Related papers: Robust Multi-Dimensional Scaling via Accelerated A…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Alternating direction multiplication is a powerful technique for solving convex optimisation problems. When challenging subproblems are encountered in the real world, it is useful to solve them by introducing neighbourhood terms. When the…

We study the well-known methods of alternating and simultaneous projections when applied to two nonorthogonal linear subspaces of a real Euclidean space. Assuming that both of the methods have a common starting point chosen from either one…

Random projection algorithm is an iterative gradient method with random projections. Such an algorithm is of interest for constrained optimization when the constraint set is not known in advance or the projection operation on the whole…

Distribution shifts are ubiquitous in real-world machine learning applications, posing a challenge to the generalization of models trained on one data distribution to another. We focus on scenarios where data distributions vary across…

The mean squared error loss is widely used in many applications, including auto-encoders, multi-target regression, and matrix factorization, to name a few. Despite computational advantages due to its differentiability, it is not robust to…

We study a class of structured convex optimization problems, which have a two-block separable objective and nonlinear functional constraints as well as affine constraints that couple the two block variables. Such problems naturally arise…

In this paper, we propose a distributed algorithm to solve planar minimum time multi-vehicle rendezvous problem with non-identical velocity constraints on cyclic digraph (topology). Motivated by the cyclic alternating projection method that…

Unsupervised change detection techniques are generally constrained to two multi-band optical images acquired at different times through sensors sharing the same spatial and spectral resolution. This scenario is suitable for a straight…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…

This paper studies the problem of extracting planar regions in uneven terrains from unordered point cloud measurements. Such a problem is critical in various robotic applications such as robotic perceptive locomotion. While existing…

In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…

We propose two training techniques for improving the robustness of Neural Networks to adversarial attacks, i.e. manipulations of the inputs that are maliciously crafted to fool networks into incorrect predictions. Both methods are…

To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME)…

Dimension reduction is often an important step in the analysis of high-dimensional data. PCA is a popular technique to find the best low-dimensional approximation of high-dimensional data. However, classical PCA is very sensitive to…

We reexamine the the classical multidimensional scaling (MDS). We study some special cases, in particular, the exact solution for the sub-space formed by the 3 dimensional principal coordinates is derived. Also we give the extreme case when…

Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the…

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…