text: Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the similarity constraints, and initially ignoring the features, we are able to learn target vectors for each instance using one of several appropriately designed loss functions. A regression model can then be constructed that maps novel feature vectors to the same target vector space, resulting in a feature extractor that computes vectors for which a predefined metric is a meaningful measure of similarity. We present results on both multiclass and multi-label classification datasets that demonstrate considerably faster convergence, as well as higher accuracy on the majority of the intrinsic evaluation tasks and all extrinsic evaluation tasks.
  @cite_21: This paper describes the development of an algorithm for verification of signatures written on a touch-sensitive pad. The signature verification algorithm is based on an artificial neural network. The novel network presented here, called a “Siamese” time delay neural network, consists of two identical networks joined at their output. During training the network learns to measure the similarity between pairs of signatures. When used for verification, only one half of the Siamese network is evaluated. The output of this half network is the feature vector for the input signature. Verification consists of comparing this feature vector with a stored feature vector for the signer. Signatures closer than a chosen threshold to this stored representation are accepted, all other signatures are rejected as forgeries. System performance is illustrated with experiments performed in the laboratory.
  @cite_6: In modern face recognition, the conventional pipeline consists of four stages: detect => align => represent => classify. We revisit both the alignment step and the representation step by employing explicit 3D face modeling in order to apply a piecewise affine transformation, and derive a face representation from a nine-layer deep neural network. This deep network involves more than 120 million parameters using several locally connected layers without weight sharing, rather than the standard convolutional layers. Thus we trained it on the largest facial dataset to-date, an identity labeled dataset of four million facial images belonging to more than 4, 000 identities. The learned representations coupling the accurate model-based alignment with the large facial database generalize remarkably well to faces in unconstrained environments, even with a simple classifier. Our method reaches an accuracy of 97.35 on the Labeled Faces in the Wild (LFW) dataset, reducing the error of the current state of the art by more than 27 , closely approaching human-level performance.
summary: The first application of neural networks to metric learning was with the introduction of Siamese networks @cite_21 . The original authors initially applied these models to signature verification, however others have since used this technique for many other domains such as face recognition and verification @cite_6 . Siamese networks are composed of two standard feed forward neural networks that have the same topology and share the same parameters. The output of these subnetworks is then compared with the cosine similarity function to produce the final output of the network, indicating whether the instances propagated through the two subnetworks are similar or not. During training the network is presented with pairs of instances labelled either positive or negative. For positive pairs the cosine similarity is maximised, whereas for negative pairs it is minimised.