Manopt, a matlab toolbox for optimization on manifolds

By Nicolas Boumal, Bamdev Mishra, Pierre-Antoine Absil, Rodolphe Sepulchre. Journal of machine learning research, 2013

1,188 citations recorded by the source corpus.

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/40f391bc3860e8cd71d7ea68ec11d80d5e12c02c

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Citations in the corpus

Understanding symmetries in deep networks (2015, methodology): “The stochastic gradient descent algorithms with the proposed updates are implemented in Matlab and Manopt [15].”
MonoCap: Monocular Human Motion Capture using a CNN Coupled with a Geometric Prior (2017, methodology): “Here, manifold optimization is adopted to update the rotations using the trust-region solver in the Manopt toolbox [70].”
Loss in Translation: Learning Bilingual Word Mapping with a Retrieval Criterion (2018, background): “As such, it can be solved using manifold optimization tools (Boumal et al., 2014).”
MU-MIMO Communications With MIMO Radar: From Co-Existence to Joint Transmission (2017, methodology): “For a complex hypersphere, the tangent space is given by [36] T The Riemannian gradient is obtained by projecting the Euclidean gradient onto T ˜T , which is [36] grad For the max SINR penalty, unfortunately, the gradient does not exist due to the non-smooth max function.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (2017, methodology): “The MANOPT package [Boumal et al., 2014] (for a Python version see [Koep and Weichwald, 2016]) provides a useful interface for many standard matrix Riemannian optimization techniques, however, extensions for tensors (especially in high dimensions) are not easy and should be performed very carefully.”
Sparse Representation for 3D Shape Estimation: A Convex Relaxation Approach (2015, methodology): “The local update of rotation is implemented by the manifold optimization over the orthogonal group with the Manopt toolbox [53].”
Riemannian Approaches in Brain-Computer Interfaces: A Review (2017, neutral): “been implemented efficiently in a MATLAB toolbox [37].”
A New Benchmark Based on Recent Advances in Multispectral Pansharpening: Revisiting Pansharpening With Classical and Emerging Pansharpening Methods (2021, methodology): “The orthonormality-constrained optimization problem with respect to F is efficiently solved by using manifold optimization [135], [136].”
Multi-Label Learning with Global and Local Label Correlation (2017, methodology): “Specifically, theMANOPT toolbox [35] is utilized to implement gradient descent with line search on the 1084 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL.”
Fréchet regression for random objects with Euclidean predictors (2016, methodology): “This smoothing step was performed in Matlab using the hades package, available at <http://www.stat.ucdavis.edu/hades/>.”
On critical points of quadratic low-rank matrix optimization problems (2020, methodology): “All methods except ALS were implemented using Manopt (Boumal et al. , 2014) with standard options except that we used exact line search to verify theoretical convergence rates.”
Linear dimensionality reduction: survey, insights, and generalizations (2014, methodology): “We implemented these methods in MATLAB, both natively for first order methods, and using the excellent manopt software library (Boumal et al., 2014) for first and second order methods (all code is available at http://github.”
Alternating Minimization Algorithms for Hybrid Precoding in Millimeter Wave MIMO Systems (2016, methodology): “Equipped with the tangent space, Riemannian gradient and retraction of the complex circle manifold Mcc, a line search based conjugate gradient method [46], which is a classical algorithm in the Euclidean space, can be developed to design the analog precoder as shown in Algorithm 1.”
Weighted Sum-Rate Maximization for Reconfigurable Intelligent Surface Aided Wireless Networks (2019, methodology): “Thus, the stationary solution of P(C) can be obtained via the Riemannian conjugate gradient (RCG) algorithm [48], which has been widely applied for the analog precoder design in hybrid precoding problem [27] and has also shown good performance in the single-user RIS-aided MISO system [49].”
Generalized BackPropagation, Étude De Cas: Orthogonality (2016, background): “The take home message from Mishra et al. (2014) is that the Euclidean geometry is not the right choice for addressing such decompositions (see for example Fig.7 in Mishra et al. (2014)), which makes our contribution theoretically more appealing.”
SE-Sync: A certifiably correct algorithm for synchronization over the special Euclidean group (2016, methodology): “We use a MATLAB implementation of SE-Sync that takes advantage of the truncated-Newton RTR [1] method supplied by Manopt [7].”