Related papers: A New Parametrization of Correlation Matrices
This work proposes novel hyperparameter-free losses for single view 3D reconstruction with morphable models (3DMM). We dispense with the hyperparameters used in other works by exploiting geometry, so that the shape of the object and the…
We define a new numerical range of an n\timesn complex matrix in terms of correlation matrices and develop some of its properties. We also define a related numerical range that arises from Alain Connes' famous embedding problem.
That parametrization and sparsity are inherently linked raises the possibility that relevant models, not obviously sparse in their natural formulation, exhibit a population-level sparsity after reparametrization. In covariance models,…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…
Several density-matrix renormalization group methods have been proposed to compute the momentum- and frequency-resolved dynamical correlation functions of low-dimensional strongly correlated systems. The most relevant approaches are…
We present a convolutional neural network for the classification of correlation responses obtained by correlation filters. The proposed approach can improve the accuracy of classification, as well as achieve invariance to the image classes…
Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including…
We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
A new version of the partial autocorrelation plot and a new family of subset autoregressive models are introduced. A comprehensive approach to model identification, estimation and diagnostic checking is developed for these models. These…
The Nonnegative Matrix Factorization (NMF) of the rating matrix has shown to be an effective method to tackle the recommendation problem. In this paper we propose new methods based on the NMF of the rating matrix and we compare them with…
This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…
Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons.…
The sample covariance matrix becomes non-invertible in high-dimensional settings, making classical multivariate statistical methods inapplicable. Various regularization techniques address this issue by imposing a structured target matrix to…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a…
A simple recursive scheme for parameterisation of n-by-n unitary matrices is presented.
We summarize our renormalization group approach for the vector model as well as the matrix model which are the discretized quantum gravity in one- and two-dimensional spacetime. A difference equation is obtained which relates free energies…