Adaptive hypergraph learning and its application in image classification

GRESS: Grouping Belief-Based Deep Contrastive Subspace Clustering

The self-expressive coefficient plays a crucial role in the self-expressiveness-based subspace clustering method. To enhance the precision of the self-expressive coefficient, we propose a novel deep subspace clustering method, named grouping belief-based deep contrastive subspace clustering (GRESS), which integrates the clustering information and higher-order relationship into the coefficient matrix. Specifically, we develop a deep contrastive subspace clustering module to enhance the learning of both self-expressive coefficients and cluster representations simultaneously. This approach enables the derivation of relatively noiseless self-expressive similarities and cluster-based similarities. To enable interaction between these two types of similarities, we propose a unique grouping belief-based affinity refinement module. This module leverages grouping belief to uncover the higher-order relationships within the similarity matrix, and integrates the well-designed noisy similarity suppression and similarity increment regularization to eliminate redundant connections while complete absent information. Extensive experimental results on four benchmark datasets validate the superiority of our proposed method GRESS over several state-of-the-art methods.

Dynamic Graph Regularized Broad Learning With Marginal Fisher Representation for Noisy Data Classification

Broad learning system (BLS) is an effective neural network requiring no deep architecture, however it is somehow fragile to noisy data. The previous robust broad models directly map features from the raw data, which inevitably learn useless or even harmful features for data representation when the inputs are corrupted by noise and outliers. To address this concern, a discriminative and robust network named as dynamic graph regularized broad learning (DGBL) with marginal fisher representation is proposed for noisy data classification. Different from the previous works, DGBL eliminates the effect of noise before the random feature mapping by the proposed robust and dynamic marginal fisher analysis (RDMFA) algorithm. The RDMFA is able to extract more robust and informative representations for classification from the latent clean data space with dynamically generated graphs. Furthermore, the dynamic graphs learned from RDMFA are incorporated as regularization terms into the objective of DGBL to enhance the discrimination capacity of the proposed network. Extensive quantitative and qualitative experiments conducted on numerous benchmark datasets demonstrate the superiority of the proposed model compared to several state-of-the-art methods.

Multichannel Image Completion With Mixture Noise: Adaptive Sparse Low-Rank Tensor Subspace Meets Nonlocal Self-Similarity

Multichannel image completion with mixture noise is a common but complex problem in the fields of machine learning, image processing, and computer vision. Most existing algorithms devote to explore global low-rank information and fail to optimize local and joint-mode structures, which may lead to oversmooth restoration results or lower quality restoration details. In this study, we propose a novel model to deal with multichannel image completion with mixture noise based on adaptive sparse low-rank tensor subspace and nonlocal self-similarity (ASLTS-NS). In the proposed model, a nonlocal similar patch matching framework cooperating with Tucker decomposition is used to explore information of global and joint modes and optimize the local structure for improving restoration quality. In order to enhance the robustness of low-rank decomposition to data missing and mixture noise, we present an adaptive sparse low-rank regularization to construct robust tensor subspace for self-weighing importance of different modes and capturing a stable inherent structure. In addition, joint tensor Frobenius and l1 regularizations are exploited to control two different types of noise. Based on alternating directions method of multipliers (ADMM), a convergent learning algorithm is designed to solve this model. Experimental results on three different types of multichannel image sets demonstrate the advantages of ASLTS-NS under five complex scenarios.

EEG Signal Epilepsy Detection With a Weighted Neighbor Graph Representation and Two-Stream Graph-Based Framework

Epilepsy is one of the most common neurological diseases. Clinically, epileptic seizure detection is usually performed by analyzing electroencephalography (EEG) signals. At present, deep learning models have been widely used for single-channel EEG signal epilepsy detection, but this method is difficult to explain the classification results. Researchers have attempted to solve interpretive problems by combining graph representation of EEG signals with graph neural network models. Recently, the combination of graph representations and graph neural network (GNN) models has been increasingly applied to single-channel epilepsy detection. By this methodology, the raw EEG signal is transformed to its graph representation, and a GNN model is used to learn latent features and classify whether the data indicates an epileptic seizure episode. However, existing methods are faced with two major challenges. First, existing graph representations tend to have high time complexity as they generally require each vertex to traverse all other vertices to construct a graph structure. Some of them also have high space complexity for being dense. Second, while separate graph representations can be derived from a single-channel EEG signal in both time and frequency domains, existing GNN models for epilepsy detection can learn from a single graph representation, which makes it hard to let the information from the two domains complement each other. For addressing these challenges, we propose a Weighted Neighbour Graph (WNG) representation for EEG signals. Reducing the redundant edges of the existing graph, WNG can be both time and space-efficient, and as informative as its less efficient counterparts. We then propose a two-stream graph-based framework to simultaneously learn features from WNG in both time and frequency domain. Extensive experiments demonstrate the effectiveness and efficiency of the proposed methods.

