Norms

Vector Norms

• Vector lp-norm with 0<p<= 2

Matrix Norms

• Matrix lp -norm with 0<p<= 2

• Matrix l(infiny)-norm

• Matrix lpq-norm with  0<p<= 2  and   0<q<= 2

• Matrix Lp-seminorm with 0<p<= 2

• Matrix Lp-quasi-norm with 0<p<= 2

• Matrix Frobenius norm

• Matrix nuclear norm

• Matrix dual norm

• Matrix Schatten-p norm with  0<p<= 2

• Matrix Log-sum nor

• Matrix max-norm

Proxy loss functions are used as surrogate of the original loss function (rank(.)) loss function for the low-rank constraint and l0-loss function for the sparsity constraint) to obtain a solvable problem.  Some loss functions are defined on norms.

Fair Use Policy

As this website gives many information that come from my research, please cite my following survey papers:

T. Bouwmans, A. Sobral, S. Javed, S. Jung, E. Zahzah, "Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset", Computer Science Review, Volume 23, pages 1-71, February 2017. [pdf]

T. Bouwmans, E. Zahzah, “Robust PCA via Principal Component Pursuit: A Review for a Comparative Evaluation in Video Surveillance”, Special Issue on Background Models Challenge, Computer Vision and Image Understanding, CVIU 2014, Volume 122, pages 22–34, May 2014. [pdf]

Note: My publications are available on Academia, ResearchGate, Researchr, ORCID and PublicationList.