Publication

Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

2017
Conference Papers

Abstract

In many sensing and control applications, data are represented in the form of symmetric positive definite (SPD) matrices. Considering the underlying geometry of this data space can be beneficial in many robotics applications. In this paper, we present an extension of Gaussian mixture regression (GMR) with input and/or output data on SPD manifolds. As the covariance of SPD datapoints is a 4th-order tensor, we develop a method for parallel transport of high order covariances on SPD manifolds. The proposed approach is experimented in the context of prosthetic hands, with the estimation of wrist movements based on spatial covariance features computed from sEMG signals.

Official source

https://infoscience.epfl.ch/entities/publication/b05e605e-828d-4d9c-92ff-e67dcc046e66

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2017
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/b05e605e-828d-4d9c-92ff-e67dcc046e66

About this result

Related concepts (32)

Data

In common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.

Estimation of covariance matrices

In statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. Estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. Simple cases, where observations are complete, can be dealt with by using the sample covariance matrix.

Covariance matrix

In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector. Any covariance matrix is symmetric and positive semi-definite and its main diagonal contains variances (i.e., the covariance of each element with itself). Intuitively, the covariance matrix generalizes the notion of variance to multiple dimensions.

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Gaussian Mixture Regression on Symmetric Positive Definite Matrices Manifolds: Application to Wrist Motion Estimation with sEMG

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