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. In this paper, two supervised methods for enhancing the classification accuracy of the Nonnegative Matrix Factorization (NMF) algorithm are presented. The idea is to extend the NMF algorithm in order to extract features that enforce not only the spatial locality, but also the separability between classes in a discriminant manner. The first method employs discriminant analysis in the features derived from NMF. In this way, a two-phase discriminant feature extraction procedure is implemented, namely NMF plus Linear Discriminant Analysis (LDA). The second method incorporates the discriminant constraints inside the NMF decomposition. Thus, a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived. The introduced methods have been applied to the problem of frontal face verification using the well-known XM2VTS database. Both methods greatly enhance the performance of NMF for frontal face verification We studied three methods to improve identification of difficult small classes by balancing imbalanced class distribution with data reduction. The new method, neighborhood cleaning rule (NCL), outperformed simple random and one-sided selection methods in experiments with ten data sets. All reduction methods improved identification of small classes (20-30 ), but the differences were insignificant. However, significant differences in accuracies, true-positive rates and true-negative rates obtained with the 3-nearest neighbor method and C4.5 from the reduced data favored NCL. The results suggest that NCL is a useful method for improving the modeling of difficult small classes, and for building classifiers to identify these classes from the real-world data. Abstract A class-dependent weighted (CDW) dissimilarity measure in vector spaces is proposed to improve the performance of the nearest neighbor (NN) classifier. In order to optimize the required weights, an approach based on Fractional Programming is presented. Experiments with several standard benchmark data sets show the effectiveness of the proposed technique.