Person re-identification aims at matching pedestrians observed from non-overlapping camera views. Feature descriptor and metric learning are two significant problems in person re-identification. A discriminative metric learning method should be capable of exploiting complex nonlinear transformations due to the large variations in feature space. In this paper, we propose a nonlinear local metric learning (NLML) method to improve the state-of-the-art performance of person re-identification on public datasets. Motivated by the fact that local metric learning has been introduced to handle the data which varies locally and deep neural network has presented outstanding capability in exploiting the nonlinearity of samples, we utilize the merits of both local metric learning and deep neural network to learn multiple sets of nonlinear transformations. By enforcing a margin between the distances of positive pedestrian image pairs and distances of negative pairs in the transformed feature subspace, discriminative information can be effectively exploited in the developed neural networks. Our experiments show that the proposed NLML method achieves the state-of-the-art results on the widely used VIPeR, GRID, and CUHK 01 datasets.
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@cite_32: The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner.
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@cite_56: In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction.
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@cite_59: 
@cite_49: 
@cite_5: Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text. How do we judge similarity? Our mental representations of the world are formed by processing large numbers of sensory in
@cite_10: Linear metric learning is a widely used methodology to learn a dissimilarity function from a set of similar dissimilar example pairs. Using a single metric may be a too restrictive assumption when handling heterogeneous datasets. Recently, local metric learning methods have been introduced to overcome this limitation. However, they are subjects to constraints preventing their usage in many applications. For example, they require knowledge of the class label of the training points. In this paper, we present a novel local metric learning method, which overcomes some limitations of previous approaches. The method first computes a Gaussian Mixture Model from a low dimensional embedding of training data. Then it estimates a set of local metrics by solving a convex optimization problem; finally, a dissimilarity function is obtained by aggregating the local metrics. Our experiments show that the proposed method achieves state-of-the-art results on four datasets.
@cite_12: Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.
@cite_20: 
: Existing metric learning methods can be mainly classified into two categories: unsupervised and supervised. Unsupervised methods seek a low-dimensional subspace to preserve the geometrical information of samples. Representative unsupervised metric learning methods include principal component analysis (PCA) @cite_30 , locality preserving projections (LPP) @cite_12 , locally linear embedding (LLE) @cite_5 , and multidimensional scaling (MDS) @cite_20 . Supervised methods learn a discriminative distance metric under which the intra-class variation is increased and the inter-class variation is decreased. Typical methods in this category include linear discriminant analysis (LDA) @cite_59 , neighborhood component analysis (NCA) @cite_56 , cosine similarity metric learning @cite_6 , large margin nearest neighbor (LMNN) @cite_32 , and information theoretic metric learning (ITML) @cite_3 , discriminative deep metric learning (DDML) @cite_49 and large margin local metric learning (LMLML) @cite_10 .