Homophily, the tendency of similar nodes to connect, is a fundamental phenomenon in network science and a critical factor in the performance of graph neural networks (GNNs). While existing studies primarily explore homophily in homogeneous graphs, where nodes share the same type, real-world networks are often more accurately modeled as heterogeneous graphs (HGs) with diverse node types and intricate cross-type interactions. This structural diversity complicates the analysis of homophily, as traditional homophily metrics fail to account for distinct label spaces across node types. To address this limitation, we introduce the Cross-Type Homophily Ratio (CHR), a novel metric that quantifies homophily based on the similarity of target information across different node types. Additionally, we propose Cross-Type Homophily-guided Graph Editing (CTHGE), a novel method for improving heterogeneous graph neural networks (HGNNs) performance by optimizing cross-type connectivity using Cross-Type Homophily Ratio. Extensive experiments on five HG datasets with nine HGNNs validate the effectiveness of CTHGE, which delivers a maximum relative performance improvement of over 25% for HGNNs on node classification tasks, offering a fresh perspective on cross-type homophily in HGs learning.

As global e-commerce platforms continue to expand, companies are entering new markets where they encounter cold-start challenges due to limited human labels and user behaviors. In this paper, we share our experiences in Coupang to provide a competitive cold-start performance of relevance matching for emerging e-commerce markets. Specifically, we present a Cold-Start Relevance Matching (CSRM) framework, utilizing a multilingual Large Language Model (LLM) to address three challenges: (1) activating cross-lingual transfer learning abilities of LLMs through machine translation tasks; (2) enhancing query understanding and incorporating e-commerce knowledge by retrieval-based query augmentation; (3) mitigating the impact of training label errors through a multi-round self-distillation training strategy. Our experiments demonstrate the effectiveness of CSRM-LLM and the proposed techniques, resulting in successful real-world deployment and significant online gains, with a 45.8% reduction in defect ratio and a 0.866% uplift in session purchase rate.

With the increasing use of time series data, particularly in critical applications and high-risk decision-making contexts, understanding and improving the explainability of time-series clustering(TSC) techniques is essential. While machine learning models excel in processing time series data, their explainability often needs enhancement, challenging human comprehension and trust. Time series data clustering, as an unsupervised learning method, extracts valuable patterns from complex datasets without prior knowledge, spanning various domains like biology and finance. However, the complexity of clustering models and their opaque decision-making processes raise concerns about understanding and trusting the results. Research in this area aims to enhance the explainability of TSC by developing new interpretation methods that not only ensure the accuracy of clustering results but also make them user-friendly and comprehensible to human users. This is crucial for overcoming challenges related to understanding and trusting the decision-making processes and outcomes of the model. In this study, we embarked on two significant endeavors: (a) We explored the use of explainable artificial intelligence (XAI) for TSC for the first time, conducting a comprehensive literature review. (b) We subdivided the research field through innovative classification methods, categorizing the explainability methods of TSC into three main categories: data preprocessing techniques based on time series data, single or hybrid methods based model training, and instance-based visualization algorithm applications. This analytical framework aims to elucidate how the explainability of TSC can be enhanced across these three dimensions, thereby improving its credibility. Our work not only opens new research avenues but also provides robust strategies for enhancing the explainability and credibility of TSC methods.

Online recruitment platforms typically employ Person-Job Fit models in the core service that automatically match suitable job seekers with appropriate job positions. While existing works leverage historical or contextual information, they often disregard a crucial aspect: job seekers' social relationships in professional networks. This paper emphasizes the importance of incorporating professional networks into the Person-Job Fit model. Our innovative approach consists of two stages: (1) defining a Workplace Heterogeneous Information Network (WHIN) to capture heterogeneous knowledge, including professional connections and pre-training representations of various entities using a heterogeneous graph neural network; (2) designing a Contextual Social Attention Graph Neural Network (CSAGNN) that supplements users' missing information with professional connections' contextual information. We introduce a job-specific attention mechanism in CSAGNN to handle noisy professional networks, leveraging pre-trained entity representations from WHIN. We demonstrate the effectiveness of our approach through experimental evaluations conducted across three real-world recruitment datasets from LinkedIn, showing superior performance compared to baseline models.

