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.
Neighbourhood Components Analysis (NCA) @cite_11 is another method developed to be used in conjunction with @math -NN classifiers. This technique attempts to find the matrix, @math , by minimising a differentiable loss function that approximates the behaviour of @math -NN in the transformed feature space.
@cite_11
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Neighborhood Components Analysis (NCA) is a popular method for learning a distance metric to be used within a k-nearest neighbors (kNN) classifier. A key assumption built into the model is that each point stochastically selects a single neighbor, which makes the model well-justified only for kNN with k = 1. However, kNN classifiers with k > 1 are more robust and usually preferred in practice. Here we present kNCA, which generalizes NCA by learning distance metrics that are appropriate for kNN with arbitrary k. The main technical contribution is showing how to efficiently compute and optimize the expected accuracy of a kNN classifier. We apply similar ideas in an unsupervised setting to yield kSNE and kt-SNE, generalizations of Stochastic Neighbor Embedding (SNE, t-SNE) that operate on neighborhoods of size k, which provide an axis of control over embeddings that allow for more homogeneous and interpretable regions. Empirically, we show that kNCA often improves classification accuracy over state of the art methods, produces qualitative differences in the embeddings as k is varied, and is more robust with respect to label noise.