chrischoy · March 13, 2021 11:50 · May 24, 2017 · May 23, 2017 · Mar 1, 2017 · Mar 1, 2017
diff --git a/smoothed_triplet_loss.py b/smoothed_triplet_loss.py
@@ -16,7 +16,7 @@ def smoothed_metric_loss(input_tensor, name='smoothed_triplet_loss', margin=1):
         # Compute the pairwise distance
         Xe = tf.expand_dims(X, 1)
         Dsq = tf.reduce_sum(tf.square(Xe - tf.transpose(Xe, (1, 0, 2))), 2, keep_dims=False)
-        D = tf.sqrt(Dsq)
+        D = tf.sqrt(Dsq + 1e-8)
         expmD = tf.exp(m - D)
 
         # Compute the loss

diff --git a/smoothed_triplet_loss.py b/smoothed_triplet_loss.py
@@ -14,9 +14,9 @@ def smoothed_metric_loss(input_tensor, name='smoothed_triplet_loss', margin=1):
         m = margin
 
         # Compute the pairwise distance
-        sq = tf.reduce_sum(X*X, 1)
-        sq = tf.reshape(sq, [-1, 1])  # turn r into a column vector
-        D = sq - 2 * tf.matmul(X, tf.transpose(X)) + tf.transpose(sq)
+        Xe = tf.expand_dims(X, 1)
+        Dsq = tf.reduce_sum(tf.square(Xe - tf.transpose(Xe, (1, 0, 2))), 2, keep_dims=False)
+        D = tf.sqrt(Dsq)
         expmD = tf.exp(m - D)
 
         # Compute the loss
@@ -32,11 +32,9 @@ def smoothed_metric_loss(input_tensor, name='smoothed_triplet_loss', margin=1):
             ind_rest = np.hstack([np.arange(0, pair_ind * 2),
                                   np.arange(pair_ind * 2 + 2, batch_size)])
 
-            i_nd_rest = [[i, k] for k in ind_rest]
-            j_nd_rest = [[j, l] for l in ind_rest]
-            J_ij = tf.log(tf.reduce_sum(tf.gather_nd(expmD, i_nd_rest))
-                    + tf.reduce_sum(tf.gather_nd(expmD, j_nd_rest))) \
-                            + tf.gather_nd(D, [[i, j]])
+            inds = [[i, k] for k in ind_rest]
+            inds.extend([[j, l] for l in ind_rest])
+            J_ij = tf.log(tf.reduce_sum(tf.gather_nd(expmD, inds))) + tf.gather_nd(D, [[i, j]])
             J_all.append(J_ij)
 
         J_all = tf.convert_to_tensor(J_all)

diff --git a/smoothed_triplet_loss.py b/smoothed_triplet_loss.py
@@ -1,9 +1,11 @@
 import tensorflow as tf
 import numpy as np
 
-def smoothed_metric_loss(input_tensor, name='smoothed_metric_loss', margin=1):
+def smoothed_metric_loss(input_tensor, name='smoothed_triplet_loss', margin=1):
     '''
     input_tensor: require a tensor with predefined dimensions (No None dimension)
+                  Every two consecutive vectors must be a positive pair. There
+                  should not be more than one pair from each class.
     '''
     with tf.variable_scope(name):
         # Song et al., Deep Metric Learning via Lifted Structured Feature Embedding
@@ -13,7 +15,7 @@ def smoothed_metric_loss(input_tensor, name='smoothed_metric_loss', margin=1):
 
         # Compute the pairwise distance
         sq = tf.reduce_sum(X*X, 1)
-        sq = tf.reshape(sq, [-1, 1])  # turn r into column vector
+        sq = tf.reshape(sq, [-1, 1])  # turn r into a column vector
         D = sq - 2 * tf.matmul(X, tf.transpose(X)) + tf.transpose(sq)
         expmD = tf.exp(m - D)
 

diff --git a/smoothed_triplet_loss.py b/smoothed_triplet_loss.py
@@ -0,0 +1,43 @@
+import tensorflow as tf
+import numpy as np
+
+def smoothed_metric_loss(input_tensor, name='smoothed_metric_loss', margin=1):
+    '''
+    input_tensor: require a tensor with predefined dimensions (No None dimension)
+    '''
+    with tf.variable_scope(name):
+        # Song et al., Deep Metric Learning via Lifted Structured Feature Embedding
+        # Define feature X \in \mathbb{R}^{N \times C}
+        X = input_tensor
+        m = margin
+
+        # Compute the pairwise distance
+        sq = tf.reduce_sum(X*X, 1)
+        sq = tf.reshape(sq, [-1, 1])  # turn r into column vector
+        D = sq - 2 * tf.matmul(X, tf.transpose(X)) + tf.transpose(sq)
+        expmD = tf.exp(m - D)
+
+        # Compute the loss
+        # Assume that the input data is aligned in a way that two consecutive data form a pair
+        batch_size, _ = X.get_shape().as_list()
+
+        # L_{ij} = \log (\sum_{i, k} exp\{m - D_{ik}\} + \sum_{j, l} exp\{m - D_{jl}\}) + D_{ij}
+        # L = \frac{1}{2|P|}\sum_{(i,j)\in P} \max(0, J_{i,j})^2
+        J_all = []
+        for pair_ind in range(batch_size // 2):
+            i = pair_ind * 2
+            j = i + 1
+            ind_rest = np.hstack([np.arange(0, pair_ind * 2),
+                                  np.arange(pair_ind * 2 + 2, batch_size)])
+
+            i_nd_rest = [[i, k] for k in ind_rest]
+            j_nd_rest = [[j, l] for l in ind_rest]
+            J_ij = tf.log(tf.reduce_sum(tf.gather_nd(expmD, i_nd_rest))
+                    + tf.reduce_sum(tf.gather_nd(expmD, j_nd_rest))) \
+                            + tf.gather_nd(D, [[i, j]])
+            J_all.append(J_ij)
+
+        J_all = tf.convert_to_tensor(J_all)
+        loss = tf.divide(tf.reduce_mean(tf.square(tf.maximum(J_all, 0))), 2.0, name='metric_loss')
+        tf.add_to_collection(tf.GraphKeys.LOSSES, loss)
+    return loss