Graph Neural Networks (GNNs) have achieved great success on a variety of tasks with graph-structural data, among which node classification is an essential one. Unsupervised Graph Domain Adaptation (UGDA) shows its practical value of reducing the labeling cost for node classification. It leverages knowledge from a labeled graph (i.e., source domain) to tackle the same task on another unlabeled graph (i.e., target domain). Most existing UGDA methods heavily rely on the labeled graph in the source domain. They utilize labels from the source domain as the supervision signal and are jointly trained on both the source graph and the target graph. However, in some real-world scenarios, the source graph is inaccessible because of privacy issues. Therefore, we propose a novel scenario named Source Free Unsupervised Graph Domain Adaptation (SFUGDA). In this scenario, the only information we can leverage from the source domain is the well-trained source model, without any exposure to the source graph and its labels. As a result, existing UGDA methods are not feasible anymore. To address the non-trivial adaptation challenges in this practical scenario, we propose a model-agnostic algorithm called SOGA for domain adaptation to fully exploit the discriminative ability of the source model while preserving the consistency of structural proximity on the target graph. We prove the effectiveness of the proposed algorithm both theoretically and empirically. The experimental results on four cross-domain tasks show consistent improvements in the Macro-F1 score and Macro-AUC.

Graph Neural Networks (GNNs) have shown superior performance in modeling graph data. Existing studies have shown that a lot of GNNs perform well on homophilic graphs while performing poorly on heterophilic graphs. Recently, researchers have turned their attention to design GNNs for heterophilic graphs by specific model design. Different from existing methods that mitigate heterophily by model design, we propose to study heterophilic graphs from an orthogonal perspective by rewiring the graph to reduce heterophily and make GNNs perform better. Through comprehensive empirical analysis, we verify the potential of graph rewiring methods. Then we propose a method namedDeepHeterophilyGraphRewiring (DHGR) to rewire graphs by adding homophilic edges and pruning heterophilic edges. The rewiring operation is implemented by comparing the similarity of neighborhood label/feature distribution of node pairs. Besides, we design a scalable implementation for DHGR to guarantee a high efficiency. DHRG can be easily used as a plug-in module, i.e., a graph pre-processing step, for any GNNs, including both GNNs for homophily and heterophily, to boost their performance on the node classification task. To the best of our knowledge, it is the first work studying graph rewiring for heterophilic graphs. Extensive experiments on 11 public graph datasets demonstrate the superiority of our proposed methods.

Recent years, Pre-trained Language models (PLMs) have swept into various fields of artificial intelligence and achieved great success. However, most PLMs, such as T5 and GPT3, have a huge amount of parameters, fine-tuning them is often expensive and time consuming, and storing them takes up a lot of space. Therefore, it is necessary to adopt a parameter-efficient approach to reduce parameters of PLMs in fine-tuning without compromising their performance in downstream tasks. In this paper, we design a novel adapter which only acts on self-attention outputs in PLMs. This adapter adopts element-wise linear transformation using Hadamard product, hence named as Hadamard adapter, requires the fewest parameters compared to previous parameter-efficient adapters. In addition, we also summarize some tuning patterns for Hadamard adapter shared by various downstream tasks, expecting to provide some guidance for further parameter reduction with shared adapters in future studies. The experiments conducted on the widely-used GLUE benchmark with several SOTA PLMs prove that the Hadamard adapter achieves competitive performance with only 0.033% parameters compared with full fine-tuning, and it has the fewest parameters compared with other adapters. Moreover, we further find that there is also some redundant layers in the Hadamard adapter which can be removed to achieve more parameter efficiency with only 0.022% parameters.

Temporal data representing chronological observations of complex systems can be ubiquitously collected in smart industry, medicine, finance and etc. In the last decade, many tasks have been studied for mining temporal data and offered significant value for various applications. Among these tasks, causal discovery aims to understand the underlying generation mechanism of temporal data and has attracted much research attention. According to whether the data is calibrated, existing causal discovery approaches can be divided into two subtasks, i.e., multivariate time-series causal discovery, and event sequence causal discovery. Previous tutorials or surveys have primarily focused on causal discovery from time-series data and disregarded the second ones. In this tutorial, we elucidate the correlation between the two subtasks and provide a comprehensive review of the existing solutions. Moreover, we offer some potential applications and summarize new perspectives for discovering causal relations from temporal data. We hope the audiences can obtain a systematic overview of this topic and inspire some new ideas for their own research.

