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Effect of triplet loss minimization in training: the positive is moved closer to the anchor than the negative.
Triplet loss is a loss function for machine learning algorithms where a reference input (called anchor) is compared to a matching input (called positive) and a non-matching input (called negative). The distance from the anchor to the positive is minimized, and the distance from the anchor to the negative input is maximized.[1][2]
An early formulation equivalent to triplet loss was introduced (without the idea of using anchors) for metric learning from relative comparisons by M. Schultze and T. Joachims in 2003.[3]
By enforcing the order of distances, triplet loss models embed in the way that a pair of samples with same labels are smaller in distance than those with different labels. Unlike t-SNE which preserves embedding orders [further explanation needed] via probability distributions, triplet loss works directly on embedded distances. Therefore, in its common implementation, it needs soft margin treatment with a slack variable in its hinge loss-style formulation. It is often used for learning similarity for the purpose of learning embeddings, such as learning to rank, word embeddings, thought vectors, and metric learning.[4]
Consider the task of training a neural network to recognize faces (e.g. for admission to a high security zone). A classifier trained to classify an instance would have to be retrained every time a new person is added to the face database. This can be avoided by posing the problem as a similarity learning problem instead of a classification problem. Here the network is trained (using a contrastive loss) to output a distance which is small if the image belongs to a known person and large if the image belongs to an unknown person. However, if we want to output the closest images to a given image, we want to learn a ranking and not just a similarity. A triplet loss is used in this case.
The loss function can be described by means of the Euclidean distance function
where is an anchor input, is a positive input of the same class as , is a negative input of a different class from , is a margin between positive and negative pairs, and is an embedding.
This can then be used in a cost function, that is the sum of all losses, which can then be used for minimization of the posed optimization problem
The indices are for individual input vectors given as a triplet. The triplet is formed by drawing an anchor input, a positive input that describes the same entity as the anchor entity, and a negative input that does not describe the same entity as the anchor entity. These inputs are then run through the network, and the outputs are used in the loss function.
^Chechik, G.; Sharma, V.; Shalit, U.; Bengio, S. (2010). "Large Scale Online Learning of Image Similarity Through Ranking" (PDF). Journal of Machine Learning Research. 11: 1109–1135.
^Schroff, F.; Kalenichenko, D.; Philbin, J. (June 2015). "FaceNet: A unified embedding for face recognition and clustering". 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). pp. 815–823. arXiv:1503.03832. doi:10.1109/CVPR.2015.7298682. ISBN 978-1-4673-6964-0. S2CID 206592766.
^Schultz, M.; Joachims, T. (2004). "Learning a distance metric from relative comparisons" (PDF). Advances in Neural Information Processing Systems. 16: 41–48.
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