Discriminative Graph Embedding Research Articles

A New Low-Rank Structurally Incoherent Algorithm for Robust Image Feature Extraction

In order to solve the problem in which structurally incoherent low-rank non-negative matrix decomposition (SILR-NMF) algorithms only consider the non-negativity of the data and do not consider the manifold distribution of high-dimensional space data, a new structurally incoherent low rank two-dimensional local discriminant graph embedding (SILR-2DLDGE) is proposed in this paper. The algorithm consists of the following three parts. Firstly, it is vital to keep the intrinsic relationship between data points. By the token, we introduced the graph embedding (GE) framework to preserve locality information. Secondly, the algorithm alleviates the impact of noise and corruption uses the L1 norm as a constraint by low-rank learning. Finally, the algorithm improves the discriminant ability by encrypting the structurally incoherent parts of the data. In the meantime, we capture the theoretical basis of the algorithm and analyze the computational cost and convergence. The experimental results and discussions on several image databases show that the proposed algorithm is more effective than the SILR-NMF algorithm.

Low-rank 2D local discriminant graph embedding for robust image feature extraction

As a popular feature extraction algorithm, the 2D local preserving projections (2DLPP) algorithm has been successfully applied in many fields. Using 2D image representation, the 2DLPP algorithm preserves the manifold attributes and retains the local information of high-dimensional space data. However, the 2DLPP algorithm may encounter some problems in real-world applications, such as a lack of discriminatory ability, singularity problems, and sensitivity to occlusion and noise in data. Therefore, this paper introduces low-rank into the 2DLPP algorithm and proposes a new feature extraction algorithm, which is the low-rank two-dimensional local discriminant graph embedding (LR-2DLDGE), to solve these problems. To improve the LR-2DLDGE algorithm robustness, we fuse the discriminant information in graph embedding and the low-rank properties of the data. The algorithm has three advantages: First, the algorithm uses a graph embedding (GE) framework to maintain the local neighbourhood discrimination information between data. Second, the LR-2DLDGE algorithm ensures that the data points are as independent as possible from different classes in the feature space. Finally, the algorithm uses the L1-norm as a constraint and reduces the influence of noise and corruption through low-rank learning. The theoretical computational complexity and convergence of the algorithm are explicated and proved. Extensive experimental results on three occluded and noisy image datasets confirm the effectively and robustness of LR-2DLDGE, respectively.

Uncorrelated discriminant graph embedding for fault classification

AbstractRecently, graph embedding methods have been successfully used in process monitoring. To improve the discriminant power, a novel supervised graph embedding method, called uncorrelated discriminant graph embedding (UDGE), is proposed. Different from the unsupervised design of locality preserving projection (LPP), UDGE utilizes both the local geometrical structure and label information to construct the similarity between different data points. The “local geometrical structure” means that each data point can be represented as a combination of its neighbours. Due to add the uncorrelated constraint, the extracted features of UDGE are statistically uncorrelated. Uncorrelated attributes are essential for dimension reduction since they contain minimum redundancy. The application of UDGE is evaluated on the Tennessee Eastman process (TEP) benchmark. Experimental results show UDGE can better separate different types of faults and provide more promising fault diagnosis performance. The code of UDGE is released in https://github.com/htz-ecust/Uncorrelated-Discriminant-Graph-Embedding-for-Fault-Classification.

Toward Efficient Image Representation: Sparse Concept Discriminant Matrix Factorization

The key ingredients of matrix factorization lie in basic learning and coefficient representation. To enhance the discriminant ability of the learned basis, discriminant graph embedding is usually introduced in the matrix factorization model. However, the existing matrix factorization methods based on graph embedding generally conduct discriminant analysis via a single type of adjacency graph, either similarity-based graphs (e.g., Laplacian eigenmaps graph) or reconstruction-based graphs (e.g., ${L}_{1}$ -graph), while ignoring the cooperation of the different types of adjacency graphs that can better depict the discriminant structure of original data. To address the above issue, we propose a novel Fisher-like criterion, based on graph embedding, to extract sufficient discriminant information via two different types of adjacency graphs. One graph preserves the reconstruction relationships of neighboring samples in the same category, and the other suppresses the similarity relationships of neighboring samples from different categories. Moreover, we also leverage the sparse coding to promote the sparsity of the coefficients. By virtue of the proposed Fisher-like criterion and sparse coding, a new matrix factorization framework called Sparse concept Discriminant Matrix Factorization (SDMF) is proposed for efficient image representation. Furthermore, we extend the Fisher-like criterion to an unsupervised context, thus yielding an unsupervised version of SDMF. Experimental results on seven benchmark datasets demonstrate the effectiveness and efficiency of the proposed SDMFs on both image classification and clustering tasks.

