arXiv subjects

Annesha Ghosh

Publications and source records attributed to Annesha Ghosh.

4 recordsLinked to original sources

arXiv2026

A scalable version of MADD for big-data classification

Distance-based classifiers are very popular, and the Euclidean distance is one of the most commonly used metrics in distance-based classifiers. However, classifiers based on the Euclidean distance often suffer in high-dimensional setups due to issues such as distance concentration, violation of neighborhood structures, and the presence of hubs. In high-dimension, low-sample-size (HDLSS) situations, a data-driven semi-metric called the Mean Absolute Difference of Distances (MADD) is known to circumvent these issues. But one major problem with MADD is that its computational complexity increases quadratically with the training sample size. As a result, the application of MADD becomes computationally challenging for big datasets that have both a high dimension as well as a large number of observations. In this paper, we propose a scalable version of MADD that significantly reduces its computational complexity while retaining its advantages. This speed-up is achieved by selecting a representative set during the computation of MADD. Further speed-ups are achieved by using the idea of Random Fourier Features, particularly when the sample size is very large. We establish that our proposed methods achieve performances similar to MADD but only at a fraction of its computing time, both theoretically as well as numerically. Our approach broadens the scope of MADD, allowing its use to big-data with a very large number of observations.

stat.ME↗

arXiv2024

On high-dimensional modifications of the nearest neighbor classifier

Nearest neighbor classifier is arguably the most simple and popular nonparametric classifier available in the literature. However, due to the concentration of pairwise distances and the violation of the neighborhood structure, this classifier often suffers in high-dimension, low-sample size (HDLSS) situations, especially when the scale difference between the competing classes dominates their location difference. Several attempts have been made in the literature to take care of this problem. In this article, we discuss some of these existing methods and propose some new ones. We carry out some theoretical investigations in this regard and analyze several simulated and benchmark datasets to compare the empirical performances of proposed methods with some of the existing ones.

stat.ML↗

arXiv2024

Classification Using Global and Local Mahalanobis Distances

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 estimate the posterior probabilities of different classes. While popular parametric classifiers like linear and quadratic discriminant analyses are mainly motivated by the normality of the underlying distributions, the proposed classifier is more flexible and free from such parametric modeling assumptions. Since the densities of elliptic distributions are functions of Mahalanobis distances, this classifier works well when the competing classes are (nearly) elliptic. In such cases, it often outperforms popular nonparametric classifiers, especially when the sample size is small compared to the dimension of the data. To cope with non-elliptic and possibly multimodal distributions, we propose a local version of the Mahalanobis distance. Subsequently, we propose another classifier based on a generalized additive model that uses the local Mahalanobis distances as features. This nonparametric classifier usually performs like the Mahalanobis distance based semiparametric classifier when the underlying distributions are elliptic, but outperforms it for several non-elliptic and multimodal distributions. We also investigate the behaviour of these two classifiers in high dimension, low sample size situations. A thorough numerical study involving several simulated and real datasets demonstrate the usefulness of the proposed classifiers in comparison to many state-of-the-art methods.

stat.ME↗

arXiv2023

Volumetric Reconstruction Resolves Off-Resonance Artifacts in Static and Dynamic PROPELLER MRI

Off-resonance artifacts in magnetic resonance imaging (MRI) are visual distortions that occur when the actual resonant frequencies of spins within the imaging volume differ from the expected frequencies used to encode spatial information. These discrepancies can be caused by a variety of factors, including magnetic field inhomogeneities, chemical shifts, or susceptibility differences within the tissues. Such artifacts can manifest as blurring, ghosting, or misregistration of the reconstructed image, and they often compromise its diagnostic quality. We propose to resolve these artifacts by lifting the 2D MRI reconstruction problem to 3D, introducing an additional "spectral" dimension to model this off-resonance. Our approach is inspired by recent progress in modeling radiance fields, and is capable of reconstructing both static and dynamic MR images as well as separating fat and water, which is of independent clinical interest. We demonstrate our approach in the context of PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction) MRI acquisitions, which are popular for their robustness to motion artifacts. Our method operates in a few minutes on a single GPU, and to our knowledge is the first to correct for chemical shift in gradient echo PROPELLER MRI reconstruction without additional measurements or pretraining data.

physics.med-ph↗