Facial expression recognition on partially occluded faces using component based ensemble stacked CNN

Facial Expression Recognition (FER) is the basis for many applications including human-computer interaction and surveillance. While developing such applications, it is imperative to understand human emotions for better interaction with machines. Among many FER models developed so far, Ensemble Stacked Convolution Neural Networks (ES-CNN) showed an empirical impact in improving the performance of FER on static images. However, the existing ES-CNN based FER models trained with features extracted from the entire face, are unable to address the issues of ambient parameters such as pose, illumination, occlusions. To mitigate the problem of reduced performance of ES-CNN on partially occluded faces, a Component based ES-CNN (CES-CNN) is proposed. CES-CNN applies ES-CNN on action units of individual face components such as eyes, eyebrows, nose, cheek, mouth, and glabella as one subnet of the network. Max-Voting based ensemble classifier is used to ensemble the decisions of the subnets in order to obtain the optimized recognition accuracy. The proposed CES-CNN is validated by conducting experiments on benchmark datasets and the performance is compared with the state-of-the-art models. It is observed from the experimental results that the proposed model has a significant enhancement in the recognition accuracy compared to the existing models.

Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

The critical node detection problem in hypergraphs using weighted node degree centrality

Network analysis is an indispensable part of today's academic field. Among the different types of networks, the more complex hypergraphs can provide an excellent challenge and new angles for analysis. This study proposes a variant of the critical node detection problem for hypergraphs using weighted node degree centrality as a form of importance metric. An analysis is done on both generated synthetic networks and real-world derived data on the topic of United States House and Senate committees, using a newly designed algorithm. The numerical results show that the combination of the critical node detection on hypergraphs with the weighted node degree centrality provides promising results and the topic is worth exploring further.

Cost-Sensitive Hypergraph Learning With F-Measure Optimization

The imbalanced issue among data is common in many machine-learning applications, where samples from one or more classes are rare. To address this issue, many imbalanced machine-learning methods have been proposed. Most of these methods rely on cost-sensitive learning. However, we note that it is infeasible to determine the precise cost values even with great domain knowledge for those cost-sensitive machine-learning methods. So in this method, due to the superiority of F-measure on evaluating the performance of imbalanced data classification, we employ F-measure to calculate the cost information and propose a cost-sensitive hypergraph learning method with F-measure optimization to solve the imbalanced issue. In this method, we employ the hypergraph structure to explore the high-order relationships among the imbalanced data. Based on the constructed hypergraph structure, we optimize the cost value with F-measure and further conduct cost-sensitive hypergraph learning with the optimized cost information. The comprehensive experiments validate the effectiveness of the proposed method.

Self-Supervised Graph Learning With Hyperbolic Embedding for Temporal Health Event Prediction

Electronic health records (EHRs) have been heavily used in modern healthcare systems for recording patients' admission information to health facilities. Many data-driven approaches employ temporal features in EHR for predicting specific diseases, readmission times, and diagnoses of patients. However, most existing predictive models cannot fully utilize EHR data, due to an inherent lack of labels in supervised training for some temporal events. Moreover, it is hard for the existing methods to simultaneously provide generic and personalized interpretability. To address these challenges, we propose Sherbet, a self-supervised graph learning framework with hyperbolic embeddings for temporal health event prediction. We first propose a hyperbolic embedding method with information flow to pretrain medical code representations in a hierarchical structure. We incorporate these pretrained representations into a graph neural network (GNN) to detect disease complications and design a multilevel attention method to compute the contributions of particular diseases and admissions, thus enhancing personalized interpretability. We present a new hierarchy-enhanced historical prediction proxy task in our self-supervised learning framework to fully utilize EHR data and exploit medical domain knowledge. We conduct a comprehensive set of experiments on widely used publicly available EHR datasets to verify the effectiveness of our model. Our results demonstrate the proposed model's strengths in both predictive tasks and interpretable abilities.

