Biology subjects

Praturu, A.

Publications and source records attributed to Praturu, A..

2 recordsLinked to original sources

bioRxiv2023

A Bayesian Approach to Non-Metric Hyperbolic Multi-Dimensional Scaling

This paper explores the intersection of hyperbolic geometry, non-metric techniques, and Bayesian frameworks to extend the capabilities of Bayesian Hyperbolic Multi-Dimensional Scaling (HMDS). While hyperbolic geometry is gaining attention for its ability to represent hierarchical relationships, traditional metrics impose constraints on distances. Non-metric techniques offer flexibility in capturing complex structures, making them suitable for scenarios where metric distances are less meaningful. The paper introduces a novel extension of Bayesian HMDS, incorporating non-metric techniques, enabling the embedding of Euclidean data within a hyperbolic space. The approach simultaneously fits for curvature and coordinates, leveraging the scaling properties of hyperbolic space. The non-metric Bayesian Hyperbolic MDS is expected to unveil new insights into hierarchical structures within complex datasets, providing a versa-tile tool for analyzing high-dimensional data flexibly and accurately. The efficacy of the proposed method is demonstrated through synthetic data experiments, showcasing its ability to capture non-linear transformations and accurately predict underlying curvature, with an emphasis on its ro-bustness to hyperparameter choices.

neuroscience↗

bioRxiv2022

A Bayesian Approach to Hyperbolic Multi-Dimensional Scaling

Recent studies have increasingly demonstrated that hyperbolic geometry confers many advantages for analyzing hierarchical structure in complex systems. However, available embedding methods do not give a precise metric for determining the dimensionality of the data, and do not vary curvature. These parameters are important for obtaining accurate, low dimensional, continuous descriptions of the data. To address this we develop a Bayesian formulation of Multi-Dimensional Scaling for embedding data in hyperbolic spaces that can fit for the optimal values of geometric parameters such as curvature and dimension. We propose a novel model of embedding uncertainty within this Bayesian framework which improves both performance and interpretability of the model. Because the method allows for variable curvature, it can also correctly embed Euclidean data using zero curvature, thus subsuming traditional Euclidean MDS models. We demonstrate that only a small amount of data is needed to constrain the geometry in our model and that the model is robust against false minima when scaling to large datasets. We apply our model to real world datasets and uncover new insights into their hierarchical structure derived from our geometric embeddings.

biophysics↗