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Found 30 papers, 8 papers with code
Hierarchical Coupled Geometry Analysis for Neuronal Structure and Activity Pattern Discovery
In the wake of recent advances in experimental methods in neuroscience, the ability to record in-vivo neuronal activity from awake animals has become feasible.
Latent common manifold learning with alternating diffusion: analysis and applications
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years.
Kernel-based Sensor Fusion with Application to Audio-Visual Voice Activity Detection
In this paper, we address the problem of multiple view data fusion in the presence of noise and interferences.
Local Canonical Correlation Analysis for Nonlinear Common Variables Discovery
In this paper, we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high-dimensional observations.
Multimodal Latent Variable Analysis
The first step in our analysis is to find the common source of variability present in all sensor measurements.
Diffusion-based nonlinear filtering for multimodal data fusion with application to sleep stage assessment
We show that without prior knowledge on the different modalities and on the measured system, our method gives rise to a data-driven representation that is well correlated with the underlying sleep process and is robust to noise and sensor-specific effects.
Mahalanonbis Distance Informed by Clustering
Specifically we show that organizing similar coordinates in clusters can be exploited for the construction of the Mahalanobis distance between samples.
Data-Driven Tree Transforms and Metrics
Often the data is such that the observations do not reside on a regular grid, and the given order of the features is arbitrary and does not convey a notion of locality.
DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling
This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds.
Parametric Manifold Learning Via Sparse Multidimensional Scaling
We propose a metric-learning framework for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds.
Intrinsic Isometric Manifold Learning with Application to Localization
Specifically, we show that our proposed method facilitates accurate localization of a moving agent from imaging data it collects.
Statistical Tomography of Microscopic Life
This enables geometric self-calibration in imaging of transparent objects.
Domain Adaptation with Optimal Transport on the Manifold of SPD matrices
We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map.
Option Discovery in the Absence of Rewards with Manifold Analysis
Options have been shown to be an effective tool in reinforcement learning, facilitating improved exploration and learning.
Spectral Discovery of Jointly Smooth Features for Multimodal Data
We show analytically that our method is guaranteed to provide a set of orthogonal functions that are as jointly smooth as possible, ordered by increasing Dirichlet energy from the smoothest to the least smooth.
Unsupervised Ensembling of Multiple Software Sensors with Phase Synchronization: A Robust Approach For Electrocardiogram-derived Respiration
We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms.
Symmetric Positive Semi-definite Riemannian Geometry with Application to Domain Adaptation
In this paper, we present new results on the Riemannian geometry of symmetric positive semi-definite (SPSD) matrices.
Kernel-based parameter estimation of dynamical systems with unknown observation functions
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system.
Spectral Flow on the Manifold of SPD Matrices for Multimodal Data Processing
Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices.
Joint Geometric and Topological Analysis of Hierarchical Datasets
At the finer (sample) level, we devise a new metric between samples based on manifold learning that facilitates quantitative structural analysis.
Discovery of Single Independent Latent Variable
Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science.
Hyperbolic Procrustes Analysis Using Riemannian Geometry
Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA).
Spatiotemporal Analysis Using Riemannian Composition of Diffusion Operators
Our approach combines three components that are often considered separately: (i) manifold learning for building operators representing the geometry of the variables, (ii) Riemannian geometry of symmetric positive-definite matrices for multiscale composition of operators corresponding to different time samples, and (iii) spectral analysis of the composite operators for extracting different dynamic modes.
ManiFeSt: Manifold-based Feature Selection for Small Data Sets
This in turn allows for the extraction of the hidden manifold underlying the features and avoids overfitting, facilitating few-sample FS.
Unsupervised Detection of Sub-Territories of the Subthalamic Nucleus During DBS Surgery with Manifold Learning
Compared to a competing supervised algorithm based on a Hidden Markov Model, our unsupervised method demonstrates similar results in the STN detection task and superior results in the DLOR detection task.
On Interference-Rejection Using Riemannian Geometry for Direction of Arrival Estimation
We consider the problem of estimating the direction of arrival of desired acoustic sources in the presence of multiple acoustic interference sources.
Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
Finding meaningful representations and distances of hierarchical data is important in many fields.
The Expected Loss of Preconditioned Langevin Dynamics Reveals the Hessian Rank
Langevin dynamics (LD) is widely used for sampling from distributions and for optimization.
Riemannian Covariance Fitting for Direction-of-Arrival Estimation
In this paper, as a remedy, we present a comprehensive study of the use of various Riemannian metrics of HPD matrices in CF.