Low-rank regularized tensor discriminant representation for image set classification

Although image set classification has attracted great attention in computer vision and pattern recognition communities, however, learning a compact and discriminative representation is still a challenge. In this paper, we present a novel tensor discriminant representation learning method to better solve the image classification task. Specifically, we first exploit the advantages of Grassmann manifold and tensor to model image sets as a high-order tensor. We then propose a transductive low-rank regularized tensor discriminant representation algorithm referred as LRRTDR to learn more intrinsic representations for image sets. Our proposed LRRTDR mainly contains two components: low-rank tensor embedding and discriminant graph embedding. The low-rank tensor embedding is to learn the lowest-rank representation from a low-dimensional subspace, which is spanned by a set of latent basis matrices. The discriminant graph embedding is to further enhance the discriminant ability of the learned representations under the graph embedding framework. To solve the optimization problem of LRRTDR, we develop an alternating direction scheme based on Iterative Shrinkage Thresholding Algorithm (ISTA). Experimental results on five publicly available datasets demonstrate that our proposed algorithm not only converges with few iterations, but also achieves better accuracy compared with state-of-the-art methods.

Tensor-driven low-rank discriminant analysis for image set classification

Classification based on image sets has recently attracted great interest in computer vision community. In this paper, we proposed a transductive Tensor-driven Low-rank Discriminant Analysis (TLRDA) model for image set classification, in which the tensor-driven low-rank approximation and the discriminant graph embedding are integrated to improve the representativeness of image sets. In addition, we develop an iterative shrinkage thresholding algorithm to better optimize the objective function of the proposed TLRDA. Experiments on seven publicly available datasets demonstrate that our proposed method is guaranteed to converge within a small number of iterations during the training procedure and obtains promising results compared with state-of-the-art methods.

Discriminative Graph Embedding for Label Propagation

In many applications, the available information is encoded in graph structures. This is a common problem in biological networks, social networks, web communities and document citations. We investigate the problem of classifying nodes' labels on a similarity graph given only a graph structure on the nodes. Conventional machine learning methods usually require data to reside in some Euclidean spaces or to have a kernel representation. Applying these methods to nodes on graphs would require embedding the graphs into these spaces. By embedding and then learning the nodes on graphs, most methods are either flexible with different learning objectives or efficient enough for large scale applications. We propose a method to embed a graph into a feature space for a discriminative purpose. Our idea is to include label information into the embedding process, making the space representation tailored to the task. We design embedding objective functions that the following learning formulations become spectral transforms. We then reformulate these spectral transforms into multiple kernel learning problems. Our method, while being tailored to the discriminative tasks, is efficient and can scale to massive data sets. We show the need of discriminative embedding on some simulations. Applying to biological network problems, our method is shown to outperform baselines.

Uncorrelated and discriminative graph embedding for face recognition

We present a novel feature extraction algorithm for face recognition called the uncorrelated and discriminative graph embedding (UDGE) algorithm, which incorporates graph embedding and local scaling method and obtains uncorrelated discriminative vectors in the projected subspace. An optimization objective function is herein defined to make the discriminative projections preserve the intrinsic neighborhood geometry of the within-class samples while enlarging the margins of between-class samples near to the class boundaries. UDGE efficiently dispenses with a prespecified parameter which is data-dependent to balance the objective of the within-class locality and the between-class locality in comparison with the linear extension of graph embedding in a face recognition scenario. Moreover, it can address the small sample-size problem, and its classification accuracy is not sensitive to neighbor samples size and weight value, as well. Extensive experiments on extended YaleB, CMU PIE, and Indian face databases demonstrate the effectiveness of UDGE.