相关论文: Online Adaptive Mahalanobis Distance Estimation

We consider the supervised classification problem of machine learning in Cayley-Klein projective geometries: We show how to learn a curved Mahalanobis metric distance corresponding to either the hyperbolic geometry or the elliptic geometry…

To classify time series by nearest neighbors, we need to specify or learn one or several distance measures. We consider variations of the Mahalanobis distance measures which rely on the inverse covariance matrix of the data. Unfortunately…

Metric learning is an important family of algorithms for classification and similarity search, but the robustness of learned metrics against small adversarial perturbations is less studied. In this paper, we show that existing metric…

Metric learning is a key problem for many data mining and machine learning applications, and has long been dominated by Mahalanobis methods. Recent advances in nonlinear metric learning have demonstrated the potential power of…

The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the…

Many researches have been devoted to learn a Mahalanobis distance metric, which can effectively improve the performance of kNN classification. Most approaches are iterative and computational expensive and linear rigidity still critically…

Distance metric learning has attracted much attention in recent years, where the goal is to learn a distance metric based on user feedback. Conventional approaches to metric learning mainly focus on learning the Mahalanobis distance metric…

Self-Organising Maps (SOM) are Artificial Neural Networks used in Pattern Recognition tasks. Their major advantage over other architectures is human readability of a model. However, they often gain poorer accuracy. Mostly used metric in SOM…

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…

Motivated by establishing theoretical foundations for various manifold learning algorithms, we study the problem of Mahalanobis distance (MD), and the associated precision matrix, estimation from high-dimensional noisy data. By relying on…

We propose a novel semiparametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to…

We propose a low-rank approach to learning a Mahalanobis metric from data. Inspired by the recent geometric mean metric learning (GMML) algorithm, we propose a low-rank variant of the algorithm. This allows to jointly learn a…

One of the basic problems in data analysis lies in choosing the optimal rescaling (change of coordinate system) to study properties of a given data-set $Y$. The classical Mahalanobis approach has its basis in the classical…

When training automated systems, it has been shown to be beneficial to adapt the representation of data by learning a problem-specific metric. This metric is global. We extend this idea and, for the widely used family of k nearest neighbors…

Metric learning seeks a transformation of the feature space that enhances prediction quality for the given task at hand. In this work we provide PAC-style sample complexity rates for supervised metric learning. We give matching lower- and…

A key element of any machine learning algorithm is the use of a function that measures the dis/similarity between data points. Given a task, such a function can be optimized with a metric learning algorithm. Although this research field has…

For many tasks and data types, there are natural transformations to which the data should be invariant or insensitive. For instance, in visual recognition, natural images should be insensitive to rotation and translation. This requirement…

The Mahalanobis distance is commonly used in multi-object trackers for measurement-to-track association. Starting with the original definition of the Mahalanobis distance we review its use in association. Given that there is no principle in…

Curve matching is a prediction technique that relies on predictive mean matching, which matches donors that are most similar to a target based on the predictive distance. Even though this approach leads to high prediction accuracy, the…

The problem of constrained clustering has attracted significant attention in the past decades. In this paper, we study the balanced $k$-center, $k$-median, and $k$-means clustering problems where the size of each cluster is constrained by…