Triplet Loss入门

﹏ヽ暗。殇╰゛Y 2022-04-08 10:22 261阅读 0赞

# Triplet Loss入门 #

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## Face verification vs. face recogntion ##

### Verification ###

>  *  Input image, name/ID
>  *  Output whether the input image is that of the claimed person.

### Recognition ###

>  *  Has a database of K peosons(or not recognized)

### Relations ###

We can use a face verification system to make a face recognition system. The accuracy of the verification system has to be high (around 99.9% or more) to be use accurately within a recognition system because the recognition system accuracy will be less than the verification system given K persons.

## One Shot Learning ##

>  *  One of the face recognition challenges is to solve one shot learning problem.
>  *  One Shot Learning: A recognition system is able to recognize a person, learning from one image.
>  *  Historically deep learning doesn’t work well with a small number of data.  
>     Instead to make this work, we will learn a similarity function:  
>      d ( i m g 1 , i m g 2 ) d( img1, img2 ) d(img1,img2) = degree of difference between images.  
>     We want d result to be low in case of the same faces.  
>     We use  τ \\tau τ as a threshold for d:  
>     If  d ( i m g 1 , i m g 2 ) < = τ d( img1, img2 ) <= \\tau d(img1,img2)<=τ Then the faces are the same.
>  *  Similarity function helps us solving the one shot learning. Also its robust to new inputs.

## Siamese Network ##

>  *  We will implement the similarity function using a type of NNs called Siamease Network in which we can pass multiple inputs to the two or more networks with the same architecture and parameters.
>  *  The loss function will be  d ( x 1 , x 2 ) = ∣ ∣ f ( x 1 ) − f ( x 2 ) ∣ ∣ 2 d(x^1, x^2) = || f(x^1) - f(x^2) ||^2 d(x1,x2)=∣∣f(x1)−f(x2)∣∣2  
>     ![2.png-97.3kB][]

## Triplet Loss ##

### Firstly ###

>  *  Triplet Loss is one of the loss functions we can use to solve the similarity distance in a Siamese network.
>  *   ∣ ∣ f ( A ) − f ( P ) ∣ ∣ 2 < = ∣ ∣ f ( A ) − f ( N ) ∣ ∣ 2 ||f(A) - f(P)||^2 <= ||f(A) - f(N)||^2 ∣∣f(A)−f(P)∣∣2<=∣∣f(A)−f(N)∣∣2
>  *   ∣ ∣ f ( A ) − f ( P ) ∣ ∣ 2 − ∣ ∣ f ( A ) − f ( N ) ∣ ∣ 2 < = 0 ||f(A) - f(P)||^2 - ||f(A) - f(N)||^2 <= 0 ∣∣f(A)−f(P)∣∣2−∣∣f(A)−f(N)∣∣2<=0
>  *   ∣ ∣ f ( A ) − f ( P ) ∣ ∣ 2 − ∣ ∣ f ( A ) − f ( N ) ∣ ∣ 2 < = − α ||f(A) - f(P)||^2 - ||f(A) - f(N)||^2 <= -\\alpha ∣∣f(A)−f(P)∣∣2−∣∣f(A)−f(N)∣∣2<=−α to make sure the NN won’t get an output if zero

### Secondly ###

>  *  Given 3 images (A, P, N)
>  *   L ( A , P , N ) = m a x ( ∣ ∣ f ( A ) − f ( P ) ∣ ∣ 2 − ∣ ∣ f ( A ) − f ( N ) ∣ ∣ 2 + a l p h a , 0 ) L(A, P, N) = max (||f(A) - f(P)||^2 - ||f(A) - f(N)||^2 + alpha , 0) L(A,P,N)=max(∣∣f(A)−f(P)∣∣2−∣∣f(A)−f(N)∣∣2\+alpha,0)
>  *  $J = \\sum(L(A\[i\], P\[i\], N\[i\]) , i) $for all triplets of images.

### Thirdly ###

>  *  During training if A, P, N are chosen randomly (Subjet to A and P are the same and A and N aren’t the same) then one of the problems this constrain is easily satisfied
>  *  What we want to do is choose triplets that are **hard** to train on.

## Offline triplet mining ##

1.最简单的想法就是离线算法，先找到B个triplets计算它们的loss然后再送进网络学习，但是这样很低效，要遍历整个网络。

## Online triplet mining ##

1.对于一个有B个样本的batch，我们最多可以产生 B 3 B^3 B3个triplets。这里面虽然有很多无效的（没有两个P，一个N），但是却可以在一个batch中产生更多的triplets。  
2.Batch hard strategy  
找到每个anchor最hardest的P和N

>  *  计算一个2D距离矩阵然后将无效的设置为0，将有效的pair留下来（ a ≠ p , a\\neq p, a̸=p, a和p有着相同的label），然后在修改后的矩阵计算每一行的最大值。
>  *  计算最小值N的时候不能将无效的设置为0（无效的是a和  
>     n有着相同的label）。

def batch_hard_triplet_loss(labels, embeddings, margin, squared=False):
        """Build the triplet loss over a batch of embeddings.
    
        For each anchor, we get the hardest positive and hardest negative to form a triplet.
    
        Args:
            labels: labels of the batch, of size (batch_size,)
            embeddings: tensor of shape (batch_size, embed_dim)
            margin: margin for triplet loss
            squared: Boolean. If true, output is the pairwise squared euclidean distance matrix.
                     If false, output is the pairwise euclidean distance matrix.
    
        Returns:
            triplet_loss: scalar tensor containing the triplet loss
        """
        # Get the pairwise distance matrix
        pairwise_dist = _pairwise_distances(embeddings, squared=squared)
    
        # For each anchor, get the hardest positive
        # First, we need to get a mask for every valid positive (they should have same label)
        mask_anchor_positive = _get_anchor_positive_triplet_mask(labels)
        mask_anchor_positive = tf.to_float(mask_anchor_positive)
    
        # We put to 0 any element where (a, p) is not valid (valid if a != p and label(a) == label(p))
        anchor_positive_dist = tf.multiply(mask_anchor_positive, pairwise_dist)
    
        # shape (batch_size, 1)
        hardest_positive_dist = tf.reduce_max(anchor_positive_dist, axis=1, keepdims=True)
    
        # For each anchor, get the hardest negative
        # First, we need to get a mask for every valid negative (they should have different labels)
        mask_anchor_negative = _get_anchor_negative_triplet_mask(labels)
        mask_anchor_negative = tf.to_float(mask_anchor_negative)
    
        # We add the maximum value in each row to the invalid negatives (label(a) == label(n))
        max_anchor_negative_dist = tf.reduce_max(pairwise_dist, axis=1, keepdims=True)
        anchor_negative_dist = pairwise_dist + max_anchor_negative_dist * (1.0 - mask_anchor_negative)
    
        # shape (batch_size,)
        hardest_negative_dist = tf.reduce_min(anchor_negative_dist, axis=1, keepdims=True)
    
        # Combine biggest d(a, p) and smallest d(a, n) into final triplet loss
        triplet_loss = tf.maximum(hardest_positive_dist - hardest_negative_dist + margin, 0.0)
    
        # Get final mean triplet loss
        triplet_loss = tf.reduce_mean(triplet_loss)
    
        return triplet_loss

[2.png-97.3kB]: /images/20220406/ce81d2a73def48d98e504fd52588d40a.png