Journal ArticleDOI
Non-Negative Patch Alignment Framework
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TLDR
A fast gradient descent (FGD) is proposed to overcome the problem of slow multiplicative update rule in NPAF and uses the Newton method to search the optimal step size, and thus converges faster than MUR.Abstract:
In this paper, we present a non-negative patch alignment framework (NPAF) to unify popular non-negative matrix factorization (NMF) related dimension reduction algorithms. It offers a new viewpoint to better understand the common property of different NMF algorithms. Although multiplicative update rule (MUR) can solve NPAF and is easy to implement, it converges slowly. Thus, we propose a fast gradient descent (FGD) to overcome the aforementioned problem. FGD uses the Newton method to search the optimal step size, and thus converges faster than MUR. Experiments on synthetic and real-world datasets confirm the efficiency of FGD compared with MUR for optimizing NPAF. Based on NPAF, we develop non-negative discriminative locality alignment (NDLA). Experiments on face image and handwritten datasets suggest the effectiveness of NDLA in classification tasks and its robustness to image occlusions, compared with representative NMF-related dimension reduction algorithms.read more
Citations
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3-D Object Retrieval and Recognition With Hypergraph Analysis
TL;DR: A hypergraph analysis approach to address the problem of view-based 3-D object retrieval and recognition by avoiding the estimation of the distance between objects by constructing multiple hypergraphs based on their 2-D views.
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Single Image Super-Resolution With Non-Local Means and Steering Kernel Regression
TL;DR: Thorough experimental results suggest that the proposed SR method can reconstruct higher quality results both quantitatively and perceptually and propose a maximum a posteriori probability framework for SR recovery.
Journal ArticleDOI
NeNMF: An Optimal Gradient Method for Nonnegative Matrix Factorization
TL;DR: A new efficient NeNMF solver is presented that applies Nesterov's optimal gradient method to alternatively optimize one factor with another fixed and can be used to solve -norm, -norm and manifold regularized NMF with the optimal convergence rate.
Journal ArticleDOI
Online Nonnegative Matrix Factorization With Robust Stochastic Approximation
TL;DR: An efficient online RSA-NMF algorithm that learns NMF in an incremental fashion and outperforms the existing online NMF (ONMF) algorithms in terms of efficiency and proves that OR- NMF almost surely converges to a local optimal solution by using the quasi-martingale.
Journal ArticleDOI
Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding
TL;DR: This paper provides an efficient EMR-SLRA optimization procedure to obtain the output feature embedding and experiments on the pattern recognition applications confirm the effectiveness of the EMR -SLRA algorithm compare with some other multiview feature dimensionality reduction approaches.
References
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Gradient-based learning applied to document recognition
Yann LeCun,Léon Bottou,Léon Bottou,Yoshua Bengio,Yoshua Bengio,Yoshua Bengio,Patrick Haffner +6 more
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
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Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Journal ArticleDOI
Nonlinear dimensionality reduction by locally linear embedding.
Sam T. Roweis,Lawrence K. Saul +1 more
TL;DR: Locally linear embedding (LLE) is introduced, an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs that learns the global structure of nonlinear manifolds.
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A global geometric framework for nonlinear dimensionality reduction.
TL;DR: An approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set and efficiently computes a globally optimal solution, and is guaranteed to converge asymptotically to the true structure.
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