Collaborative filtering (CF) is an important research direction in recommender systems that aims to make recommendations given the information on user-item interactions. Graph CF has attracted more and more attention in recent years due to its effectiveness in leveraging high-order information in the user-item bipartite graph for better recommendations. Specifically, recent studies show the success of graph neural networks (GNN) for CF is attributed to its low-pass filtering effects. However, current researches lack a study of how different signal components contributes to recommendations, and how to design strategies to properly use them well. To this end, from the view of spectral transformation, we analyze the important factors that a graph filter should consider to achieve better performance. Based on the discoveries, we design JGCF, an efficient and effective method for CF based on Jacobi polynomial bases and frequency decomposition strategies. Extensive experiments on four widely used public datasets show the effectiveness and efficiency of the proposed methods, which brings at most 27.06% performance gain on Alibaba-iFashion. Besides, the experimental results also show that JGCF is better at handling sparse datasets, which shows potential in making recommendations for cold-start users.

Tables are widely used for data storage and presentation due to their high flexibility in layout. The importance of tables as information carriers and the complexity of tabular data understanding attract a great deal of research on large-scale pre-training for tabular data. However, most of the works design models for specific types of tables, such as relational tables and tables with well-structured headers, neglecting tables with complex layouts. In real-world scenarios, there are many such tables beyond their target scope that cannot be well supported. In this paper, we propose GetPt, a unified pre-training architecture for general table representation applicable even to tables with complex structures and layouts. First, we convert a table to a heterogeneous graph with multiple types of edges to represent the layout of the table. Based on the graph, a specially designed transformer is applied to jointly model the semantics and structure of the table. Second, we devise the Alternate Attention Network (AAN) to better model the contextual information across multiple granularities of a table including tokens, cells, and the table. To better support a wide range of downstream tasks, we further employ three pre-training objectives and pre-train the model on a large table dataset. We fine-tune and evaluate GetPt model on two representative tasks, table type classification, and table structure recognition. Experiments show that GetPt outperforms existing state-of-the-art methods on these tasks.

Graph Neural Networks (GNNs) have shown expressive performance on graph representation learning by aggregating information from neighbors. Recently, some studies have discussed the importance of modeling neighborhood distribution on the graph. However, most existing GNNs aggregate neighbors' features through single statistic (e.g., mean, max, sum), which loses the information related to neighbor's feature distribution and therefore degrades the model performance. In this paper, inspired by the method of moment in statistical theory, we propose to model neighbor's feature distribution with multi-order moments. We design a novel GNN model, namely Mix-Moment Graph Neural Network (MM-GNN), which includes a Multi-order Moment Embedding (MME) module and an Element-wise Attention-based Moment Adaptor module. MM-GNN first calculates the multi-order moments of the neighbors for each node as signatures, and then use an Element-wise Attention-based Moment Adaptor to assign larger weights to important moments for each node and update node representations. We conduct extensive experiments on 15 real-world graphs (including social networks, citation networks and web-page networks etc.) to evaluate our model, and the results demonstrate the superiority of MM-GNN over existing state-of-the-art models.

With a good code search engine, developers can reuse existing code snippets and accelerate software development process. Current code search methods can be divided into two categories: traditional information retrieval (IR) based and deep learning (DL) based approaches. DL-based approaches include the cross-encoder paradigm and the bi-encoder paradigm. However, both approaches have certain limitations. The inference of IR-based and bi-encoder models are fast; however, they are not accurate enough; while cross-encoder models can achieve higher search accuracy but consume more time. In this work, we propose TOSS, a two-stage fusion code search framework that can combine the advantages of different code search methods. TOSS first uses IR-based and bi-encoder models to efficiently recall a small number of top-K code candidates, and then uses fine-grained cross-encoders for finer ranking. Furthermore, we conduct extensive experiments on different code candidate volumes and multiple programming languages to verify the effectiveness of TOSS. We also compare TOSS with six data fusion methods. Experimental results show that TOSS is not only efficient, but also achieves state-of-the-art accuracy with an overall mean reciprocal ranking (MRR) score of 0.763, compared to the best baseline result on the CodeSearchNet benchmark of 0.713.

