Related papers: Functional Multidimensional Scaling

We consider the minimization of non-convex quadratic forms regularized by a cubic term, which exhibit multiple saddle points and poor local minima. Nonetheless, we prove that, under mild assumptions, gradient descent approximates the…

The scalar-on-function regression model has become a popular analysis tool to explore the relationship between a scalar response and multiple functional predictors. Most of the existing approaches to estimate this model are based on the…

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope…

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study 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…

Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that…

Standard multidimensional scaling takes as input a dissimilarity matrix of general term $\delta _{ij}$ which is a numerical value. In this paper we input $\delta _{ij}=[\underline{\delta _{ij}},\overline{\delta _{ij}}]$ where…

Invariant-based models for incompressible isotropic hyperelasticity are typically formulated as functions of the first and second invariants, $W = W(\bar{I}_1, \bar{I}_2)$. A widely used class of models employs separable representations of…

Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important…

In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with…

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…

Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…

Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…

We use a rank one Gaussian perturbation to derive a smooth stochastic approximation of the maximum eigenvalue function. We then combine this smoothing result with an optimal smooth stochastic optimization algorithm to produce an efficient…

Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…

This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…

The paradigm of differentiable programming has significantly enhanced the scope of machine learning via the judicious use of gradient-based optimization. However, standard differentiable programming methods (such as autodiff) typically…