A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We calculate Euclidean distance degrees for common manifold optimization types.
Study infinite Euclidean distance discriminants of algebraic varieties.
Paper proposes a method to recover point configurations from noisy distance data.
Matrix profile has been recently proposed as a promising technique to the problem of all-pairs-similarity search on time series. Efficient algorithms have been proposed for computing it, e.g., STAMP, STOMP and SCRIMP++. All these algorithms use the z-normalized Euclidean distance to measure the distance between subsequ…
The study compares Euclidean and cosine distances in medical drug prescription prediction.
Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.
Extends manifold learning to non-Euclidean metrics.
Euclidean nets reveal properties of higher-dimensional manifolds.
New Sliced-Wasserstein distances for non-Euclidean data.
We address noisy Euclidean distances in high dimensions, estimating noise levels and correcting distances.
Smooth maps preserve distances on specific revolution surfaces.
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to a distance based on Pearson Correlation. This has profound impact on many distanc…
Paper tackles robust Euclidean distance estimation with sparse outliers.
Introduces Grassmann Distance Complexity to measure algebraic set nearest point problems.
Study rigidity by logarithmic capacity and related functions.
A new method compares unaligned datasets using log-Euclidean signatures of SPD matrices.
The paper studies convexity of products of squared Euclidean distances.
We study the use of power weighted shortest path distance functions for clustering high dimensional Euclidean data, under the assumption that the data is drawn from a collection of disjoint low dimensional manifolds. We argue, theoretically and experimentally, that this leads to higher clustering accuracy. We also pres…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow …
Generating point clouds, e.g., molecular structures, in arbitrary rotations, translations, and enumerations remains a challenging task. Meanwhile, neural networks utilizing symmetry invariant layers have been shown to be able to optimize their training objective in a data-efficient way. In this spirit, we present an ar…
This paper addresses Gaussian Process regression over probability measures, revealing a non-stationarity issue between Euclidean and Wasserstein kernels.
In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between …
The paper describes distances on Sol-type groups using novel geometric techniques.
Graph-based methods provide a powerful tool set for many non-parametric frameworks in Machine Learning. In general, the memory and computational complexity of these methods is quadratic in the number of examples in the data which makes them quickly infeasible for moderate to large scale datasets. A significant effort t…
APGD algorithm reconstructs point set from partial distance measurements.
Permutation invariant network learns Wasserstein metrics.
New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…
A fast binary embedding method preserves Euclidean distances in high-dimensional data.
A Euclidean (or hyperbolic) circle packing on a closed triangulated surface with prescribed inversive distance is locally determined by its cone angles. We prove this by applying a variational principle.
The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and v…
In this paper we demonstrate how the geometrically motivated algorithm to determine whether a two generator real Mobius group acting on the Poincare plane is or is not discrete can be interpreted as a non-Euclidean Euclidean algorithm. That is, the algorithm can be viewed as an application of the Euclidean division alg…
The article generalizes Clairaut's formula for geodesics on submanifolds.
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the so-called regularized kernel estimate. We show that such an estimate can be chara…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for anal…
FastMap-D embeds directed graphs using potential fields.
A new tensorial metric describes geometry in 4D space.
Upper bound for max-sliced 2-Wasserstein distance between measures.
A scalable version of MADD improves big-data classification speed.
We study surfaces with decorations and prove uniformization in non-Euclidean geometries.
Most random ReLU networks are vulnerable to small, Euclidean adversarial perturbations.
The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in I^3 with the constant relative curvature (analogue of the Gaussian cu…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a useful constraint, both theoretically--to prove convergence and optimality guar…
LOT framework speeds up event distance computation in collider physics.
We study left-invariant distances on Lie groups for which there exists a one-parameter family of homothetic automorphisms. The main examples are Carnot groups, in particular the Heisenberg group with the standard dilations. We are interested in criteria implying that, locally and away from the diagonal, the distance is…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous (i.e. corresponding to each other), as far as possible, and the Procrust…
We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other compact set of the cube as a tangent at all points or just in a den…
Study the hanging chain shape around a circle.