Generative hypergraph models and spectral embedding

Many complex systems involve interactions between more than two agents. Hypergraphs capture these higher-order interactions through hyperedges that may link more than two nodes. We consider the problem of embedding a hypergraph into low-dimensional Euclidean space so that most interactions are short-range. This embedding is relevant to many follow-on tasks, such as node reordering, clustering, and visualization. We focus on two spectral embedding algorithms customized to hypergraphs which recover linear and periodic structures respectively. In the periodic case, nodes are positioned on the unit circle. We show that the two spectral hypergraph embedding algorithms are associated with a new class of generative hypergraph models. These models generate hyperedges according to node positions in the embedded space and encourage short-range connections. They allow us to quantify the relative presence of periodic and linear structures in the data through maximum likelihood. They also improve the interpretability of node embedding and provide a metric for hyperedge prediction. We demonstrate the hypergraph embedding and follow-on tasks-including quantifying relative strength of structures, clustering and hyperedge prediction-on synthetic and real-world hypergraphs. We find that the hypergraph approach can outperform clustering algorithms that use only dyadic edges. We also compare several triadic edge prediction methods on high school and primary school contact hypergraphs where our algorithm improves upon benchmark methods when the amount of training data is limited.

Hypergraph and Uncertain Hypergraph Representation Learning Theory and Methods

With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

Analysis of Hypergraph Signals via High-Order Total Variation

Beyond pairwise relationships, interactions among groups of agents do exist in many real-world applications, but they are difficult to capture by conventional graph models. Generalized from graphs, hypergraphs have been introduced to describe such high-order group interactions. Inspired by graph signal processing (GSP) theory, an existing hypergraph signal processing (HGSP) method presented a spectral analysis framework relying on the orthogonal CP decomposition of adjacency tensors. However, such decomposition may not exist even for supersymmetric tensors. In this paper, we propose a high-order total variation (HOTV) form of a hypergraph signal (HGS) as its smoothness measure, which is a hyperedge-wise measure aggregating all signal values in each hyperedge instead of a pairwise one in most existing work. Further, we propose an HGS analysis framework based on the Tucker decomposition of the hypergraph Laplacian induced by the aforementioned HOTV. We construct an orthonormal basis from the HOTV, by which a new spectral transformation of the HGS is introduced. Then, we design hypergraph filters in both vertex and spectral domains correspondingly. Finally, we illustrate the advantages of the proposed framework by applications in label learning.

Capturing the grouping and compactness of high-level semantic feature for saliency detection

Saliency detection is an important and challenging research topic due to the variety and complexity of the background and saliency regions. In this paper, we present a novel unsupervised saliency detection approach by exploiting the grouping and compactness characteristics of the high-level semantic features. First, for the high-level semantic feature, the elastic net based hypergraph model is adopted to discover the group structure relationships of salient regional points, and the calculation of the spatial distribution is constructed to detect the compactness of the saliency regions. Next, the grouping-based and compactness-based saliency maps are improved by a propagation algorithm. The propagation process uses an enhanced similarity matrix, which fuses the low-level deep feature and the high-level semantic feature through cross diffusion. Results on four benchmark datasets with pixel-wise accurate labeling demonstrate the effectiveness of the proposed method. Particularly, the proposed unsupervised method achieves competitive performance with deep learning-based methods.

