Module dimdrop.util.tsne
Code taken from https://github.com/kylemcdonald/Parametric-t-SNE
MIT License
Copyright (c) 2016 Kyle McDonald
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Source code
"""
Code taken from https://github.com/kylemcdonald/Parametric-t-SNE
MIT License
Copyright (c) 2016 Kyle McDonald
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is furnished
to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
"""
import numpy as np
def compute_joint_probabilities(
samples,
batch_size=5000,
d=2,
perplexity=30,
tol=1e-5,
verbose=0
):
v = d - 1
# Initialize some variables
n = samples.shape[0]
batch_size = min(batch_size, n)
# Precompute joint probabilities for all batches
if verbose > 0:
print('Precomputing P-values...')
batch_count = int(n / batch_size)
P = np.zeros((batch_count, batch_size, batch_size))
for i, start in enumerate(range(0, n - batch_size + 1, batch_size)):
curX = samples[start:start+batch_size] # select batch
# compute affinities using fixed perplexity
P[i], beta = x2p(curX, perplexity, tol, verbose=verbose)
# make sure we don't have NaN's
P[i][np.isnan(P[i])] = 0
# / 2 # make symmetric
P[i] = (P[i] + P[i].T)
# obtain estimation of joint probabilities
P[i] = P[i] / P[i].sum()
P[i] = np.maximum(P[i], np.finfo(P[i].dtype).eps)
return P
def x2p(X, u=15, tol=1e-4, print_iter=500, max_tries=50, verbose=0):
# Initialize some variables
n = X.shape[0] # number of instances
P = np.zeros((n, n)) # empty probability matrix
beta = np.ones(n) # empty precision vector
logU = np.log(u) # log of perplexity (= entropy)
# Compute pairwise distances
if verbose > 0:
print('Computing pairwise distances...')
sum_X = np.sum(np.square(X), axis=1)
# note: translating sum_X' from matlab to numpy means using reshape to add
# a dimension
D = sum_X + sum_X[:, None] + -2 * X.dot(X.T)
# Run over all datapoints
if verbose > 0:
print('Computing P-values...')
for i in range(n):
if verbose > 1 and print_iter and i % print_iter == 0:
print('Computed P-values {} of {} datapoints...'.format(i, n))
# Set minimum and maximum values for precision
betamin = float('-inf')
betamax = float('+inf')
# Compute the Gaussian kernel and entropy for the current precision
indices = np.concatenate((np.arange(0, i), np.arange(i + 1, n)))
Di = D[i, indices]
H, thisP = Hbeta(Di, beta[i])
# Evaluate whether the perplexity is within tolerance
Hdiff = H - logU
tries = 0
while abs(Hdiff) > tol and tries < max_tries:
# If not, increase or decrease precision
if Hdiff > 0:
betamin = beta[i]
if np.isinf(betamax):
beta[i] *= 2
else:
beta[i] = (beta[i] + betamax) / 2
else:
betamax = beta[i]
if np.isinf(betamin):
beta[i] /= 2
else:
beta[i] = (beta[i] + betamin) / 2
# Recompute the values
H, thisP = Hbeta(Di, beta[i])
Hdiff = H - logU
tries += 1
# Set the final row of P
P[i, indices] = thisP
if verbose > 0:
print('Mean value of sigma: {}'.format(np.mean(np.sqrt(1 / beta))))
print('Minimum value of sigma: {}'.format(np.min(np.sqrt(1 / beta))))
print('Maximum value of sigma: {}'.format(np.max(np.sqrt(1 / beta))))
return P, beta
def Hbeta(D, beta):
P = np.exp(-D * beta)
sumP = np.sum(P)
if sumP == 0:
sumP = 1
H = np.log(sumP) + beta * np.sum(np.multiply(D, P)) / sumP
P = P / sumP
return H, PFunctions
def Hbeta(D, beta)-
Source code
def Hbeta(D, beta): P = np.exp(-D * beta) sumP = np.sum(P) if sumP == 0: sumP = 1 H = np.log(sumP) + beta * np.sum(np.multiply(D, P)) / sumP P = P / sumP return H, P def compute_joint_probabilities(samples, batch_size=5000, d=2, perplexity=30, tol=1e-05, verbose=0)-
Source code
def compute_joint_probabilities( samples, batch_size=5000, d=2, perplexity=30, tol=1e-5, verbose=0 ): v = d - 1 # Initialize some variables n = samples.shape[0] batch_size = min(batch_size, n) # Precompute joint probabilities for all batches if verbose > 0: print('Precomputing P-values...') batch_count = int(n / batch_size) P = np.zeros((batch_count, batch_size, batch_size)) for i, start in enumerate(range(0, n - batch_size + 1, batch_size)): curX = samples[start:start+batch_size] # select batch # compute affinities using fixed perplexity P[i], beta = x2p(curX, perplexity, tol, verbose=verbose) # make sure we don't have NaN's P[i][np.isnan(P[i])] = 0 # / 2 # make symmetric P[i] = (P[i] + P[i].T) # obtain estimation of joint probabilities P[i] = P[i] / P[i].sum() P[i] = np.maximum(P[i], np.finfo(P[i].dtype).eps) return P def x2p(X, u=15, tol=0.0001, print_iter=500, max_tries=50, verbose=0)-
Source code
def x2p(X, u=15, tol=1e-4, print_iter=500, max_tries=50, verbose=0): # Initialize some variables n = X.shape[0] # number of instances P = np.zeros((n, n)) # empty probability matrix beta = np.ones(n) # empty precision vector logU = np.log(u) # log of perplexity (= entropy) # Compute pairwise distances if verbose > 0: print('Computing pairwise distances...') sum_X = np.sum(np.square(X), axis=1) # note: translating sum_X' from matlab to numpy means using reshape to add # a dimension D = sum_X + sum_X[:, None] + -2 * X.dot(X.T) # Run over all datapoints if verbose > 0: print('Computing P-values...') for i in range(n): if verbose > 1 and print_iter and i % print_iter == 0: print('Computed P-values {} of {} datapoints...'.format(i, n)) # Set minimum and maximum values for precision betamin = float('-inf') betamax = float('+inf') # Compute the Gaussian kernel and entropy for the current precision indices = np.concatenate((np.arange(0, i), np.arange(i + 1, n))) Di = D[i, indices] H, thisP = Hbeta(Di, beta[i]) # Evaluate whether the perplexity is within tolerance Hdiff = H - logU tries = 0 while abs(Hdiff) > tol and tries < max_tries: # If not, increase or decrease precision if Hdiff > 0: betamin = beta[i] if np.isinf(betamax): beta[i] *= 2 else: beta[i] = (beta[i] + betamax) / 2 else: betamax = beta[i] if np.isinf(betamin): beta[i] /= 2 else: beta[i] = (beta[i] + betamin) / 2 # Recompute the values H, thisP = Hbeta(Di, beta[i]) Hdiff = H - logU tries += 1 # Set the final row of P P[i, indices] = thisP if verbose > 0: print('Mean value of sigma: {}'.format(np.mean(np.sqrt(1 / beta)))) print('Minimum value of sigma: {}'.format(np.min(np.sqrt(1 / beta)))) print('Maximum value of sigma: {}'.format(np.max(np.sqrt(1 / beta)))) return P, beta