Related papers: quollr: An R Package for Visualizing 2-D Models fr…
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…
Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…
In an era where the exponential growth of image data driven by the Internet of Things (IoT) is outpacing traditional storage solutions, this work explores and advances the potential of Implicit Neural Representation (INR) as a…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
Astronomical data is often uncertain with errors that are heteroscedastic (different for each data point) and covariant between different dimensions. Assuming that a set of D-dimensional data points can be described by a (D - 1)-dimensional…
The growing number of dimensionality reduction methods available for data visualization has recently inspired the development of quality assessment measures, in order to evaluate the resulting low-dimensional representation independently…
Reducing dimensionality is a key preprocessing step in many data analysis applications to address the negative effects of the curse of dimensionality and collinearity on model performance and computational complexity, to denoise the data or…
Holographic Reduced Representations (HRR) are a method for performing symbolic AI on top of real-valued vectors by associating each vector with an abstract concept, and providing mathematical operations to manipulate vectors as if they were…
This work proposes Quor, a simple yet effective nonparametric method to compare independent samples with respect to corresponding quantiles of their populations. The method is solely based on the order statistics of the samples, and…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Discovering patterns of the complex high-dimensional data is a long-standing problem. Dimension Reduction (DR) and Intrinsic Dimension Estimation (IDE) are two fundamental thematic programs that facilitate geometric understanding of the…
Molecular simulations produce very high-dimensional data-sets with millions of data points. As analysis methods are often unable to cope with so many dimensions, it is common to use dimensionality reduction and clustering methods to reach a…
Signal compression based on implicit neural representation (INR) is an emerging technique to represent multimedia signals with a small number of bits. While INR-based signal compression achieves high-quality reconstruction for relatively…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
Dimensionality reduction (DR) is an important technique for data exploration and knowledge discovery. However, most of the main DR methods are either linear (e.g., PCA), do not provide an explicit mapping between the original data and its…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
To solve key biomedical problems, experimentalists now routinely measure millions or billions of features (dimensions) per sample, with the hope that data science techniques will be able to build accurate data-driven inferences. Because…
Data visualization is the process by which data of any size or dimensionality is processed to produce an understandable set of data in a lower dimensionality, allowing it to be manipulated and understood more easily by people. The goal of…
A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically,…
Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…