zip(range(1,len(mu)+1), np.array(sorted(mu, key=lambda x: x[1]))[:,0].astype(int)))
mu = dict(mu)
F_i = {}
for i in mu:
F_i[sigma_i[i]] = i/N
x = np.log([mu[i] for i in sorted(mu.keys())])
y = np.array([1-F_i[i] for i in sorted(mu.keys())])
x = x[y>0]
y = y[y>0]
y = -1*np.log(y)
d = np.linalg.lstsq(np.vstack([x, np.zeros(len(x))]).T, y, rcond=None)[0][0]
return d
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