GUI for Robust PCA Recoverability Experiments
Download GUI
The GUIs are developed in MATALB® on Windows and Linux platforms. Please download and install the appropriate Matlab Compiler Runtime (MCR) as well.
The GUI provides the following functionalities:
- Evaluate sufficient conditions for recovery over a selected range of ranks and sparsities, size, low-rank and sparse matrix types.
- Recoverable region for a selected range fractional sparsities, size, low-rank and sparse matrix types.
- Input - output mapping between fractional-ranks fractional-sparsities.
- Recovery error of the low-rank component.
- Recovery error of the sparse component.
The software reproduces experiments listed in [1] and [2]. The sufficient conditions used are from [1]. Matrix constructions and further details of the experiments can be found in [2].
Main GUI
The portal to the GUIs of each experiment. User will select experiments and click Launch open a separate GUI for the experiment. When clicked on an experiment, a brief description of the experiment will be displayed.
Sufficient Condition Values
Dots indicate the condition values of the sufficient conditions presented in [1]. The green surface indicate the condition threshold 1/12. Users select the matrix size to test, the number of realizations, sparse and low-rank matrix type and the ranges for sparsity and ranks.
Recoverable Regions
Fractional-rank and fractional-sparsity combinations below the curves are 100% recoverable for corresponding matrix size. Users select the sparse and low-rank matrix type, the range of fractional-sparsities to test and the list of matrix sizes to test. The users also specify the number of repetitions to be made to verify 100% recoverability.
Input-Output Fractional-rank Fractional-spasity Mapping
The mapping between the input pair of fractional rank of the low-rank component, fractional-sparsity of the sparse component and the output pair of fractional rank of the low-rank component, fractional-sparsity of the sparse component. Results indicate that failed recoveries tend to result in a half-rank low-rank component and half-sparse sparse component. Users specify the matrix size to test, the number of repetitions, sparse and low-rank matrix types, and ranges of fractional-ranks and fractional-sparsities.
Recovery Error of the Low-rank Component
The growth of error in recovering the low-rank component for a range of fractional-ranks with sparsity of the sparse component kept fixed. User specifies the matrix size to test, number of repetitions, type of the sparse and low-rank components, the fixed fractional-sparsity of the sparse component, the range of fractional-ranks of the low-rank components, and the types of the errors. Two types of errors can be found: normalized norm errors and alignment errors. Normalized norm errors use spectral, nuclear, Frobenius and infinity norms. Alignment errors check principal angles and geodesic distances.
Recovery Error of the Sparse Component
The growth of error in recovering the sparse component for a range of fractional-sparsities with rank of the low-rank component kept fixed. User specifies the matrix size to test, number of repetitions, type of the sparse and low-rank components, the fixed fractional-rank of the low-rank component, the range of fractional-sparsities of the sparse components, and the types of the errors. Two types of errors can be found: normalized norm errors and detection errors. Normalized norm errors use one, spectral, Frobenius and infinity norms. Alignment errors check detection rate and false positive rate.
References
[1] V. Chandrasekaran, S. Sanghavi, P.A. Parrilo, and A.S. Willsky, Rank-Sparsity Incoherence for Matrix Decomposition, SIAM Journal on Optimization, Vol. 21, No. 2, June 2011.
[2] V.W. Bandara, L.L. Scharf, R.C. Paffenroth, A.P. Jayasumana, and P.C. DuToit, Empirical Recovery Regions of Robust PCA, In review. (PDF available upon request)
[3] V.W. Bandara, Ph.D. Dissertation, Spring 2014.