نتایج جستجو برای: frobenius norm

تعداد نتایج: 48366  

Journal: :Journal of Optimization Theory and Applications 2021

Low-rank inducing unitarily invariant norms have been introduced to convexify problems with low-rank/sparsity constraint. They are the convex envelope of a unitary norm and indicator function an upper bounding rank The most well-known member this family is so-called nuclear norm. To solve optimization involving such proximal splitting methods, efficient ways evaluating mapping low-rank needed. ...

Journal: :CoRR 2016
Duy Khuong Nguyen Tu Bao Ho

Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence (NMF-KL) is one of the most significant NMF problems and equivalent to Probabilistic Latent Semantic Indexing (PLSI), which has been successfully applied in many applications. For sparse count data, a Poisson distribution and KL divergence provide sparse models and sparse representation, which describe the random variation ...

2017
Prachi Chaudhary Pawan Kumar Dahiya

This paper discusses the existing optimization techniques and then Genetic Algorithm has been applied as optimization technique in order to enhance the response. Surface Acoustic Wave Filters are particular Band Pass Filters which are currently used in electronic equipments for qualitative communication. Developers of SAW Filters have faced challenges that arise from design complications, limit...

Journal: :CoRR 2017
Cyprien Gilet Marie Deprez Jean-Baptiste Caillau Michel Barlaud

This paper deals with unsupervised clustering with feature selection. The problem is to estimate both labels and a sparse projection matrix of weights. To address this combinatorial non-convex problem maintaining a strict control on the sparsity of the matrix of weights, we propose an alternating minimization of the Frobenius norm criterion. We provide a new efficient algorithm named K-sparse w...

2012
MARTIN J. WAINWRIGHT

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix with a second matrix endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including factor...

2014
Alex Beutel Partha Pratim Talukdar Abhimanu Kumar Christos Faloutsos Evangelos E. Papalexakis Eric P. Xing

Given multiple data sets of relational data that share a number of dimensions, how can we efficiently decompose our data into the latent factors? Factorization of a single matrix or tensor has attracted much attention, as, e.g., in the Netflix challenge, with users rating movies. However, we often have additional, side, information, like, e.g., demographic data about the users, in the Netflix e...

Journal: :CoRR 2017
Zeng Yu Tianrui Li Ning Yu Yi Pan Hongmei Chen Bing Liu

This paper aims to develop a new and robust approach to feature representation. Motivated by the success of AutoEncoders, we first theoretical summarize the general properties of all algorithms that are based on traditional Auto-Encoders: 1) The reconstruction error of the input or corrupted input can not be lower than a lower bound, which can be viewed as a guiding principle for reconstructing...

2015
Gregory S. Chirikjian

In a flurry of articles in the mid to late 1990s, various metrics for the group of rigid-body motions, SE(3), were introduced for measuring distance between any two reference frames or rigid-body motions. During this time, it was shown that one can choose a smooth distance function that is invariant under either all left shifts or all right shifts, but not both. For example, if one defines the ...

Journal: :Numerical Linear Algebra With Applications 2021

Abstract In this article, we find necessary and sufficient conditions to identify pairs of matrices X Y for which there exists such that is positive semidefinite . Such a called dissipative mapping taking We also provide two different characterizations the set all mappings, use them characterize unique with minimal Frobenius norm. The minimal‐norm then used determine distance asymptotic instabi...

2011
Alekh Agarwal Sahand Negahban Martin J. Wainwright

We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation X of the sum of an (approximately) low rank matrix Θ⋆ with a second matrix Γ⋆ endowed with a complementary form of low-dimensional structure; this set-up includes many statistical models of interest, including ...

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