Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport

In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semi-definiteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise, and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes

Revisión sistemática de sistemas inteligentes de transporte (ITS) a través de internet de las cosas (IOT) para problemas de transporte terrestre de pasajeros

Trabajo de InvestigaciónEl desarrollo de este trabajo fue realizar una revisión sistemática de sistemas inteligentes de transporte (ITS) a través de internet de las cosas (IOT) para problemas de transporte terrestre de pasajeros, siguiendo la metodología de revisión sistemática de Barbara Kitchenham, definiendo palabras y frases para generar cadenas de busqueda e ir agregando criterios de inclusión y exclusión, en el proceso de búsqueda en bases de datos científicas, con el fin de realizar un análisis cuantitativo, mostrando una caracterización de términos referentes a la investigación.INTRODUCCIÓN 1. GENERALIDADES 2. PLANIFICACION DE LA REVICION SISTEMATICA. 3. RESULTADOS CONCLUCIONES RECOMENDACIONES BIBLIOGRAFÍA ANEXOSPregradoIngeniero de Sistema

Regularization and Interpolation of Positive Matrices

We construct certain matricial analogues of mass transport for positive-definite matrices of equal trace. The framework aims to devise ways of interpolating positive-definite matrices that tradeoff between 'aligning up their eigenstructure' and 'scaling the corresponding eigenvalues.' Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts

Regularization and Interpolation of Positive Matrices

We construct certain matricial analogues of mass transport for positive definite matrices of equal trace. The framework aims to devise ways of interpolating positive definite matrices that tradeoff between "aligning up their eigenstructure" and "scaling the corresponding eigenvalues". Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts

Regularization and Interpolation of Positive Matrices

We construct certain matricial analogues of mass transport for positive definite matrices of equal trace. The framework aims to devise ways of interpolating positive definite matrices that tradeoff between “aligning up their eigenstructure” and “scaling the corresponding eigenvalues”. Motivation for the work is provided by power spectral analysis of multivariate time series where linear interpolation between matrix-valued power spectra generates push-pop unrealistic and undesirable artifacts