三元组损失

一、什么是三元组损失？

三元组损失（Triplet Loss）是深度学习中用于学习特征表示的重要损失函数，最初在FaceNet论文中提出，后被广泛应用于人脸识别、行人重识别（ReID）等任务。其核心思想是通过锚点样本（Anchor）、正样本（Positive）和负样本（Negative）的三元组，让同类样本的特征距离更近，不同类样本的特征距离更远。

二、代码结构解析

完整示例代码：

class TripletLoss(nn.Module):
    """Triplet loss with hard positive/negative mining.
    
    Reference:
        Hermans et al. In Defense of the Triplet Loss for Person Re-Identification. arXiv:1703.07737.
    
    Imported from `<https://github.com/Cysu/open-reid/blob/master/reid/loss/triplet.py>`_.
    
    Args:
        margin (float, optional): margin for triplet. Default is 0.3.
    """

    def __init__(self, margin=0.3):
        super(TripletLoss, self).__init__()
        self.margin = margin
        self.ranking_loss = nn.MarginRankingLoss(margin=margin)

    def forward(self, inputs, targets):
        """
        Args:
            inputs (torch.Tensor): feature matrix with shape (batch_size, feat_dim).
            targets (torch.LongTensor): ground truth labels with shape (num_classes).
        """
        n = inputs.size(0)
        
  #步骤1：计算特征距离矩阵
        # Compute pairwise distance, replace by the official when merged
        dist = torch.pow(inputs, 2).sum(dim=1, keepdim=True).expand(n, n)
        dist = dist + dist.t()
        dist.addmm_(inputs, inputs.t(), beta=1, alpha=-2)
        dist = dist.clamp(min=1e-12).sqrt() # for numerical stability

        # For each anchor, find the hardest positive and negative
        mask = targets.expand(n, n).eq(targets.expand(n, n).t())
        dist_ap, dist_an = [], []
        for i in range(n):
            dist_ap.append(dist[i][mask[i]].max().unsqueeze(0))
            dist_an.append(dist[i][mask[i] == 0].min().unsqueeze(0))
        dist_ap = torch.cat(dist_ap)
        dist_an = torch.cat(dist_an)

        # Compute ranking hinge loss
        y = torch.ones_like(dist_an)
        return self.ranking_loss(dist_an, dist_ap, y)

步骤1：计算特征距离矩阵

\[D_{i j}\,=\,{\sqrt{\vert\vert x_{i}\,-\,x_{j}\vert\vert^{2}}}\]