Kernel Low-Rank Representation for face recognition

Nguyen, Hoang-Vu; Yang, Wankou; Shen, Fumin; Sun, Changyin

doi:10.1016/j.neucom.2014.12.051

Cited by 42 publications

(14 citation statements)

References 52 publications

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“…To make the low-rank model effectively deal with the nonlinear structure of data, [11] proposed the kernel low-rank representation (KLRR) graph for semisupervised classification by using kernel trick. As a nonlinear extension of LRR, KLRR also showed excellent performance in face recognition [21].…”

Section: Introductionmentioning

confidence: 99%

Manifold Adaptive Kernelized Low-Rank Representation for Semisupervised Image Classification

et al. 2018

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Constructing a powerful graph that can effectively depict the intrinsic connection of data points is the critical step to make the graph-based semisupervised learning algorithms achieve promising performance. Among popular graph construction algorithms, low-rank representation (LRR) is a very competitive one that can simultaneously explore the global structure of data and recover the data from noisy environments. Therefore, the learned low-rank coefficient matrix in LRR can be used to construct the data affinity matrix. Consider the existing problems such as the following: (1) the essentially linear property of LRR makes it not appropriate to process the possible nonlinear structure of data and (2) learning performance can be greatly enhanced by exploring the structure information of data; we propose a new manifold kernelized low-rank representation (MKLRR) model that can perform LRR in the data manifold adaptive kernel space. Specifically, the manifold structure can be incorporated into the kernel space by using graph Laplacian and thus the underlying geometry of data is reflected by the wrapped kernel space. Experimental results of semisupervised image classification tasks show the effectiveness of MKLRR. For example, MKLRR can, respectively, obtain 96.13%, 98.09%, and 96.08% accuracies on ORL, Extended Yale B, and PIE data sets when given 5, 20, and 20 labeled face images per subject.

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Section: Introductionmentioning

confidence: 99%

Manifold Adaptive Kernelized Low-Rank Representation for Semisupervised Image Classification

et al. 2018

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“…For any two points x and x , we use a kernel function (x , x ) = ⟨Φ(x ), Φ(x )⟩ to map the data into a kernel feature space. Some commonly used kernels are including the Gaussian radial basis function (RBF) kernel (x, y) = exp(−‖x − y‖ 2 / 2 ), polynomial kernel (x, y) = ( + ⟨x, y⟩) , and sigmoid kernel (x, y) = tanh(⟨x, y⟩ + ) [2,31].…”

Section: Kernel Sdamentioning

confidence: 99%

Low-Rank Kernel-Based Semisupervised Discriminant Analysis

Xia

Shui-dong

et al. 2016

Applied Computational Intelligence and Soft Computing

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Semisupervised Discriminant Analysis (SDA) aims at dimensionality reduction with both limited labeled data and copious unlabeled data, but it may fail to discover the intrinsic geometry structure when the data manifold is highly nonlinear. The kernel trick is widely used to map the original nonlinearly separable problem to an intrinsically larger dimensionality space where the classes are linearly separable. Inspired by low-rank representation (LLR), we proposed a novel kernel SDA method called low-rank kernel-based SDA (LRKSDA) algorithm where the LRR is used as the kernel representation. Since LRR can capture the global data structures and get the lowest rank representation in a parameter-free way, the low-rank kernel method is extremely effective and robust for kinds of data. Extensive experiments on public databases show that the proposed LRKSDA dimensionality reduction algorithm can achieve better performance than other related kernel SDA methods.

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“…By applying the dimensionality reduction to F , (9) can be modified as follows:

\min_{c} ∥ P^{T} ϕ ()(, x) - P^{T} Φ_{B} bold-italicc ∥^{2} + λ_{1} ∥ double-struckd ⊙ bold-italicc ∥^{2} + λ_{2} ∥ bold-italicc ∥_{l^{0}}

where

bold-italicP = falsefalse{p_{1}, p_{2}, \dots, p_{s} falsefalse} \in R^{D \times s}

is the transformation matrix of F . As mentioned in [39], the transformation matrix is related to the images such that dot products of images can be replaced by the kernel. By applying the representation of the transformation matrix in a kernel‐based dimensionality reduction method in KPCA, the projection vector is a linear combination of images in F , as follows:

p_{i} = \sum_{j = 1}^{m} α_{i j} ϕ false(b_{j} false)

where α i = [ α i 1 , α i 2 , …, α in ] T is called the pseudo‐transformation vector corresponding to the j th transformation vector.…”

Section: Kernel Locality‐constrained Sparse Codingmentioning

confidence: 99%

Kernel locality‐constrained sparse coding for head pose estimation

Kim

Sohn

Kim

et al. 2016

IET Computer Vision

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In many situations, it would be practical for a computer system user interface to have a model of where a person is looking and what the user is paying attention to. In this study, the authors describe a novel feature coding method for head pose estimation. The widely‐used sparse coding (SC) method encodes a test sample using a sparse linear combination of training samples. However, it does not consider the underlying structure of the data in the feature space. In contrast, locality‐constrained linear coding (LLC) utilises locality constraints to project each input data into its local‐coordinate system. Based on the recent success of LLC, the authors introduce locality‐constrained sparse coding (LSC) to overcome the limitation of Sparse Coding. The authors also propose kernel locality‐constrained sparse coding, which is a non‐linear extension of LSC. By using kernel tricks, the authors implicitly map the input data into the kernel feature space associated with the kernel function. In experiments, the proposed algorithm was applied to a head pose estimation application. Experimental results demonstrated the increased effectiveness and robustness of the method.

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Kernel Low-Rank Representation for face recognition

Cited by 42 publications

References 52 publications

Manifold Adaptive Kernelized Low-Rank Representation for Semisupervised Image Classification

Manifold Adaptive Kernelized Low-Rank Representation for Semisupervised Image Classification

Low-Rank Kernel-Based Semisupervised Discriminant Analysis

Kernel locality‐constrained sparse coding for head pose estimation

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