However, it still encounters scalability problem when handling large data. This work gives a new formulation that learns the low-rank cosine similarity metric by embedding the triplet constraints into a matrix to further reduce the complexity and the size of involved matrices. The idea of embedding the evaluation of loss functions into matrices is interesting. For Stiefel manifolds, rather than following the projection and retraction convention, it adopts the optimization algorithm proposed by Wen et al. (Ref. Generally, this paper is well-written with promising results.

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several largescale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner.

In recent years, we have witnessed a surge of interests in learning a suitable distance metric from weakly supervised data. Most existing methods aim to pull all the similar samples closer while push the dissimilar ones as far as possible. However, when some classes of the dataset exhibit multimodal distribution, these goals conflict and thus can hardly be concurrently satisfied. Additionally, to ensure a valid metric, many methods require a repeated eigenvalue decomposition process, which is expensive and numerically unstable. Therefore, how to learn an appropriate distance metric from weakly supervised data remains an open but challenging problem. To address this issue, in this paper, we propose a novel weakly supervised metric learning algorithm, named MultimoDal Aware weakly supervised Metric Learning (MDaML). MDaML partitions the data space into several clusters and allocates the local cluster centers and weight for each sample. Then, combining it with the weighted triplet loss can further enhance the local separability, which encourages the local dissimilar samples to keep a large distance from the local similar samples. Meanwhile, MDaML casts the metric learning problem into an unconstrained optimization on the SPD manifold, which can be efficiently solved by Riemannian Conjugate Gradient Descent (RCGD). Extensive experiments conducted on 13 datasets validate the superiority of the proposed MDaML.

Researchers from all over the world contribute to this repository as a prelude to the peer review process for publication in traditional journals. We hope to save you some time by picking out articles that represent the most promise for the typical data scientist. The articles listed below represent a fraction of all articles appearing on the preprint server. They are listed in no particular order with a link to each paper along with a brief overview. Especially relevant articles are marked with a "thumbs up" icon.

The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have several limitations. We explore a deep learning formulation of constrained clustering and in particular explore how it can extend the field of constrained clustering. We show that our formulation can not only handle standard together/apart constraints without the well documented negative effects reported but can also model instance level constraints (level-of-difficulty), cluster level constraints (balancing cluster size) and triplet constraints. The first two are new ways for domain experts to enforce guidance whilst the later importantly allows generating ordering constraints from continuous side-information.

Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet constraints. However, the number of constraints is quadratic or even cubic in the number of the original examples, which makes it challenging for DML to handle the large-scale data set. Besides, the real-world data may contain various uncertainty, especially for the image data. The uncertainty can mislead the learning procedure and cause the performance degradation. By investigating the image data, we find that the original data can be observed from a small set of clean latent examples with different distortions. In this work, we propose the margin preserving metric learning framework to learn the distance metric and latent examples simultaneously. By leveraging the ideal properties of latent examples, the training efficiency can be improved significantly while the learned metric also becomes robust to the uncertainty in the original data. Furthermore, we can show that the metric is learned from latent examples only, but it can preserve the large margin property even for the original data. The empirical study on the benchmark image data sets demonstrates the efficacy and efficiency of the proposed method.

Hierarchical clustering (HC) is a widely used data analysis tool, ubiquitous in information retrieval, data mining, and machine learning (see a survey by Berkhin [2006]). This clustering technique represents a given dataset as a binary tree; each leaf represents an individual data point and each internal node represents a cluster on the leaves of its descendants. HC has become the most popular method for gene expression data analysis Eisen et al. [1998], and also has been used in the analysis of social networks Leskovec et al. [2014], Mann et al. [2008], bioinformatics Diez et al. [2015], image and text classification Steinbach et al. [2000], and even in analysis of financial markets Tumminello et al. [2010]. It is attractive because it provides richer information at all levels of granularity simultaneously, compared to more traditional flat clustering approaches like k-means or k-median. Recently, Dasgupta [2016] formulated HC as a combinatorial optimization problem, giving a principled way to compare the performance of different HC algorithms. This optimization viewpoint has since received a lot of attention Roy and Pokutta [2016], Charikar and Chatziafratis [2017], Cohen-Addad et al. [2017], Moseley and Wang [2017], Cohen-Addad et al. [2018] that has led not only to the development of new algorithms but also to theoretical justifications for the observed success of popular HC algorithms (e.g.

Affective image understanding has been extensively studied in the last decade since more and more users express emotion via visual contents. While current algorithms based on convolutional neural networks aim to distinguish emotional categories in a discrete label space, the task is inherently ambiguous. This is mainly because emotional labels with the same polarity (i.e., positive or negative) are highly related, which is different from concrete object concepts such as cat, dog and bird. To the best of our knowledge, few methods focus on leveraging such characteristic of emotions for affective image understanding. In this work, we address the problem of understanding affective images via deep metric learning and propose a multi-task deep framework to optimize both retrieval and classification goals. We propose the sentiment constraints adapted from the triplet constraints, which are able to explore the hierarchical relation of emotion labels. We further exploit the sentiment vector as an effective representation to distinguish affective images utilizing the texture representation derived from convolutional layers. Extensive evaluations on four widely-used affective datasets, i.e., Flickr and Instagram, IAPSa, Art Photo, and Abstract Paintings, demonstrate that the proposed algorithm performs favorably against the state-of-the-art methods on both affective image retrieval and classification tasks.

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics;2) we develop upper and lower (minimax) bounds on the generalization error; 3)we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric; 4) we also bound the accuracy of the learned metric relative to the underlying true generative metric. All the results involve novel mathematical approaches to the metric learning problem, and also shed new light on the special case of ordinal embedding (aka non-metric multidimensional scaling).

Fine-grained visual categorization (FGVC) is to categorize objects into subordinate classes instead of basic classes. One major challenge in FGVC is the co-occurrence of two issues: 1) many subordinate classes are highly correlated and are difficult to distinguish, and 2) there exists the large intra-class variation (e.g., due to object pose). This paper proposes to explicitly address the above two issues via distance metric learning (DML). DML addresses the first issue by learning an embedding so that data points from the same class will be pulled together while those from different classes should be pushed apart from each other; and it addresses the second issue by allowing the flexibility that only a portion of the neighbors (not all data points) from the same class need to be pulled together. However, feature representation of an image is often high dimensional, and DML is known to have difficulty in dealing with high dimensional feature vectors since it would require $\mathcal{O}(d^2)$ for storage and $\mathcal{O}(d^3)$ for optimization. To this end, we proposed a multi-stage metric learning framework that divides the large-scale high dimensional learning problem to a series of simple subproblems, achieving $\mathcal{O}(d)$ computational complexity. The empirical study with FVGC benchmark datasets verifies that our method is both effective and efficient compared to the state-of-the-art FGVC approaches.