Multi-attribute Cognitive Decision Making via Convex Combination of Weighted Vector Similarity Measures for Single-Valued Neutrosophic Sets

Similarity measure (SM) proves to be a necessary tool in cognitive decision making processes. A single-valued neutrosophic set (SVNS) is just a particular instance of neutrosophic sets (NSs), which is capable of handling uncertainty and impreciseness/vagueness with a better degree of accuracy. The present article proposes two new weighted vector SMs for SVNSs, by taking the convex combination of vector SMs of Jaccard and Dice and Jaccard and cosine vector SMs. The applications of the proposed measures are validated by solving few multi-attribute decision-making (MADM) problems under neutrosophic environment. Moreover, to prevent the spread of COVID-19 outbreak, we also demonstrate the problem of selecting proper antivirus face mask with the help of our newly constructed measures. The best deserving alternative is calculated based on the highest SM values between the set of alternatives with an ideal alternative. Meticulous comparative analysis is presented to show the effectiveness of the proposed measures with the already established ones in the literature. Finally, illustrative examples are demonstrated to show the reliability, feasibility, and applicability of the proposed decision-making method. The comparison of the results manifests a fair agreement of the outcomes for the best alternative, proving that our proposed measures are effective. Moreover, the presented SMs are assured to have multifarious applications in the field of pattern recognition, image clustering, medical diagnosis, complex decision-making problems, etc. In addition, the newly constructed measures have the potential of being applied to problems of group decision making where the human cognition-based thought processes play a major role.

Detecting High Frequency Oscillations for Stereoelectroencephalography in Epilepsy via Hypergraph Learning

Successful epilepsy surgeries depend highly on pre-operative localization of epileptogenic zones. Stereoelectroencephalography (SEEG) records interictal and ictal activities of the epilepsy in order to precisely find and localize epileptogenic zones in clinical practice. While it is difficult to find distinct ictal onset patterns generated the seizure onset zone from SEEG recordings in a confined region, high frequency oscillations are commonly considered as putative biomarkers for the identification of epileptogenic zones. Therefore, automatic and accurate detection of high frequency oscillations in SEEG signals is crucial for timely clinical evaluation. This work formulates the detection of high frequency oscillations as a signal segment classification problem and develops a hypergraph-based detector to automatically detect high frequency oscillations such that human experts can visually review SEEG signals. We evaluated our method on 4,000 signal segments from clinical SEEG recordings that contain both ictal and interictal data obtained from 19 patients who suffer from refractory focal epilepsy. The experimental results demonstrate the effectiveness of the proposed detector that can successfully localize interictal high frequency oscillations and outperforms multiple peer machine learning methods. In particular, the proposed detector achieved 90.7% in accuracy, 80.9% in sensitivity, and 96.9% in specificity.

Multimedia Retrieval Through Unsupervised Hypergraph-Based Manifold Ranking

Accurately ranking images and multimedia objects are of paramount relevance in many retrieval and learning tasks. Manifold learning methods have been investigated for ranking mainly due to their capacity of taking into account the intrinsic global manifold structure. In this paper, a novel manifold ranking algorithm is proposed based on the hypergraphs for unsupervised multimedia retrieval tasks. Different from traditional graph-based approaches, which represent only pairwise relationships, hypergraphs are capable of modeling similarity relationships among a set of objects. The proposed approach uses the hyperedges for constructing a contextual representation of data samples and exploits the encoded information for deriving a more effective similarity function. An extensive experimental evaluation was conducted on nine public datasets including diverse retrieval scenarios and multimedia content. Experimental results demonstrate that high effectiveness gains can be obtained in comparison with the state-of-the-art methods.

How to achieve auto-identification in Raman analysis by spectral feature extraction & Adaptive Hypergraph

With the miniaturization of Raman spectrometers, Raman spectroscopy (including Surface-enhanced Raman spectroscopy) has been widely applied to various fields, especially towards rapid detection applications. In order to deal with the accompanied massive databases, large numbers of Raman spectra require to be handled and identified in an effective and automatic manner. This paper proposes an algorithm of material auto-identification, which makes use of machine learning methods to analyze Raman spectra. Firstly, a universal method of spectral feature extraction is designed to automatically process Raman spectra after the background subtraction. Secondly, the extracted feature vectors are used to classify and identify target materials by Adaptive Hypergraph (AH), an efficient classifier in the field of machine learning, in a manner of automation with an accuracy rate of ~99%. Compared with Support Vector Machine (SVM) and Random Forest (RF), two typical methods of classification, the AH classifier provides better performance free of tuning any parameter facing different targets. Thirdly, Cubic Spline Interpolation is introduced to enhance the universal of the proposed algorithm between different databases from different Raman spectrometers with variant vendors. The identification accuracy rate is up to 98% using the high frequency sampling spectra as the learning and the low frequency sampling ones as the testing, respectively.