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One of the fundamental problems within the field of machine learning is dimensionality reduction. Dimensionality reduction methods make it possible to combat the so-called curse of dimensionality, visualize high-dimensional data and, in…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
We introduce a new method that efficiently computes a set of viewpoints and trajectories for high-quality 3D reconstructions in outdoor environments. Our goal is to automatically explore an unknown area, and obtain a complete 3D scan of a…
Sufficient dimension reduction aims for reduction of dimensionality of a regression without loss of information by replacing the original predictor with its lower-dimensional subspace. Partial (sufficient) dimension reduction arises when…
This paper presents an efficient algorithm for the least-squares problem using the point-to-plane cost, which aims to jointly optimize depth sensor poses and plane parameters for 3D reconstruction. We call this least-squares problem…
Cross-flow turbines harness kinetic energy in wind or moving water. Due to their unsteady fluid dynamics, it can be difficult to predict the interplay between aspects of rotor geometry and turbine performance. This study considers the…
One of the central issues of several machine learning applications on real data is the choice of the input features. Ideally, the designer should select only the relevant, non-redundant features to preserve the complete information…
This paper investigates the problem of planning a minimum-length tour for a three-dimensional Dubins airplane model to visually inspect a series of targets located on the ground or exterior surface of objects in an urban environment.…
The varying coefficient model has received broad attention from researchers as it is a powerful dimension reduction tool for non-parametric modeling. Most existing varying coefficient models fitted with polynomial spline assume equidistant…
In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are…
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…
The computational cost of traditional Computational Fluid Dynamics-based Aerodynamic Shape Optimization severely restricts design space exploration. This paper introduces TripOptimizer, a fully differentiable deep learning framework for…
Distributed deep neural networks (DNNs) have become central to modern computer vision, yet their deployment on resource-constrained edge devices remains hindered by substantial parameter counts, computational demands, and the probability of…
Fr\'echet regression has received considerable attention to model metric-space valued responses that are complex and non-Euclidean data, such as probability distributions and vectors on the unit sphere. However, existing Fr\'echet…
The innovative bladeless design of the AirMultiplier, patented by Dyson in 2009, has generated significant interest due to its unique approach to air circulation that leverages the Coanda effect. In this study, we present a comprehensive…
A method is introduced to perform simultaneous sparse dimension reduction on two blocks of variables. Beyond dimension reduction, it also yields an estimator for multivariate regression with the capability to intrinsically deselect…
Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…
Supervised dimensionality reduction has emerged as an important theme in the last decade. Despite the plethora of models and formulations, there is a lack of a simple model which aims to project the set of patterns into a space defined by…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…