A Tensor-Based Formulation of Hetero-Functional Graph Theory

Recently, hetero-functional graph theory (HFGT) has developed as a means to mathematically model the structure of large-scale complex flexible engineering systems. It does so by fusing concepts from network science and model-based systems engineering (MBSE). For the former, it utilizes multiple graph-based data structures to support a matrix-based quantitative analysis. For the latter, HFGT inherits the heterogeneity of conceptual and ontological constructs found in model-based systems engineering including system form, system function, and system concept. These diverse conceptual constructs indicate multi-dimensional rather than two-dimensional relationships. This paper provides the first tensor-based treatment of hetero-functional graph theory. In particular, it addresses the “system concept” and the hetero-functional adjacency matrix from the perspective of tensors and introduces the hetero-functional incidence tensor as a new data structure. The tensor-based formulation described in this work makes a stronger tie between HFGT and its ontological foundations in MBSE. Finally, the tensor-based formulation facilitates several analytical results that provide an understanding of the relationships between HFGT and multi-layer networks.

MDGCN: Multiple Graph Convolutional Network Based on the Differential Calculation for Passenger Flow Forecasting in Urban Rail Transit

Passenger flow forecasting plays an important role in urban rail transit (URT) management. However, complex spatial and temporal correlations make this task extremely challenging. Previous work has been done by capturing spatiotemporal correlations of historical data. However, the spatiotemporal relationship between stations not only is limited to geospatial adjacency, but also lacks different perspectives of station correlation analysis. To fully capture the spatiotemporal correlations, we propose a deep learning model based on graph convolutional neural networks called MDGCN. Firstly, we identify the heterogeneity of stations under two spaces by the Multi-graph convolutional layer. Secondly, we designed the Diff-graph convolutional layer to identify the changing trend of heterogeneous features and used the attention mechanism unit with the LSTM unit to achieve adaptive fusion of multiple features and modeling of temporal correlation. We evaluate this model on real datasets. Compared to the best baselines, the root-mean-square errors of MDGCN are improved by 1%–15% for different prediction intervals.

Privacy Preservation in Online Social Networks Using Multiple-Graph-Properties-Based Clustering to Ensure k-Anonymity, l-Diversity, and t-Closeness

As per recent progress, online social network (OSN) users have grown tremendously worldwide, especially in the wake of the COVID-19 pandemic. Today, OSNs have become a core part of many people’s daily lifestyles. Therefore, increasing dependency on OSNs encourages privacy requirements to protect users from malicious sources. OSNs contain sensitive information about each end user that intruders may try to leak for commercial or non-commercial purposes. Therefore, ensuring different levels of privacy is a vital requirement for OSNs. Various privacy preservation methods have been introduced recently at the user and network levels, but ensuring k-anonymity and higher privacy model requirements such as l-diversity and t-closeness in OSNs is still a research challenge. This study proposes a novel method that effectively anonymizes OSNs using multiple-graph-properties-based clustering. The clustering method introduces the goal of achieving privacy of edge, node, and user attributes in the OSN graph. This clustering approach proposes to ensure k-anonymity, l-diversity, and t-closeness in each cluster of the proposed model. We first design the data normalization algorithm to preprocess and enhance the quality of raw OSN data. Then, we divide the OSN data into different clusters using multiple graph properties to satisfy the k-anonymization. Furthermore, the clusters ensure improved k-anonymization by a novel one-pass anonymization algorithm to address l-diversity and t-closeness privacy requirements. We evaluate the performance of the proposed method with state-of-the-art methods using a “Yelp real-world dataset”. The proposed method ensures high-level privacy preservation compared to state-of-the-art methods using privacy metrics such as anonymization degree, information loss, and execution time.

Hyperspectral Band Selection via Spatial-Spectral Weighted Region-wise Multiple Graph Fusion-Based Spectral Clustering

In this paper, we propose a hyperspectral band selection method via spatial-spectral weighted region-wise multiple graph fusion-based spectral clustering, referred to as RMGF briefly. Considering that different objects have different reflection characteristics, we use a superpixel segmentation algorithm to segment the first principal component of original hyperspectral image cube into homogeneous regions. For each superpixel, we construct a corresponding similarity graph to reflect the similarity between band pairs. Then, a multiple graph diffusion strategy with theoretical convergence guarantee is designed to learn a unified graph for partitioning the whole hyperspectral cube into several subcubes via spectral clustering. During the graph diffusion process, the spatial and spectral information of each superpixel are embedded to make spatial/spectral similar superpixels contribute more to each other. Finally, the band containing minimum noise in each subcube is selected to represent the whole subcube. Extensive experiments are conducted on three public datasets to validate the superiority of the proposed method when compared with other state-of-the-art ones.