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Found 10 papers, 4 papers with code
A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks.
Operator Splitting for Learning to Predict Equilibria in Convex Games
Systems of competing agents can often be modeled as games.
JFB: Jacobian-Free Backpropagation for Implicit Networks
Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences.
Distributed Low-rank Matrix Factorization With Exact Consensus
Low-rank matrix factorization is a problem of broad importance, owing to the ubiquity of low-rank models in machine learning contexts.
Provable Bregman-divergence based Methods for Nonconvex and Non-Lipschitz Problems
Therefore, this work not only develops guaranteed optimization methods for non-Lipschitz smooth problems but also solves an open problem of showing the second-order convergence guarantees for these alternating minimization methods.
Spherical Principal Component Analysis
However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis.
Dropping Symmetry for Fast Symmetric Nonnegative Matrix Factorization
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks.
Global Optimality in Distributed Low-rank Matrix Factorization
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization variables appear only locally at a single node in the network.
Optimized Structured Sparse Sensing Matrices for Compressive Sensing
We consider designing a robust structured sparse sensing matrix consisting of a sparse matrix with a few non-zero entries per row and a dense base matrix for capturing signals efficiently We design the robust structured sparse sensing matrix through minimizing the distance between the Gram matrix of the equivalent dictionary and the target Gram of matrix holding small mutual coherence.
Geometry of Factored Nuclear Norm Regularization
In spite of the nonconvexity of the factored formulation, we prove that when the convex loss function $f(X)$ is $(2r, 4r)$-restricted well-conditioned, each critical point of the factored problem either corresponds to the optimal solution $X^\star$ of the original convex optimization or is a strict saddle point where the Hessian matrix has a strictly negative eigenvalue.
