Triplet Loss 

Triplet loss is a loss function for deep learning, which refers to minimizing the distance between the anchor point and the positive sample with the same identity, and minimizing the distance between the anchor point and the negative sample with different identities.

The term "triplet" refers to three data points:Anchor Point,PunctualandNegative PointThe anchor is the central data point for which the embedding is to be learned, the positive points are data points that are similar to the anchor (e.g. images of the same individual), and the negative points are data points that are completely different from the anchor (e.g. images of unrelated individuals).

Mathematically, triplet loss can be expressed as:

• f() represents the function responsible for generating the embedding.
• a = anchor image
• p means positive image
• n represents negative image
• Ɑ represents the margin hyperparameter, which sets the lower limit of the interval between positive and negative embedding distances.

The core of the triplet loss function lies in the margin α, which is a hyperparameter that sets the minimum required difference between the squared distances of the positive and negative anchor embeddings. By imposing this margin, the loss function encourages an ideal distribution between positive and negative distances, creating an environment that is conducive to learning meaningful representations. These positive and negative distances are calculated using a distance metric (usually Euclidean distance). 

Triplet Loss is based on the fundamental goal of learning embeddings that highlight the intrinsic relationships between data points. This is different from traditional loss functions, which are mainly designed for tasks such as classification or value prediction. In scenarios such as face recognition, subtle differences in facial features are crucial, and embeddings (or encodings) that can distinguish individuals in a way that is not easy to achieve with raw pixels are invaluable.

Triplet Loss was invented as a solution to this challenge. By encouraging the neural network to learn embeddings based on the context of positive and negative examples relative to the anchor instance, it opens the door to obtaining discriminative features that essentially capture the essence of the data relationships.

Triple selection strategy

Selecting the right triplet is crucial to the effectiveness of Triplet Loss. In practice, randomly selecting triples may lead to slow convergence or suboptimal solutions. Therefore, multiple strategies are used to effectively select informative triplets:

• Online triplet mining:Instead of using all possible triplets, online triplet mining selects triplets based on the loss value. Only the most challenging triplets, i.e., triplets with loss values close to zero, are used for gradient calculation. This approach speeds up convergence and focuses the learning process on difficult examples.

• Hard Negative Mining:The negative samples selected for the triplet should be harder to distinguish from the anchors than the positive samples. Hard negative mining involves selecting the negative samples that violate the margin the most, thus ensuring that the network learns more effectively from challenging instances.

• Semi-hard negative excavation:Aims to strike a balance between randomly chosen negatives and hard negatives. Semi-hard negatives are negatives that are farther from the anchor than positives but still have a positive loss value. They provide a middle ground that helps the network generalize better without converging to a simple solution.

Triplet Loss variant

The basic formula of Triplet Loss has undergone several changes and enhancements to improve its effectiveness:

• Batch Hard Triplet Loss:Instead of selecting the hardest negative example for each anchor positive pair, this method considers the hardest negative example in a batch of training examples. This accounts for intra-batch variation and can be computationally more efficient.

• Contrastive loss:The triplet loss can be viewed as an extension of the contrastive loss, where instead of triplets, pairs of anchored positive and anchored negative examples are considered.

• Quadruple loss:This extension involves adding a second positive example to the triplet, further emphasizing the relationship between the anchor and the positive example.

• Proxy-based losses:Agent-based methods involve learning a set of agent vectors that represent different categories. These agents act as landmarks in the embedding space, making it easier to form triplets and learn meaningful representations.

Application of Triplet Loss

Triplet Loss has applications in various fields, especially when learning meaningful embeddings is crucial:

• Face Recognition: One of the earliest applications of Triplet Loss is in the field of computer vision, specifically face recognition. By learning embeddings that minimize intra-person variance and maximize inter-person variance, Triplet Loss helps create robust and discriminative facial embeddings.

• Image Retrieval: Triplet Loss can be used to build content-based image retrieval systems. Images are encoded as embeddings, and retrieving similar images becomes a matter of finding embeddings that are close to the embedding of the query image.

• Person Re-identification:In scenarios such as video surveillance, the triplet loss can be used to develop models that can recognize the same person in different camera views, even under different lighting and poses.

• Information Retrieval:In natural language processing, triplet loss can be adapted to learn embeddings of text documents, enabling similarity-based search and clustering.

References

【1】https://encord.com/glossary/triplet-loss-definition/