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Triplet.py
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from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.framework import dtypes
import tensorflow as tf
def pairwise_distance(feature, squared=False):
"""Computes the pairwise distance matrix with numerical stability.
output[i, j] = || feature[i, :] - feature[j, :] ||_2
Args:
feature: 2-D Tensor of size [number of data, feature dimension].
squared: Boolean, whether or not to square the pairwise distances.
Returns:
pairwise_distances: 2-D Tensor of size [number of data, number of data].
"""
pairwise_distances_squared = math_ops.add(
math_ops.reduce_sum(math_ops.square(feature), axis=[1], keepdims=True),
math_ops.reduce_sum(
math_ops.square(array_ops.transpose(feature)),
axis=[0],
keepdims=True)) - 2.0 * math_ops.matmul(feature,
array_ops.transpose(feature))
# Deal with numerical inaccuracies. Set small negatives to zero.
pairwise_distances_squared = math_ops.maximum(pairwise_distances_squared, 0.0)
# Get the mask where the zero distances are at.
error_mask = math_ops.less_equal(pairwise_distances_squared, 0.0)
# Optionally take the sqrt.
if squared:
pairwise_distances = pairwise_distances_squared
else:
pairwise_distances = math_ops.sqrt(
pairwise_distances_squared + tf.cast(error_mask, tf.float32) * 1e-16)
# math_ops.to_float(error_mask)
# Undo conditionally adding 1e-16.
pairwise_distances = math_ops.multiply(
pairwise_distances, tf.cast(math_ops.logical_not(error_mask), tf.float32))
# math_ops.to_float(math_ops.logical_not(error_mask))
num_data = array_ops.shape(feature)[0]
# Explicitly set diagonals to zero.
mask_offdiagonals = array_ops.ones_like(pairwise_distances) - array_ops.diag(
array_ops.ones([num_data]))
pairwise_distances = math_ops.multiply(pairwise_distances, mask_offdiagonals)
return pairwise_distances
def masked_maximum(data, mask, dim=1):
"""Computes the axis wise maximum over chosen elements.
Args:
data: 2-D float `Tensor` of size [n, m].
mask: 2-D Boolean `Tensor` of size [n, m].
dim: The dimension over which to compute the maximum.
Returns:
masked_maximums: N-D `Tensor`.
The maximized dimension is of size 1 after the operation.
"""
axis_minimums = math_ops.reduce_min(data, dim, keepdims=True)
masked_maximums = math_ops.reduce_max(
math_ops.multiply(data - axis_minimums, mask), dim,
keepdims=True) + axis_minimums
return masked_maximums
def masked_minimum(data, mask, dim=1):
"""Computes the axis wise minimum over chosen elements.
Args:
data: 2-D float `Tensor` of size [n, m].
mask: 2-D Boolean `Tensor` of size [n, m].
dim: The dimension over which to compute the minimum.
Returns:
masked_minimums: N-D `Tensor`.
The minimized dimension is of size 1 after the operation.
"""
axis_maximums = math_ops.reduce_max(data, dim, keepdims=True)
masked_minimums = math_ops.reduce_min(
math_ops.multiply(data - axis_maximums, mask), dim,
keepdims=True) + axis_maximums
return masked_minimums
def triplet_loss(labels, embeddings, margin=1.0):
"""
Calculates triplet loss using semi-hard triplets. For details, see Weinberger et al.
Code adapted from https://github.com/omoindrot/tensorflow-triplet-loss/blob/master/model/triplet_loss.py
:param labels: label information of each mini-batch
:param embeddings: network output for a given batch
:param margin: margin parameter
:return: triplet loss
"""
labels = tf.cast(labels, dtype='int32')
# Build pairwise squared distance matrix.
pdist_matrix = pairwise_distance(embeddings, squared=True)
# Build pairwise binary adjacency matrix.
adjacency = math_ops.equal(labels, array_ops.transpose(labels))
# Invert so we can select negatives only.
adjacency_not = math_ops.logical_not(adjacency)
# global batch_size
batch_size = array_ops.size(labels) # was 'array_ops.size(labels)'
# Compute the mask.
pdist_matrix_tile = array_ops.tile(pdist_matrix, [batch_size, 1])
mask = math_ops.logical_and(
array_ops.tile(adjacency_not, [batch_size, 1]),
math_ops.greater(
pdist_matrix_tile, array_ops.reshape(
array_ops.transpose(pdist_matrix), [-1, 1])))
mask_final = array_ops.reshape(
math_ops.greater(
math_ops.reduce_sum(
math_ops.cast(mask, dtype=dtypes.float32), 1, keepdims=True),
0.0), [batch_size, batch_size])
mask_final = array_ops.transpose(mask_final)
adjacency_not = math_ops.cast(adjacency_not, dtype=dtypes.float32)
mask = math_ops.cast(mask, dtype=dtypes.float32)
# negatives_outside: smallest D_an where D_an > D_ap.
negatives_outside = array_ops.reshape(
masked_minimum(pdist_matrix_tile, mask), [batch_size, batch_size])
negatives_outside = array_ops.transpose(negatives_outside)
# negatives_inside: largest D_an.
negatives_inside = array_ops.tile(
masked_maximum(pdist_matrix, adjacency_not), [1, batch_size])
semi_hard_negatives = tf.where( # array_ops
mask_final, negatives_outside, negatives_inside)
loss_mat = math_ops.add(margin, pdist_matrix - semi_hard_negatives)
mask_positives = math_ops.cast(
adjacency, dtype=dtypes.float32) - array_ops.diag(
array_ops.ones([batch_size]))
# In lifted-struct, the authors multiply 0.5 for upper triangular
# in semi-hard, they take all positive pairs except the diagonal.
num_positives = math_ops.reduce_sum(mask_positives)
num_positives = math_ops.add(num_positives, 1e-16) # to avoid NAN div by zero
semi_hard_triplet_loss_distance = math_ops.truediv(
math_ops.reduce_sum(
math_ops.maximum(
math_ops.multiply(loss_mat, mask_positives), 0.0)),
num_positives,
name='triplet_semi-hard_loss')
return semi_hard_triplet_loss_distance