112 lines
3.5 KiB
Cython
112 lines
3.5 KiB
Cython
from libc cimport math
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cimport cython
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import numpy as np
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cimport numpy as np
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cdef extern from "numpy/npy_math.h":
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float NPY_INFINITY
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cdef double EPSILON_DBL = 1e-7
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cdef double PERPLEXITY_TOLERANCE = 1e-5
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@cython.boundscheck(False)
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cpdef np.ndarray[np.float_t, ndim=2] _binary_search_perplexity(
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np.ndarray[np.float_t, ndim=2] affinities, double desired_perplexity,
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int verbose):
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"""Binary search for sigmas of conditional Gaussians.
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We are looking for sigma = sqrt(1/beta) so that the perplexity
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of the conditional distribution p_i|j matches approximately the
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desired value. p_i|j are Gaussian distributed.
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The idea has been proposed in "Stochastic Neighbor Embedding"
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Geoffrey Hinton and Sam Roweis, 2003.
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Parameters
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----------
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affinities : array-like, shape (n_samples, n_samples)
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Distances between training samples.
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desired_perplexity : double
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Desired perplexity (2^entropy) of the conditional Gaussians.
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verbose : int
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Verbosity level.
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Returns
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-------
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P : array, shape (n_samples, n_samples)
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Probabilities of conditional Gaussian distributions p_i|j.
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"""
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# Maximum number of binary search steps
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cdef int n_steps = 100
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cdef int n_samples = affinities.shape[0]
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cdef np.ndarray[np.float_t, ndim=2] P = np.ndarray((n_samples, n_samples),
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dtype=np.double)
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# Precisions of conditional Gaussian distrubutions
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cdef double beta
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cdef double beta_min
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cdef double beta_max
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cdef double beta_sum = 0.0
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# Now we go to log scale
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cdef double desired_entropy = math.log(desired_perplexity)
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cdef double entropy_diff
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cdef double entropy
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cdef double sum_Pi
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cdef double sum_disti_Pi
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cdef int i
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cdef int j
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for i in range(n_samples):
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beta_min = -NPY_INFINITY
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beta_max = NPY_INFINITY
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beta = 1.0
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# Binary search of precision for i-th conditional distribution
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for _ in range(n_steps):
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# Compute current entropy and corresponding probabilities
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for j in range(n_samples):
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P[i, j] = math.exp(-affinities[i, j] * beta)
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P[i, i] = 0.0
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sum_Pi = 0.0
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for j in range(n_samples):
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sum_Pi += P[i, j]
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if sum_Pi == 0.0:
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sum_Pi = EPSILON_DBL
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sum_disti_Pi = 0.0
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for j in range(n_samples):
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P[i, j] /= sum_Pi
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sum_disti_Pi += affinities[i, j] * P[i, j]
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entropy = math.log(sum_Pi) + beta * sum_disti_Pi
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entropy_diff = entropy - desired_entropy
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if math.fabs(entropy_diff) <= PERPLEXITY_TOLERANCE:
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break
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if entropy_diff > 0.0:
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beta_min = beta
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if beta_max == NPY_INFINITY:
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beta *= 2.0
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else:
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beta = (beta + beta_max) / 2.0
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else:
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beta_max = beta
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if beta_min == -NPY_INFINITY:
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beta /= 2.0
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else:
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beta = (beta + beta_min) / 2.0
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beta_sum += beta
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if verbose and ((i + 1) % 1000 == 0 or i + 1 == n_samples):
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print("[t-SNE] Computed conditional probabilities for sample "
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"%d / %d" % (i + 1, n_samples))
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if verbose:
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print("[t-SNE] Mean sigma: %f"
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% np.mean(math.sqrt(n_samples / beta_sum)))
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return P
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