# Estimating Positive Definite Matrices using Frechet Mean

### Mehdi Jahromi, Kon Wong, Aleksandar Jeremic

#### Abstract

Estimation of covariance matrices is a common problem in signal processing applications. Commonly applied techniques based on the cost optimization (e.g. maximum likelihood estimation) result in an unconstrained estimation in which the positive definite nature of covariance matrices is ignored. Consequently this may result in accurate estimation of the covariance matrix which may affect overall performance of the system. In this paper we propose to estimate the covariance matrix using Fréchet mean which ensures that the estimate also has positive definite structure. We demonstrate the applicability of the proposed technique on both estimation and classification accuracy using numerical simulations. In addition we discuss some of the preliminary results we obtained by applying our techniques to high content cell imaging data set.

#### References

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#### Paper Citation

#### in Harvard Style

Jahromi M., Wong K. and Jeremic A. (2015). **Estimating Positive Definite Matrices using Frechet Mean** . In *Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2015)* ISBN 978-989-758-069-7, pages 295-299. DOI: 10.5220/0005277902950299

#### in Bibtex Style

@conference{biosignals15,

author={Mehdi Jahromi and Kon Wong and Aleksandar Jeremic},

title={Estimating Positive Definite Matrices using Frechet Mean},

booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2015)},

year={2015},

pages={295-299},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005277902950299},

isbn={978-989-758-069-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2015)

TI - Estimating Positive Definite Matrices using Frechet Mean

SN - 978-989-758-069-7

AU - Jahromi M.

AU - Wong K.

AU - Jeremic A.

PY - 2015

SP - 295

EP - 299

DO - 10.5220/0005277902950299