User engagement prediction plays a critical role in designing interaction strategies to grow user engagement and increase revenue in online social platforms. Through the in-depth analysis of the real-world data from the world's largest professional social platforms, i.e., LinkedIn, we find that users expose diverse engagement patterns, and a major reason for the differences in user engagement patterns is that users have different intents. That is, people have different intents when using LinkedIn, e.g., applying for jobs, building connections, or checking notifications, which shows quite different engagement patterns. Meanwhile, user intents and the corresponding engagement patterns may change over time. Although such pattern differences and dynamics are essential for user engagement prediction, differentiating user engagement patterns based on user dynamic intents for better user engagement forecasting has not received enough attention in previous works. In this paper, we proposed a Dynamic Intent Guided Meta Network (DIGMN), which can explicitly model user intent varying with time and perform differentiated user engagement forecasting. Specifically, we derive some interpretable basic user intents as prior knowledge from data mining and introduce prior intents to explicitly model dynamic user intent. Furthermore, based on the dynamic user intent representations, we propose a meta-predictor to perform differentiated user engagement forecasting. Through a comprehensive evaluation of LinkedIn anonymous user data, our method outperforms state-of-the-art baselines significantly, i.e., 2.96% and 3.48% absolute error reduction, on coarse-grained and fine-grained user engagement prediction tasks, respectively, demonstrating the effectiveness of our method.

With the rapid development of the World Wide Web (WWW), heterogeneous graphs (HG) have explosive growth. Recently, heterogeneous graph neural network (HGNN) has shown great potential in learning on HG. Current studies of HGNN mainly focus on some HGs with strong homophily properties (nodes connected by meta-path tend to have the same labels), while few discussions are made in those that are less homophilous. Recently, there have been many works on homogeneous graphs with heterophily. However, due to heterogeneity, it is non-trivial to extend their approach to deal with HGs with heterophily. In this work, based on empirical observations, we propose a meta-path-induced metric to measure the homophily degree of a HG. We also find that current HGNNs may have degenerated performance when handling HGs with less homophilous properties. Thus it is essential to increase the generalization ability of HGNNs on non-homophilous HGs. To this end, we propose HDHGR, a homophily-oriented deep heterogeneous graph rewiring approach that modifies the HG structure to increase the performance of HGNN. We theoretically verify HDHGR. In addition, experiments on real-world HGs demonstrate the effectiveness of HDHGR, which brings at most more than 10% relative gain.

Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.

Learning rate is one of the most important hyper-parameters that has significant influence for neural network training. Learning rate schedules are widely used in real practice to adjust the learning rate according to pre-defined schedules for the fast convergence and good generalization. However, existing learning rate schedules are all heuristic algorithms and lack theoretical support. Therefore, people usually choose the learning rate schedules through multiple ad-hoc trial, and the obtained learning rate schedules are sub-optimal. To boost the performance of the obtained sub-optimal learning rate schedule, we propose a generic learning rate schedule plugin, called LEArning Rate Perturbation (LEAP), which can be applied to various learning rate schedules to improve the model training by introducing a certain perturbation to the learning rate. We found that, with such simple yet effective strategy, training processing exponentially favors flat minima rather than sharp minima with guaranteed convergence, which leads to better generalization ability. In addition, we conduct extensive experiments which show that training with LEAP can improve the performance of various deep learning models on diverse datasets using various learning rate schedules (including constant learning rate).

Computing trajectory similarities is a critical and fundamental task for various spatial-temporal applications, such as clustering, prediction, and anomaly detection. Traditional similarity metrics, i.e. DTW and Hausdorff, suffer from quadratic computation complexity, leading to their inability on large-scale data. To solve this problem, many trajectory representation learning techniques are proposed to approximate the metric space while reducing the complexity of similarity computation. Nevertheless, these works are designed based on RNN backend, resulting in a serious performance decline on long trajectories. In this paper, we propose a novel graph-based method, namely TrajGAT, to explicitly model the hierarchical spatial structure and improve the performance of long trajectory similarity computation. TrajGAT consists of two main modules, i.e. , graph construction and trajectory encoding. For graph construction, TrajGAT first employs PR quadtree to build the hierarchical structure of the whole spatial area, and then constructs a graph for each trajectory based on the original records and the leaf nodes of the quadtree. For trajectory encoding, we replace the self-attention in Transformer with graph attention and design an encoder to represent the generated graph trajectory. With these two modules, TrajGAT can capture the long-term dependencies of trajectories while reducing the GPU memory usage of Transformer. Our experiments on two real-life datasets show that TrajGAT not only improves the performance on long trajectories but also outperforms the state-of-the-art methods on mixture trajectories significantly.

