Related papers: Optimal Rescaling and the Mahalanobis Distance
For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…
Rerandomization, a design that utilizes pretreatment covariates and improves their balance between different treatment groups, has received attention recently in both theory and practice. From a survey by Bruhn and McKenzie (2009), there…
Mahalanobis metrics are widely used in machine learning in conjunction with methods like $k$-nearest neighbors, $k$-means clustering, and $k$-medians clustering. Despite their importance, there has not been any prior work on applying…
In the past decade, various exact balancing-based weighting methods were introduced to the causal inference literature. Exact balancing alleviates the extreme weight and model misspecification issues that may incur when one implements…
Randomization ensures that observed and unobserved covariates are balanced, on average. However, randomizing units to treatment and control often leads to covariate imbalances in realization, and such imbalances can inflate the variance of…
Mahalanobis distance between treatment group and control group covariate means is often adopted as a balance criterion when implementing a rerandomization strategy. However, this criterion may not work well for high-dimensional cases…
Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A multivariate depth function is a function which, given a…
Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More…
Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis…
The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the…
In the field of machine learning, model performance is usually assessed by randomly splitting data into training and test sets. Different random splits, however, can yield markedly different performance estimates, so a genuinely good model…
A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are…
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…
A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of…
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 are interested in the large-scale learning of Mahalanobis distances, with a particular focus on person re-identification. We propose a metric learning formulation called Weighted Approximate Rank Component Analysis (WARCA). WARCA…
Interval-valued data are one of the most common symbolic data types, which enables the preservation of the underlying variability of the data. The interval mean and covariance matrix can be estimated using the barycenter approach based on…
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…