Robust Discriminative Metric Learning for Image Representation

Metric learning has attracted significant attentions in the past decades, for the appealing advances in various realworld applications such as person re-identification and face recognition. Traditional supervised metric learning attempts to seek a discriminative metric, which could minimize the pairwise distance of within-class data samples, while maximizing the pairwise distance of data samples from various classes. However, it is still a challenge to build a robust and discriminative metric, especially for corrupted data in the real-world application. In this paper, we propose a Robust Discriminative Metric Learning algorithm (RDML) via fast low-rank representation and denoising strategy. To be specific, the metric learning problem is guided by a discriminative regularization by incorporating the pair-wise or class-wise information. Moreover, low-rank basis learning is jointly optimized with the metric to better uncover the global data structure and remove noise. Furthermore, fast low-rank representation is implemented to mitigate the computational burden and make sure the scalability on large-scale datasets. Finally, we evaluate our learned metric on several challenging tasks, e.g., face recognition/verification, object recognition, and image clustering. The experimental results verify the effectiveness of the proposed algorithm by comparing to many metric learning algorithms, even deep learning ones

Escaping the Curse of Dimensionality in Similarity Learning: Efficient Frank-Wolfe Algorithm and Generalization Bounds

International audienceSimilarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large, poor generalization is to be expected and training becomes intractable due to high computational and memory costs. In this paper, we propose a similarity learning method that can efficiently deal with high-dimensional sparse data. This is achieved through a parameterization of similarity functions by convex combinations of sparse rank-one matrices, together with the use of a greedy approximate Frank-Wolfe algorithm which provides an efficient way to control the number of active features. We show that the convergence rate of the algorithm, as well as its time and memory complexity, are independent of the data dimension. We further provide a theoretical justification of our modeling choices through an analysis of the generalization error, which depends logarithmically on the sparsity of the solution rather than on the number of features. Our experiments on datasets with up to one million features demonstrate the ability of our approach to generalize well despite the high dimensionality as well as its superiority compared to several competing methods

Escaping the Curse of Dimensionality in Similarity Learning: Efficient Frank-Wolfe Algorithm and Generalization Bounds

Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large, poor generalization is to be expected and training becomes intractable due to high computational and memory costs. In this paper, we propose a similarity learning method that can efficiently deal with high-dimensional sparse data. This is achieved through a parameterization of similarity functions by convex combinations of sparse rank-one matrices, together with the use of a greedy approximate Frank-Wolfe algorithm which provides an efficient way to control the number of active features. We show that the convergence rate of the algorithm, as well as its time and memory complexity, are independent of the data dimension. We further provide a theoretical justification of our modeling choices through an analysis of the generalization error, which depends logarithmically on the sparsity of the solution rather than on the number of features. Our experiments on datasets with up to one million features demonstrate the ability of our approach to generalize well despite the high dimensionality as well as its superiority compared to several competing methods

Efficient Stochastic Optimization for Low-Rank Distance Metric Learning

Although distance metric learning has been successfully applied to many real-world applications, learning a distance metric from large-scale and high-dimensional data remains a challenging problem. Due to the PSD constraint, the computational complexity of previous algorithms per iteration is at least O(d2) where d is the dimensionality of the data.In this paper, we develop an efficient stochastic algorithm  for a class of distance metric learning problems with nuclear norm regularization, referred to as low-rank DML. By utilizing the low-rank structure of the intermediate solutions and stochastic gradients, the complexity of our algorithm has a linear dependence on the dimensionality d. The key idea is to maintain all the iterates  in factorized representations  and construct  stochastic gradients that are low-rank. In this way, the projection onto the PSD cone can be implemented efficiently by incremental SVD. Experimental results on several data sets validate the effectiveness and efficiency of our method