Network Embedding aims to learn a function mapping the nodes to Euclidean space contribute to multiple learning analysis tasks on networks. However, both the noisy information behind the real-world networks and the overfitting problem negatively impact the quality of embedding vectors. To tackle these problems, researchers utilize Adversarial Perturbations on Parameters (APP) and achieve state-of-the-art performance. Unlike the mainstream methods introducing perturbations on the network structure or the data feature, Adversarial Training for Network Embedding (AdvTNE) adopts APP to directly perturb the model parameters, thus providing a new chance to understand the mechanism behind it. In this paper, we explain APP theoretically from an optimization perspective. Considering the Power-law property of networks and the optimization objective, we analyze the reason for its remarkable results on network embedding. Based on the above analysis and the Sigmoid saturation region problem, we propose a new Sine-base activation to enhance the performance of AdvTNE. We conduct extensive experiments on four real networks to validate the effectiveness of our method in node classification and link prediction. The results demonstrate that our method is competitive with state-of-the-art methods.

Graph Neural Networks (GNNs) are widely used on a variety of graph-based machine learning tasks. For node-level tasks, GNNs have strong power to model the homophily property of graphs (i.e., connected nodes are more similar), while their ability to capture heterophily property is often doubtful. This is partially caused by the design of the feature transformation with the same kernel for the nodes in the same hop and the followed aggregation operator. One kernel cannot model the similarity and the dissimilarity (i.e., the positive and negative correlation) between node features simultaneously even though we use attention mechanisms like Graph Attention Network (GAT), since the weight calculated by attention is always a positive value. In this paper, we propose a novel GNN model based on a bi-kernel feature transformation and a selection gate. Two kernels capture homophily and heterophily information respectively, and the gate is introduced to select which kernel we should use for the given node pairs. We conduct extensive experiments on various datasets with different homophily-heterophily properties. The experimental results show consistent and significant improvements against state-of-the-art GNN methods.

Recently, deep learning methods have become mainstream in code search since they do better at capturing semantic correlations between code snippets and search queries and have promising performance. However, code snippets have diverse information from different dimensions, such as business logic, specific algorithm, and hardware communication, so it is hard for a single code representation module to cover all the perspectives. On the other hand, as a specific query may focus on one or several perspectives, it is difficult for a single query representation module to represent different user intents. In this paper, we propose MuCoS, a multi-model ensemble learning architecture for semantic code search. It combines several individual learners, each of which emphasizes a specific perspective of code snippets. We train the individual learners on different datasets which contain different perspectives of code information, and we use a data augmentation strategy to get these different datasets. Then we ensemble the learners to capture comprehensive features of code snippets. The experiments show that MuCoS has better results than the existing state-of-the-art methods. Our source code and data are anonymously available at https://github.com/Xzh0u/MuCoS.

Graph Convolutional Networks (GCNs) have become the prevailing approach to efficiently learn representations from graph-structured data. Current GCN models adopt a neighborhood aggregation mechanism based on two primary operations, aggregation and combination. The workload of these two processes is determined by the input graph structure, making the graph input the bottleneck of processing GCN. Meanwhile, a large amount of task-irrelevant information in the graphs would hurt the model generalization performance. This brings the opportunity of studying how to remove the redundancy in the graphs. In this paper, we aim to accelerate GCN models by removing the task-irrelevant edges in the graph. We present AdaptiveGCN, an efficient and supervised graph sparsification framework. AdaptiveGCN adopts an edge predictor module to get edge selection strategies by learning the downstream task feedback signals for each GCN layer separately and adaptively in the training stage, then only inference with the selected edges in the test stage to speed up the GCN computation. The experimental results indicate that AdaptiveGCN could yield 43% (on CPU) and 39% (on GPU) GCN model speed-up averagely with comparable model performance on public graph learning benchmarks.

Initialization plays a critical role in the training of deep neural networks (DNN). Existing initialization strategies mainly focus on stabilizing the training process to mitigate gradient vanish/explosion problems. However, these initialization methods are lacking in consideration about how to enhance generalization ability. The Information Bottleneck (IB) theory is a well-known understanding framework to provide an explanation about the generalization of DNN. Guided by the insights provided by IB theory, we design two criteria for better initializing DNN. And we further design a neuron campaign initialization algorithm to efficiently select a good initialization for a neural network on a given dataset. The experiments on MNIST dataset show that our method can lead to a better generalization performance with faster convergence.

