Related papers: Local biplots for multi-dimensional scaling, with …
The purpose of this article is to investigate the relationship between suborbifolds and orbifold embeddings. In particular, we give natural definitions of the notion of suborbifold and orbifold embedding and provide many examples.…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
We present theory and practice for robust implementations of bivariate Jacobi set and Reeb space algorithms. Robustness is a fundamental topic in computational geometry that deals with the issues of numerical errors and degenerate cases in…
The problem of joint estimation of multiple graphical models from high dimensional data has been studied in the statistics and machine learning literature, due to its importance in diverse fields including molecular biology, neuroscience…
We introduce an adaptive scattered data fitting scheme as extension of local least squares approximations to hierarchical spline spaces. To efficiently deal with non-trivial data configurations, the local solutions are described in terms of…
We show that relative compactified Jacobians of one-parameter smoothings of a nodal curve of genus g are Mumford models of the generic fiber. Each such model is given by an admissible polytopal decomposition of the skeleton of the Jacobian.…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…
We establish how a two-dimensional local field can be described as a locally convex space once an embedding of a local field into it has been fixed. We study the resulting spaces from a functional analytic point of view: in particular we…
Multidimensional scaling (MDS) is a family of methods that embed a given set of points into a simple, usually flat, domain. The points are assumed to be sampled from some metric space, and the mapping attempts to preserve the distances…
In this article we discuss local aspects of 2-functors defined on the path 2-groupoid of a smooth manifold; in particular, local trivializations and descent data. This is a contribution to a project that provides an axiomatic formulation of…
The generalized Donaldson-Thomas invariants counting one dimensional semistable sheaves on Calabi-Yau 3-folds are conjectured to satisfy a certain multiple cover formula. This conjecture is equivalent to Pandharipande-Thomas's strong…
A temporal network -- a collection of snapshots recording the evolution of a network whose links appear and disappear dynamically -- can be interpreted as a trajectory in graph space. In order to characterize the complex dynamics of such…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
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…
Firstly, we reduce the long-standing problem of ascertaining the Hilbert-Schmidt probability that a generic pair of qubits is separable to that of determining the specific nature of a one-dimensional (separability) function of the radial…
Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
We show bifurcation of localized spike solutions from spatially constant states in systems of nonlocally coupled equations in the whole space. The main assumptions are a generic bifurcation of saddle-node or transcritical type for spatially…
Multidimensional scaling (MDS) is the act of embedding proximity information about a set of $n$ objects in $d$-dimensional Euclidean space. As originally conceived by the psychometric community, MDS was concerned with embedding a fixed set…