On The Effect of Hyperedge Weights On Hypergraph Learning

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms

Joint Hypergraph Learning and Sparse Regression for Feature Selection

In this paper, we propose a unified framework for improved structure estimation and feature selection. Most existing graph-based feature selection methods utilise a static representation of the structure of the available data based on the Laplacian matrix of a simple graph. Here on the other hand, we perform data structure learning and feature selection simultaneously. To improve the estimation of the manifold representing the structure of the selected features, we use a higher order description of the neighbour- hood structures present in the available data using hypergraph learning. This allows those features which participate in the most significant higher order relations to be se- lected, and the remainder discarded, through a sparsification process. We formulate a single objective function to capture and regularise the hypergraph weight estimation and feature selection processes. Finally, we present an optimization algorithm to re- cover the hyper graph weights and a sparse set of feature selection indicators. This process offers a number of advantages. First, by adjusting the hypergraph weights, we preserve high-order neighborhood relations reflected in the original data, which cannot be modeled by a simple graph. Moreover, our objective function captures the global discriminative structure of the features in the data. Comprehensive experiments on 9 benchmark data sets show that our method achieves statistically significant improve- ment over state-of-art feature selection methods, supporting the effectiveness of the proposed method

Semisupervised hypergraph discriminant learning for dimensionality reduction of hyperspectral image.

Semisupervised learning is an effective technique to represent the intrinsic features of a hyperspectral image (HSI), which can reduce the cost to obtain the labeled information of samples. However, traditional semisupervised learning methods fail to consider multiple properties of an HSI, which has restricted the discriminant performance of feature representation. In this article, we introduce the hypergraph into semisupervised learning to reveal the complex multistructures of an HSI, and construct a semisupervised discriminant hypergraph learning (SSDHL) method by designing an intraclass hypergraph and an interclass graph with the labeled samples. SSDHL constructs an unsupervised hypergraph with the unlabeled samples. In addition, a total scatter matrix is used to measure the distribution of the labeled and unlabeled samples. Then, a low-dimensional projection function is constructed to compact the properties of the intraclass hypergraph and the unsupervised hypergraph, and simultaneously separate the characteristics of the interclass graph and the total scatter matrix. Finally, according to the objective function, we can obtain the projection matrix and the low-dimensional features. Experiments on three HSI data sets (Botswana, KSC, and PaviaU) show that the proposed method can achieve better classification results compared with a few state-of-the-art methods. The result indicates that SSDHL can simultaneously utilize the labeled and unlabeled samples to represent the homogeneous properties and restrain the heterogeneous characteristics of an HSI

BOURNE: Bootstrapped Self-supervised Learning Framework for Unified Graph Anomaly Detection

Graph anomaly detection (GAD) has gained increasing attention in recent years due to its critical application in a wide range of domains, such as social networks, financial risk management, and traffic analysis. Existing GAD methods can be categorized into node and edge anomaly detection models based on the type of graph objects being detected. However, these methods typically treat node and edge anomalies as separate tasks, overlooking their associations and frequent co-occurrences in real-world graphs. As a result, they fail to leverage the complementary information provided by node and edge anomalies for mutual detection. Additionally, state-of-the-art GAD methods, such as CoLA and SL-GAD, heavily rely on negative pair sampling in contrastive learning, which incurs high computational costs, hindering their scalability to large graphs. To address these limitations, we propose a novel unified graph anomaly detection framework based on bootstrapped self-supervised learning (named BOURNE). We extract a subgraph (graph view) centered on each target node as node context and transform it into a dual hypergraph (hypergraph view) as edge context. These views are encoded using graph and hypergraph neural networks to capture the representations of nodes, edges, and their associated contexts. By swapping the context embeddings between nodes and edges and measuring the agreement in the embedding space, we enable the mutual detection of node and edge anomalies. Furthermore, we adopt a bootstrapped training strategy that eliminates the need for negative sampling, enabling BOURNE to handle large graphs efficiently. Extensive experiments conducted on six benchmark datasets demonstrate the superior effectiveness and efficiency of BOURNE in detecting both node and edge anomalies