Related papers: Linearized Diffusion Map
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…
The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However,…
This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…
Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance…
Linear dimensionality reduction techniques are powerful tools for image analysis as they allow the identification of important features in a data set. In particular, nonnegative matrix factorization (NMF) has become very popular as it is…
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…
We investigate the performance of distributed least-mean square (LMS) algorithms for parameter estimation over sensor networks where the regression data of each node are corrupted by white measurement noise. Under this condition, we show…
Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…
In this paper, we address the challenging task of achieving multi-view dimensionality reduction. The goal is to effectively use the availability of multiple views for extracting a coherent low-dimensional representation of the data. The…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
The diffusion based distributed learning approaches have been found to be a viable solution for learning over linearly separable datasets over a network. However, approaches till date are suitable for linearly separable datasets and need to…
In this paper, we present the linear decomposition method (LDM), which we developed to detect and analyze pulsar profile variations and mode changing behaviour. We developed LDM utilizing the likelihood function approach assuming the…
Accurate prediction of physical fields is critical in various engineering applications, including thermal management in electronic systems, airfoil shape optimization in aerospace, and flow field control in hypersonic vehicles. This study…
The diffusion model has recently emerged as a potent approach in computer vision, demonstrating remarkable performances in the field of generative artificial intelligence. Capable of producing high-quality synthetic images, diffusion models…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
LiDAR scene generation is critical for mitigating real-world LiDAR data collection costs and enhancing the robustness of downstream perception tasks in autonomous driving. However, existing methods commonly struggle to capture geometric…
Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…
This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…
Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform…
Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…