Prototype learning and collaborative representation using Grassmann manifolds for image set classification

Dong, Wei; Shen, Xiaobo; Sun, Quansen; Gao, Xizhan; Yan, Wenzhu

doi:10.1016/j.patcog.2019.107123

Cited by 19 publications

(9 citation statements)

References 16 publications

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“…The propsoed approach is related to two previous works [53], [54]. In this part, we summarize some essential differences between our method and those introduced in [53] and [54] in the following two paragraphs.…”

Section: Relation With the Previous Workmentioning

confidence: 97%

“…Relation With [53]. In fact, both the proposed algorithm and [53] try to generalise the Euclidean collaborative representation to the Riemannian manifold-valued feature representations for the sake of improving the image set classification performnce on some challenging visual scenarions.…”

Section: Relation With the Previous Workmentioning

confidence: 99%

“…In fact, both the proposed algorithm and [53] try to generalise the Euclidean collaborative representation to the Riemannian manifold-valued feature representations for the sake of improving the image set classification performnce on some challenging visual scenarions. However, there exist some fundamental differences among them: 1) for feature representation, the propsoed approach is executed in the scenario of SPD manifiold, while [53] is carrried out in the context of Grassmann manifold; 2) based on the generated Grassmann manifold-valued features, [53] constructs the P +V model to encode the inter-class similarity information and the intra-class variational information of the data, while the propsoed approach does not consider this explicitly; 3) with the constructed P + V model, [53] implements the collaborative representation framework with prototype learning in the space spanned by a set of symmetric matrices. As a result, the dictionary learning problem could be converted into standard Euclidean problem.…”

Section: Relation With the Previous Workmentioning

confidence: 99%

See 2 more Smart Citations

Collaborative Representation for SPD Matrices with Application to Image-Set Classification

Chu¹,

Wang²,

Wu³

2022

Preprint

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Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear variational information directly. Recent advances illustrate that how to effectively model these nonlinear variational information and learn invariant representations is an open challenge in the community of computer vision and pattern recognition To this end, we try to design a new algorithm to handle this problem. Firstly, the second-order statistic, i.e., covariance matrix is applied to model the original image sets. Due to the space formed by a set of nonsingular covariance matrices is a wellknown Symmetric Positive Definite (SPD) manifold, generalising the Euclidean collaborative representation to the SPD manifold is not an easy task. Then, we devise two strategies to cope with this issue. One attempts to embed the SPD manifoldvalued data representations into an associated tangent space via the matrix logarithm map. Another is to embed them into a Reproducing Kernel Hilbert Space (RKHS) by utilizing the Riemannian kernel function. After these two treatments, CRC is applicable to the SPD manifold-valued features. The evaluations on four banchmarking datasets justify its effectiveness.

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Section: Relation With the Previous Workmentioning

confidence: 97%

Section: Relation With the Previous Workmentioning

confidence: 99%

Section: Relation With the Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

Collaborative Representation for SPD Matrices with Application to Image-Set Classification

Chu¹,

Wang²,

Wu³

2022

Preprint

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“…As an efficient and useful extension to SRC, CRC has demonstrated its ability to generate both discriminative and collaborative representations 3 . Since then, it has been extended in various ways and applied to many pattern recognition tasks, including face recognition, 6‐9 image classification, 10‐14 disease or fault diagnosis, 15‐18 object tracking, 19,20 audio classification, 21 and so on.…”

Section: Introductionmentioning

confidence: 99%

Class mean‐weighted discriminative collaborative representation for classification

Gou

Song

et al. 2021

Int J Intell Syst

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Representation-based classification (RBC) has been attracting a great deal of attention in pattern recognition. As a typical extension to RBC, collaborative representation-based classification (CRC) has demonstrated its superior performance in various image classification tasks. Ideally, we expect that the learned class-specific representations for a testing sample are discriminative, and the representation computed for the true class dominates the final representation of the testing sample. Most existing CRC-based methods can learn pattern discrimination, but cannot differentiate the contribution of class-specific representations to the classification of each testing sample. It is challenging for a representation-based classifier to retain both properties. To address this challenge and further improve CRC's classification performance, we propose a novel CRC-based method, class mean-weighted discriminative collaborative representation-based classifier (CMW-DCRC). Its objective function penalises the standard l 2 -norm residuals with two discriminative regularisation terms. A decorrelating term makes the class-specific representations more discriminative, and a newly designed class meanweighted term that promotes the training samples from individual classes to competitively reconstruct the testing sample while boosting the contribution of the true class. To further enhance the robustness of CRC, we extend CMW-DCRC by replacing the l 2 -norm coding residual with a l 1 -norm coding residual, and solve the optimisation problem with an iteratively reweighted least square algorithm. Extensive experimental results on nine image data sets have shown that our methods outperform the state-of-the-art RBC-based methods.

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“…Image classification using non-Euclidean manifolds such as a Grassmann manifold and the Symmetric Positive Definite (SPD) manifold [41] is becoming increasingly more attractive. The weights of the iterative manifold embedding (IME) layer are learned by unsupervised strategy, which has been used to analyze the intrinsic manifolds of data sets with missing data [42].…”

Section: Introductionmentioning

confidence: 99%

Classification of Infrared Objects in Manifold Space Using Kullback-Leibler Divergence of Gaussian Distributions of Image Points

Zhu

Lou

et al. 2020

Symmetry

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Infrared image recognition technology can work day and night and has a long detection distance. However, the infrared objects have less prior information and external factors in the real-world environment easily interfere with them. Therefore, infrared object classification is a very challenging research area. Manifold learning can be used to improve the classification accuracy of infrared images in the manifold space. In this article, we propose a novel manifold learning algorithm for infrared object detection and classification. First, a manifold space is constructed with each pixel of the infrared object image as a dimension. Infrared images are represented as data points in this constructed manifold space. Next, we simulate the probability distribution information of infrared data points with the Gaussian distribution in the manifold space. Then, based on the Gaussian distribution information in the manifold space, the distribution characteristics of the data points of the infrared image in the low-dimensional space are derived. The proposed algorithm uses the Kullback-Leibler (KL) divergence to minimize the loss function between two symmetrical distributions, and finally completes the classification in the low-dimensional manifold space. The efficiency of the algorithm is validated on two public infrared image data sets. The experiments show that the proposed method has a 97.46% classification accuracy and competitive speed in regards to the analyzed data sets.

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Prototype learning and collaborative representation using Grassmann manifolds for image set classification

Cited by 19 publications

References 16 publications

Collaborative Representation for SPD Matrices with Application to Image-Set Classification

Collaborative Representation for SPD Matrices with Application to Image-Set Classification

Class mean‐weighted discriminative collaborative representation for classification

Classification of Infrared Objects in Manifold Space Using Kullback-Leibler Divergence of Gaussian Distributions of Image Points

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