26 accepted papers
Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods…
In this paper, we introduce EMD-Based Hyperbolic Diffusion Distance (EMD-HDD), a new method for constructing a meaningful distance metric for hierarchical data with latent hierarchical structure. Our method relies on hyperbolic geometry, diffusion geometry, and the Earth Mover’s Distance (EMD). Spec…
High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an unsupervised method for jointly learning hierarchical representations…
Learning shared representations is a primary area of multimodal representation learning. The current approaches to achieve a shared embedding space rely heavily on paired samples from each modality, which are significantly harder to obtain than unpaired ones. In this work, we demonstrate that shared…
We address the problem of multichannel audio signal enhancement in reverberant environments with interfering sources. We propose an approach that leverages the Riemannian geometry of the spatial correlation matrices of the received signals to estimate the relative transfer function (RTF) of the desi…
We propose a novel functorial graph coarsening method that preserves inner products between node features, a property often overlooked by existing approaches focusing primarily on structural fidelity. By treating node features as functions on the graph and preserving their inner products, our method…
In this paper, we introduce Supervised Diffusion Maps (SDM) and Semi-Supervised Diffusion Maps (SSDM), which transform the well-known unsupervised dimensionality reduction algorithm, Diffusion Maps, into supervised and semi-supervised learning tools. The proposed methods, SDM and SSDM, are based on…
Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically designed for data with a latent feature hierarchy, i.e., th…
Direct Position Determination (DPD) is the state-of-the-art solution for emitter localization using multiple phased arrays. This paper shows that DPD can be recast as a covariance-fitting (CF) problem that minimizes the Euclidean distance between a sample covariance matrix ${\mathbf{\hat R}}$ and it…
Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of shift equivariance, which is the basis of convolution network…
In this paper, we present Hyperbolic Diffusion Procrustes Analysis (HDPA), a new method for informative representation of hierarchical datasets based on hyperbolic geometry, diffusion geometry, and Procrustes analysis. Our method jointly embeds multiple datasets in a product manifold of hyperbolic s…
Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to…
In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian geometry, a composite kernel is computed, extracting the diff…
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Speci…
Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science. In this work, we consider data given as an invertible mixture of two statistically independent components, and assume that one of the components is observed while the other is hidde…
In this paper, we consider the problem of aligning data sets of short temporal signals without any a-priori known correspondence. We present a method combining Koopman operator theory and the Riemannian geometry of symmetric positive-definite (SPD) matrices. First, by taking a Koopman operator theor…
Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely…
Options have been shown to be an effective tool in reinforcement learning, facilitating improved exploration and learning. In this paper, we present an approach based on spectral graph theory and derive an algorithm that systematically discovers options without access to a specific reward or task as…
In this paper, we propose a new unsupervised domain adaptation method based on the Riemannian geometry of Symmetric Positive-Definite (SPD) matrices. The proposed domain adaptation is based on parallel transport (PT) and moments alignment. We show that this method facilitates meaningful comparisons…
This paper investigates localization of an arbitrary number of simultaneously active speakers in an acoustic enclosure. We propose an algorithm capable of estimating the number of speakers, using reliability information to obtain robust estimation results in adverse acoustic scenarios and estimating…
Despite attracting significant research efforts, the problem of source localization in noisy and reverberant environments remains challenging. Novel learning-based methods attempt to solve the problem by modelling the acoustic environment from the observed data. Typically, appropriate feature vector…
We achieve tomography of 3D volumetric natural objects, where each projected 2D image corresponds to a different specimen. Each specimen has unknown random 3D orientation, location, and scale. This imaging scenario is relevant to microscopic and mesoscopic organisms, aerosols and hydrosols viewed na…
In this paper we address the detection of Alzheimer's disease based solely on EEG recordings. We assume that the state of Alzheimer's disease can be described by a latent manifold, captured by the EEG sensors and apply alternating diffusion to reveal this common underlying manifold from multiple EEG…
Recently, a supervised graph-based target detection method was proposed based on a new affinity measure between a set of target training patches and a test image. In this paper, we propose a new high-resolution detection score, which enhances the performance of the previous method by utilizing the k…
Sound source localization is addressed by a novel Bayesian approach using a data-driven geometric model. The goal is to recover the target function that attaches each acoustic sample, formed by the measured signals, with its corresponding position. The estimation is derived by maximizing the posteri…
In this paper, we address the problem of multimodal signal processing and present a manifold learning method to extract the common source of variability from multiple measurements. This method is based on alternating-diffusion and is particularly adapted to time series. We show that the common sourc…