Random Walks on Hypergraphs with Edge-Dependent Vertex Weights

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex weights: hypergraphs where every vertex $v$ has a weight $\gamma_e(v)$ for each incident hyperedge $e$ that describes the contribution of $v$ to the hyperedge $e$. We derive a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hypergraphs. Moreover, we give conditions under which random walks on such hypergraphs are equivalent to random walks on graphs. As a corollary, we show that current machine learning methods that rely on Laplacians derived from random walks on hypergraphs with edge-independent vertex weights do not utilize higher-order relationships in the data. Finally, we demonstrate the advantages of hypergraphs with edge-dependent vertex weights on ranking applications using real-world datasets.Comment: Accepted to ICML 201

Next Generation of Product Search and Discovery

Online shopping has become an important part of people’s daily life with the rapid development of e-commerce. In some domains such as books, electronics, and CD/DVDs, online shopping has surpassed or even replaced the traditional shopping method. Compared with traditional retailing, e-commerce is information intensive. One of the key factors to succeed in e-business is how to facilitate the consumers’ approaches to discover a product. Conventionally a product search engine based on a keyword search or category browser is provided to help users find the product information they need. The general goal of a product search system is to enable users to quickly locate information of interest and to minimize users’ efforts in search and navigation. In this process human factors play a significant role. Finding product information could be a tricky task and may require an intelligent use of search engines, and a non-trivial navigation of multilayer categories. Searching for useful product information can be frustrating for many users, especially those inexperienced users. This dissertation focuses on developing a new visual product search system that effectively extracts the properties of unstructured products, and presents the possible items of attraction to users so that the users can quickly locate the ones they would be most likely interested in. We designed and developed a feature extraction algorithm that retains product color and local pattern features, and the experimental evaluation on the benchmark dataset demonstrated that it is robust against common geometric and photometric visual distortions. Besides, instead of ignoring product text information, we investigated and developed a ranking model learned via a unified probabilistic hypergraph that is capable of capturing correlations among product visual content and textual content. Moreover, we proposed and designed a fuzzy hierarchical co-clustering algorithm for the collaborative filtering product recommendation. Via this method, users can be automatically grouped into different interest communities based on their behaviors. Then, a customized recommendation can be performed according to these implicitly detected relations. In summary, the developed search system performs much better in a visual unstructured product search when compared with state-of-art approaches. With the comprehensive ranking scheme and the collaborative filtering recommendation module, the user’s overhead in locating the information of value is reduced, and the user’s experience of seeking for useful product information is optimized

Low-Rank Hypergraph Hashing for Large-Scale Remote Sensing Image Retrieval

[EN] As remote sensing (RS) images increase dramatically, the demand for remote sensing image retrieval (RSIR) is growing, and has received more and more attention. The characteristics of RS images, e.g., large volume, diversity and high complexity, make RSIR more challenging in terms of speed and accuracy. To reduce the retrieval complexity of RSIR, a hashing technique has been widely used for RSIR, mapping high-dimensional data into a low-dimensional Hamming space while preserving the similarity structure of data. In order to improve hashing performance, we propose a new hash learning method, named low-rank hypergraph hashing (LHH), to accomplish for the large-scale RSIR task. First, LHH employs a l(2-1) norm to constrain the projection matrix to reduce the noise and redundancy among features. In addition, low-rankness is also imposed on the projection matrix to exploit its global structure. Second, LHH uses hypergraphs to capture the high-order relationship among data, and is very suitable to explore the complex structure of RS images. Finally, an iterative algorithm is developed to generate high-quality hash codes and efficiently solve the proposed optimization problem with a theoretical convergence guarantee. Extensive experiments are conducted on three RS image datasets and one natural image dataset that are publicly available. The experimental results demonstrate that the proposed LHH outperforms the existing hashing learning in RSIR tasks.This research was supported in part by the Natural Science Foundation of China under Grant 61673220.Kong, J.; Sun, Q.; Mukherjee, M.; Lloret, J. (2020). Low-Rank Hypergraph Hashing for Large-Scale Remote Sensing Image Retrieval. Remote Sensing. 12(7):1-19. https://doi.org/10.3390/rs1207116411912

Learning View-Model Joint Relevance for 3D Object Retrieval

3D object retrieval has attracted extensive research efforts and become an important task in recent years. It is noted that how to measure the relevance between 3D objects is still a difficult issue. Most of the existing methods employ just the model-based or view-based approaches, which may lead to incomplete information for 3D object representation. In this paper, we propose to jointly learn the view-model relevance among 3D objects for retrieval, in which the 3D objects are formulated in different graph structures. With the view information, the multiple views of 3D objects are employed to formulate the 3D object relationship in an object hypergraph structure. With the model data, the model-based features are extracted to construct an object graph to describe the relationship among the 3D objects. The learning on the two graphs is conducted to estimate the relevance among the 3D objects, in which the view/model graph weights can be also optimized in the learning process. This is the first work to jointly explore the view-based and model-based relevance among the 3D objects in a graph-based framework. The proposed method has been evaluated in three data sets. The experimental results and comparison with the state-of-the-art methods demonstrate the effectiveness on retrieval accuracy of the proposed 3D object retrieval method

Hypergraph Neural Networks

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-the-art methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods.Comment: Accepted in AAAI'201