Tabular data are ubiquitous for the widespread applications of tables and hence have attracted the attention of researchers to extract underlying information. One of the critical problems in mining tabular data is how to understand their inherent semantic structures automatically. Existing studies typically adopt Convolutional Neural Network (CNN) to model the spatial information of tabular structures yet ignore more diverse relational information between cells, such as the hierarchical and paratactic relationships. To simultaneously extract spatial and relational information from tables, we propose a novel neural network architecture, TabularNet. The spatial encoder of TabularNet utilizes the row/column-level Pooling and the Bidirectional Gated Recurrent Unit (Bi-GRU) to capture statistical information and local positional correlation, respectively. For relational information, we design a new graph construction method based on the WordNet tree and adopt a Graph Convolutional Network (GCN) based encoder that focuses on the hierarchical and paratactic relationships between cells. Our neural network architecture can be a unified neural backbone for different understanding tasks and utilized in a multitask scenario. We conduct extensive experiments on three classification tasks with two real-world spreadsheet data sets, and the results demonstrate the effectiveness of our proposed TabularNet over state-of-the-art baselines.

Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

Traffic flow forecasting is of great significance for improving the efficiency of transportation systems and preventing emergencies. Due to the highly non-linearity and intricate evolutionary patterns of short-term and long-term traffic flow, existing methods often fail to take full advantage of spatial-temporal information, especially the various temporal patterns with different period shifting and the characteristics of road segments. Besides, the globality representing the absolute value of traffic status indicators and the locality representing the relative value have not been considered simultaneously. This paper proposes a neural network model that focuses on the globality and locality of traffic networks as well as the temporal patterns of traffic data. The cycle-based dilated deformable convolution block is designed to capture different time-varying trends on each node accurately. Our model can extract both global and local spatial information since we combine two graph convolutional network methods to learn the representations of nodes and edges. Experiments on two real-world datasets show that the model can scrutinize the spatial-temporal correlation of traffic data, and its performance is better than the compared state-of-the-art methods. Further analysis indicates that the locality and globality of the traffic networks are critical to traffic flow prediction and the proposed TSSRGCN model can adapt to the various temporal traffic patterns.

To depict ubiquitous relational data in real world, network data have been widely applied in modeling complex relationships. Projecting vertices to low dimensional spaces, quoted as Network Embedding, would thus be applicable to diverse real-world predicative tasks. Numerous works exploiting pairwise proximities, one characteristic owned by real networks, the clustering property, namely vertices are inclined to form communities of various ranges and hence form a hierarchy consisting of communities, has barely received attention from researchers. In this paper, we propose our network embedding framework, abbreviated SpaceNE, preserving hierarchies formed by communities through subspaces, manifolds with flexible dimensionalities and are inherently hierarchical. Moreover, we propose that subspaces are able to address further problems in representing hierarchical communities, including sparsity and space warps. Last but not least, we proposed constraints on dimensions of subspaces to denoise, which are further approximated by differentiable functions such that joint optimization is enabled, along with a layer-wise scheme to alleviate the overhead cause by the vast number of parameters. We conduct various experiments with results demonstrating our model's effectiveness in addressing community hierarchies.

Network embedding is a method to learn low-dimensional representation vectors for nodes in complex networks. In real networks, nodes may have multiple tags but existing methods ignore the abundant semantic and hierarchical information of tags. This information is useful to many network applications and usually very stable. In this paper, we propose a tag representation learning model, Tag2Vec, which mixes nodes and tags into a hybrid network. Firstly, for tag networks, we define semantic distance as the proximity between tags and design a novel strategy, parameterized random walk, to generate context with semantic and hierarchical information of tags adaptively. Then, we propose hyperbolic Skip-gram model to express the complex hierarchical structure better with lower output dimensions. We evaluate our model on the NBER U.S. patent dataset and WordNet dataset. The results show that our model can learn tag representations with rich semantic information and it outperforms other baselines.

Recently, real-time air quality estimation has attracted more and more attention from all over the world, which is close to our daily life. With the prevalence of mobile sensors, there is an emerging way to monitor the air quality with mobile sensors on vehicles. Compared with traditional expensive monitor stations, mobile sensors are cheaper and more abundant, but observations from these sensors have unstable spatial and temporal distributions, which results in the existing model could not work very well on this type of data. In this article, taking advantage of air quality data from mobile sensors, we propose an real-time urban air quality estimation method based on the Gaussian Process Regression for air pollution of the unmonitored areas, pivoting on the diffusion effect and the accumulation effect of air pollution. In order to meet the real-time demands, we propose a two-layer ensemble learning framework and a self-adaptivity mechanism to improve computational efficiency and adaptivity. We evaluate our model with real data from mobile sensor system located in Beijing, China. And the experiments show that our proposed model is superior to the state-of-the-art spatial regression methods in both precision and time performances.