Related papers: Manifold Learning for Source Separation in Confusi…

Heterogeneous data fusion can enhance the robustness and accuracy of an algorithm on a given task. However, due to the difference in various modalities, aligning the sensors and embedding their information into discriminative and compact…

Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…

We discuss spatial fluctuations in the gravitational wave background arising from unresolved Galactic binary sources, such as close white dwarf binaries, due to the fact the galactic binary source distribution is anisotropic. We introduce a…

Score-based methods, such as diffusion models and Bayesian inverse problems, are often interpreted as learning the data distribution in the low-noise limit ($\sigma \to 0$). In this work, we propose an alternative perspective: their success…

The unprecedented sensitivity of the Laser Interferometer Gravitational-Wave Observatory, which enables the detection of distant astrophysical sources, also renders the detectors highly susceptible to low-frequency ground motion. Persistent…

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the space-based gravitational-wave (GW) detector. However, a large fraction of captures will not be individually…

The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space. It is scheduled to fly in the early 2030's. LISA design predicts sensitivity levels that enable the detection a Stochastic Gravitational Wave…

The Laser Interferometer Space Antenna (LISA) mission features a three-spacecraft long-arm constellation intended to detect gravitational wave sources in the low-frequency band up to 1 Hz via laser interferometry. The paper presents an…

The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…

Transient noise appearing in the data from gravitational-wave detectors frequently causes problems, such as instability of the detectors and overlapping or mimicking gravitational-wave signals. Because transient noise is considered to be…

There has been an emerging trend in non-Euclidean statistical analysis of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain…

The detection of gravitational waves has inaugurated the era of gravitational astronomy and opened new avenues for the multimessenger study of cosmic sources. Thanks to their sensitivity, the Advanced LIGO and Advanced Virgo interferometers…

Armstrong et al. have recently presented new ways of combining signals to precisely cancel laser frequency noise in spaceborne interferometric gravitational wave detectors such as LISA. One of these combinations, the symmetrized Sagnac…

Automatically learning features, especially robust features, has attracted much attention in the machine learning community. In this paper, we propose a new method to learn non-linear robust features by taking advantage of the data manifold…

Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To…