Related papers: Interpretable Discriminative Dimensionality Reduct…
An implicit neural representation (INR) is a neural network that approximates a spatiotemporal function. Many memory-intensive visualization tasks, including modern 4D CT scanning methods, represent data natively as INRs. While INRs are…
Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
Volume Rendering is an important technique for visualizing three-dimensional scalar data grids and is commonly employed for scientific and medical image data. Direct Volume Rendering (DVR) is a well established and efficient rendering…
Reduced-rank linear discriminant analysis (RRLDA) is a foundational method of dimension reduction for classification that has been useful in a wide range of applications. The goal is to identify an optimal subspace to project the…
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…
Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…
Manifold learning techniques play a pivotal role in machine learning by revealing lower-dimensional embeddings within high-dimensional data, thus enhancing both the efficiency and interpretability of data analysis by transforming the data…
In recent years, accelerated MRI reconstruction based on deep learning has led to significant improvements in image quality with impressive results for high acceleration factors. However, from a clinical perspective image quality is only…
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have…
Dimensionality reduction can be applied to hyperspectral images so that the most useful data can be extracted and processed more quickly. This is critical in any situation in which data volume exceeds the capacity of the computational…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…
In this article we present the basics of manifold relevance determination (MRD) as introduced in \cite{mrd}, and some applications where the technology might be of particular use. Section 1 acts as a short tutorial of the ideas developed in…
Building fair deep neural networks (DNNs) is a crucial step towards achieving trustworthy artificial intelligence. Delving into deeper factors that affect the fairness of DNNs is paramount and serves as the foundation for mitigating model…
Classical metric and non-metric multidimensional scaling (MDS) variants are widely known manifold learning (ML) methods which enable construction of low dimensional representation (projections) of high dimensional data inputs. However,…
Latent space models are widely used for analyzing high-dimensional discrete data matrices, such as patient-feature matrices in electronic health records (EHRs), by capturing complex dependence structures through low-dimensional embeddings.…