Overview of the atomic norm and examples of applications and implementations
Atomic norm overview
The atomic norm is a type of norm used in fields such as optimisation and signal ...
スパースモデリング
Overview of the Frank-Wolff method and examples of its application and implementation.
Overview of the Frank Wolff method
The Frank-Wolfe method is a numerical algorithm for solving non-linear optim...
Overview of the Frobenius norm and examples of algorithms and implementations
Overview of the Frobenius norm.
The Frobenius norm is a type of matrix norm and will be defined as the...
Overview of the trace norm and related algorithms and implementation examples
Trace norm overview
The trace norm (or nuclear norm) is a type of matrix norm, which can be defined as...
Overview of Group Regularization with Duplicates and Examples of Implementations
Overview
Overlapping group regularization (Overlapping Group Lasso) is a type of regularization method...
Robust Principal Component Analysis Overview and Implementation Examples
Robust Principal Component Analysis(RPCA)
Robust Principal Component Analysis (RPCA) is a method for finding a...
Overview of sparse modeling and its application and implementation
Sparse Modeling Overview
Sparse modeling is a technique that uses sparsity (sparse properties) in the ...
Protected: Mathematical Properties and Optimization of Sparse Machine Learning with Atomic Norm
Mathematical properties and optimization of sparse machine learning with atomic norm for digital transformation, artificial intelligence, and machine learning tasks L∞ norm, dual problem, robust principal component analysis, foreground image extraction, low-rank matrix, sparse matrix, Lagrange multipliers, auxiliary variables, augmented Lagrangian functions, indicator functions, spectral norm, robust principal component analysis, Frank-Wolfe method, alternating multiplier method in duals, L1 norm constrained squared regression problem, regularization parameter, empirical error, curvature parameter, atomic norm, prox operator, convex hull, norm equivalence, dual norm
Protected: Definition and Examples of Sparse Machine Learning with Atomic Norm
Definitions and examples in sparse machine learning with atomic norm used in digital transformation, artificial intelligence, and machine learning tasks nuclear norm of tensors, nuclear norm, higher-order tensor, trace norm, K-order tensor, atom set, dirty model, dirty model, multitask learning, unconstrained optimization problem, robust principal component analysis, L1 norm, group L1 norm, L1 error term, robust statistics, Frobenius norm, outlier estimation, group regularization with overlap, sum of atom sets, element-wise sparsity of vectors, groupwise sparsity of group-wise sparsity, matrix low-rankness
Protected: Sparse Machine Learning with Overlapping Sparse Regularization
Sparse machine learning with overlapping sparse regularization for digital transformation, artificial intelligence, and machine learning tasks main problem, dual problem, relative dual gap, dual norm, Moreau's theorem, extended Lagrangian, alternating multiplier method, stopping conditions, groups with overlapping L1 norm, extended Lagrangian, prox operator, Lagrangian multiplier vector, linear constraints, alternating direction multiplier method, constrained minimization problem, multiple linear ranks of tensors, convex relaxation, overlapping trace norm, substitution matrix, regularization method, auxiliary variables, elastic net regularization, penalty terms, Tucker decomposition Higher-order singular value decomposition, factor matrix decomposition, singular value decomposition, wavelet transform, total variation, noise division, compressed sensing, anisotropic total variation, tensor decomposition, elastic net