Related papers: A Theoretical Analysis of Joint Manifolds

This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

We present a data compression and dimensionality reduction scheme for data fusion and aggregation applications to prevent data congestion and reduce energy consumption at network connecting points such as cluster heads and gateways. Our…

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…

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce…

A mixture of Gaussians fit to a single curved or heavy-tailed cluster will report that the data contains many clusters. To produce more appropriate clusterings, we introduce a model which warps a latent mixture of Gaussians to produce…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

This paper presents a technique which exploits the occurrence of certain events as observed by different sensors, to detect and classify objects. This technique explores the extent of dependence between features being observed by the…

The commonly used latent space embedding techniques, such as Principal Component Analysis, Factor Analysis, and manifold learning techniques, are typically used for learning effective representations of homogeneous data. However, they do…

High-dimensional images, or images with a high-dimensional attribute vector per pixel, are commonly explored with coordinated views of a low-dimensional embedding of the attribute space and a conventional image representation. Nowadays,…

Sensor signals acquired in the industrial process contain rich information which can be analyzed to facilitate effective monitoring of the process, early detection of system anomalies, quick diagnosis of fault root causes, and intelligent…

Deep neural networks have been used widely to learn the latent structure of datasets, across modalities such as images, shapes, and audio signals. However, existing models are generally modality-dependent, requiring custom architectures and…

Multimodal deep learning methods capture synergistic features from multiple modalities and have the potential to improve accuracy for stress detection compared to unimodal methods. However, this accuracy gain typically comes from high…

The high-dimensional data setting, in which p >> n, is a challenging statistical paradigm that appears in many real-world problems. In this setting, learning a compact, low-dimensional representation of the data can substantially help…

Detection with high dimensional multimodal data is a challenging problem when there are complex inter- and intra- modal dependencies. While several approaches have been proposed for dependent data fusion (e.g., based on copula theory),…

The problem of learning the structure of a high dimensional graphical model from data has received considerable attention in recent years. In many applications such as sensor networks and proteomics it is often expensive to obtain samples…

Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more…

This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…

Despite high-dimensionality of images, the sets of images of 3D objects have long been hypothesized to form low-dimensional manifolds. What is the nature of such manifolds? How do they differ across objects and object classes? Answering…

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such…