The Experts below are selected from a list of 34245 Experts worldwide ranked by ideXlab platform
Jiawei Han - One of the best experts on this subject based on the ideXlab platform.
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on Trivial Solution and scale transfer problems in graph regularized nmf
International Joint Conference on Artificial Intelligence, 2011Co-Authors: Chris Ding, Jiawei HanAbstract:Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from Trivial Solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized non-negative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and coclustering on benchmark text data sets demonstrate that the proposed models outperform the original models as well as many other state-of-the-art clustering methods.
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IJCAI - On Trivial Solution and scale transfer problems in graph regularized NMF
2011Co-Authors: Chris Ding, Jiawei HanAbstract:Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from Trivial Solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized non-negative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and coclustering on benchmark text data sets demonstrate that the proposed models outperform the original models as well as many other state-of-the-art clustering methods.
Chris Ding - One of the best experts on this subject based on the ideXlab platform.
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on Trivial Solution and scale transfer problems in graph regularized nmf
International Joint Conference on Artificial Intelligence, 2011Co-Authors: Chris Ding, Jiawei HanAbstract:Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from Trivial Solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized non-negative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and coclustering on benchmark text data sets demonstrate that the proposed models outperform the original models as well as many other state-of-the-art clustering methods.
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IJCAI - On Trivial Solution and scale transfer problems in graph regularized NMF
2011Co-Authors: Chris Ding, Jiawei HanAbstract:Combining graph regularization with nonnegative matrix (tri-)factorization (NMF) has shown great performance improvement compared with traditional nonnegative matrix (tri-)factorization models due to its ability to utilize the geometric structure of the documents and words. In this paper, we show that these models are not well-defined and suffering from Trivial Solution and scale transfer problems. In order to solve these common problems, we propose two models for graph regularized non-negative matrix (tri-)factorization, which can be applied for document clustering and co-clustering respectively. In the proposed models, a Normalized Cut-like constraint is imposed on the cluster assignment matrix to make the optimization problem well-defined. We derive a multiplicative updating algorithm for the proposed models, and prove its convergence. Experiments of clustering and coclustering on benchmark text data sets demonstrate that the proposed models outperform the original models as well as many other state-of-the-art clustering methods.
Taoufik Hmidi - One of the best experts on this subject based on the ideXlab platform.
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On the V-states for the Generalized Quasi-Geostrophic Equations
Communications in Mathematical Physics, 2015Co-Authors: Zineb Hassainia, Taoufik HmidiAbstract:We prove the existence of the V-states for the generalized inviscid SQG equations with $\alpha\in ]0,1[.$ These structures are special rotating simply connected patches with $m-$ fold symmetry bifurcating from the Trivial Solution at some explicit values of the angular velocity. This produces, inter alia, an infinite family of non stationary global Solutions with uniqueness.
Ferenc Hartung - One of the best experts on this subject based on the ideXlab platform.
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Linearized stability for a class of neutral functional differential equations with state-dependent delays
Nonlinear Analysis: Theory Methods & Applications, 2008Co-Authors: Ferenc HartungAbstract:Abstract In this paper we formulate a stability theorem by means of linearization around a Trivial Solution in the case of autonomous neutral functional differential equations with state-dependent delays. We prove that if the Trivial Solution of the linearized equation is exponentially stable, then the Trivial Solution of the nonlinear equation is exponentially stable as well. As an application of the main result, explicit stability conditions are given.
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Exponential stability of a state-dependent delay system
Discrete & Continuous Dynamical Systems - A, 2007Co-Authors: István Györi, Ferenc HartungAbstract:In this paper we study exponential stability of the Trivial Solution of the state-dependent delay system $\dot x(t)=\sum_{i=1}^m A_{i}(t)x(t-\tau_{i}(t,x_t))$. We show that under mild assumptions, the Trivial Solution of the state-dependent system is exponentially stable if and only if the Trivial Solution of the corresponding linear time-dependent delay system $\dot y(t)=\sum_{i=1}^m A_{i}(t)y(t-\tau_{i}(t, 0))$ is exponentially stable. We also compare the order of the exponential stability of the nonlinear equation to that of its linearized equation. We show that in some cases, the two orders are equal. As an application of our main result, we formulate a necessary and sufficient condition for the exponential stability of the Trivial Solution of a threshold-type delay system.
Oscar Jarrín - One of the best experts on this subject based on the ideXlab platform.
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A short note on the uniqueness of the Trivial Solution for the steady-state Navier-Stokes equations
arXiv: Analysis of PDEs, 2019Co-Authors: Oscar JarrínAbstract:In this note, we extend some previous results given in [3] which deal to sufficient conditions to prove the uniqueness of the Trivial Solution for the 3D steady-state Navier-Stokes equations. This results are also known as a Liouville-type results for the stationary Navier-Stokes.
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Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces
2018Co-Authors: Diego Chamorro, Oscar Jarrín, Pierre-gilles Lemarié-rieussetAbstract:Uniqueness of Leray Solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations and under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the Trivial Solution U = 0 is the unique Solution. This type of results are known as Liouville theorems.
