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.
The paper introduces a statistical distance matrix for better feature representation and clustering.
New curvature concept preserves graph distances under operations.
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 paper shows how to recover true node positions from a graph or similarity matrix.
Paper proposes a method to recover point configurations from noisy distance data.
Two algorithms estimate Wasserstein distance matrices from few entries for manifold learning.
Two new algorithms select matrix rows and columns to preserve distances.
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We r…
Unified framework for hyperbolic embeddings from mixed data types.
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…
In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the cost function. The first proposed problem is control for positive definite Hermiti…
Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative coefficient matrix, and the coefficient matrix is used as the new representation. …
I-BBS identifies latent sub-manifolds from distance matrices, robust to noise.
Paper tackles robust Euclidean distance estimation with sparse outliers.
Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression matrix to be low-rank or sparse. Some other methodologies introduce factorizati…
Method uses NMF for clustering with partial distance measurements.
The problem of filtering information from large correlation matrices is of great importance in many applications. We have recently proposed the use of the Kullback-Leibler distance to measure the performance of filtering algorithms in recovering the underlying correlation matrix when the variables are described by a mu…
Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization variables. A remedy is non-alternating schemes. However, due to a lack of Lipschitz conti…
We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense …
APGD algorithm reconstructs point set from partial distance measurements.
We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation …
Model tracks structural changes in Brownian particle configurations on a sphere.
The original k-means clustering method works only if the exact vectors representing the data points are known. Therefore calculating the distances from the centroids needs vector operations, since the average of abstract data points is undefined. Existing algorithms can be extended for those cases when the sole input i…
We investigate some geometric properties of the real algebraic variety of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart-Young-Mirsky-type theorem for the distance function from a generic matrix to points in . We exhibit conne…
Study of metrics on positive-definite matrices from power potential, linking to power means.
A new method efficiently approximates Gromov-Wasserstein distance.
Introduces new Wasserstein distances for more intrinsic metrics.
Python package for SPD matrix distances, reproducible and extensible.
This study examines the relationship between PLS and OLS regression using eigenvalue distributions.
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
Positive definite matrices abound in a dazzling variety of applications. This ubiquity can be in part attributed to their rich geometric structure: positive definite matrices form a self-dual convex cone whose strict interior is a Riemannian manifold. The manifold view is endowed with a "natural" distance function whil…
We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched…
OMD monitors stock market dynamics through matrix trajectories, revealing crisis patterns and sector rotations.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
Wasserstein t-SNE embeds hierarchical datasets considering within-unit distributions.
We proved a matrix Li-Yau-Hamilton type gradient estimates for the positive solutin of the heat equation on complete Kaehler manifolds with nonnegative bisectional curvature. As a consequence we obtain a comparison theorem for the distance function under this curvature assumption.
A method for community detection in multilayer networks using data matrices.
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to largely outperform the sample covariance matrix estimate and to compete with state…
LOT Wassmap speeds up Wasserstein space manifold learning.
OMD monitors stock market dynamics through matrix trajectories and reveals crisis patterns.
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the hi…
The paper uses distance covariance to improve fairness in machine learning models.
Study on deep matrix factorization with Bures-Wasserstein loss, focusing on critical points and convergence.
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is mainly exploited for the task of classification, this paper is developed to study th…
Paper analyzes singular subspace estimation in noisy matrix models.
We propose a non-parametric regression methodology, Random Forests on Distance Matrices (RFDM), for detecting genetic variants associated to quantitative phenotypes representing the human brain's structure or function, and obtained using neuroimaging techniques. RFDM, which is an extension of decision forests, requires…
Sharp bounds for max-sliced Wasserstein distances derived for empirical distributions.
This paper proposes a representational model for grid cells. In this model, the 2D self-position of the agent is represented by a high-dimensional vector, and the 2D self-motion or displacement of the agent is represented by a matrix that transforms the vector. Each component of the vector is a unit or a cell. The mode…