Academic literature on the topic 'Positional Node Embeddings'

Graph neural networks (GNNs) have significantly improved the representation power for graph-structured data. Despite of the recent success of GNNs, the graph convolution in most GNNs have two limitations. Since the graph convolution is performed in a small local neighborhood on the input graph, it is inherently incapable to capture long-range dependencies between distance nodes. In addition, when a node has neighbors that belong to different classes, i.e., heterophily, the aggregated messages from them often negatively affect representation learning. To address the two common problems of graph convolution, in this paper, we propose Deformable Graph Convolutional Networks (Deformable GCNs) that adaptively perform convolution in multiple latent spaces and capture short/long-range dependencies between nodes. Separated from node representations (features), our framework simultaneously learns the node positional embeddings (coordinates) to determine the relations between nodes in an end-to-end fashion. Depending on node position, the convolution kernels are deformed by deformation vectors and apply different transformations to its neighbor nodes. Our extensive experiments demonstrate that Deformable GCNs flexibly handles the heterophily and achieve the best performance in node classification tasks on six heterophilic graph datasets. Our code is publicly available at https://github.com/mlvlab/DeformableGCN.

Sentiment Analysis is an essential research topic in the field of natural language processing (NLP) and has attracted the attention of many researchers in the last few years. Recently, deep neural network (DNN) models have been used for sentiment analysis tasks, achieving promising results. Although these models can analyze sequences of arbitrary length, utilizing them in the feature extraction layer of a DNN increases the dimensionality of the feature space. More recently, graph neural networks (GNNs) have achieved a promising performance in different NLP tasks. However, previous models cannot be transferred to a large corpus and neglect the heterogeneity of textual graphs. To overcome these difficulties, we propose a new Transformer-based graph convolutional network for heterogeneous graphs called Sentiment Transformer Graph Convolutional Network (ST-GCN). To the best of our knowledge, this is the first study to model the sentiment corpus as a heterogeneous graph and learn document and word embeddings using the proposed sentiment graph transformer neural network. In addition, our model offers an easy mechanism to fuse node positional information for graph datasets using Laplacian eigenvectors. Extensive experiments on four standard datasets show that our model outperforms the existing state-of-the-art models.

GNNs have been proven to perform highly effectively in various node-level, edge-level, and graph-level prediction tasks in several domains. Existing approaches mainly focus on static graphs. However, many graphs change over time and their edge may disappear, or the node/edge attribute may alter from one time to the other. It is essential to consider such evolution in the representation learning of nodes in time-varying graphs. In this paper, we propose a Temporal Multilayer Position-Aware Graph Neural Network (TMP-GNN), a node embedding approach for dynamic graphs that incorporates the interdependence of temporal relations into embedding computation. We evaluate the performance of TMP-GNN on two different representations of temporal multilayered graphs. The performance is assessed against the most popular GNNs on a node-level prediction task. Then, we incorporate TMP-GNN into a deep learning framework to estimate missing data and compare the performance with their corresponding competent GNNs from our former experiment, and a baseline method. Experimental results on four real-world datasets yield up to 58% lower ROCAUC for the pair-wise node classification task, and 96% lower MAE in missing feature estimation, particularly for graphs with a relatively high number of nodes and lower mean degree of connectivity.

Following the significant success of the transformer in NLP and computer vision, this paper attempts to extend it to 3D triangle mesh. The aim is to determine the shape’s global representation using the transformer and capture the inherent manifold information. To this end, this paper proposes a novel learning framework named Navigation Geodesic Distance Transformer (NGD-Transformer) for 3D mesh. Specifically, this approach combined farthest point sampling with the Voronoi segmentation algorithm to spawn uniform and non-overlapping manifold patches. However, the vertex number of these patches was inconsistent. Therefore, self-attention graph pooling is employed for sorting the vertices on each patch and screening out the most representative nodes, which were then reorganized according to their scores to generate tokens and their raw feature embeddings. To better exploit the manifold properties of the mesh, this paper further proposed a novel positional encoding called navigation geodesic distance positional encoding (NGD-PE), which encodes the geodesic distance between vertices relatively and spatial symmetrically. Subsequently, the raw feature embeddings and positional encodings were summed as input embeddings fed to the graph transformer encoder to determine the global representation of the shape. Experiments on several datasets were conducted, and the experimental results show the excellent performance of our proposed method.

Monitoring and predicting the deformation of surrounding rocks in the rock tunnel construction process is of great significance. This study implemented a wireless sensor network (WSN), including gateway transmission, relay point, and sensor nodes, to obtain high granularity deformation data during construction. A transformer model is proposed, which considers the construction sequence into the positional embedding and has an attention module to deeply learn the high dimensionality correlation between the nearby deformation data and the tunnel face deformation. The attention-enhanced LSTM model and the LSTM model are also constructed to compare them with the performance of the transformer model. A site study conducted on a shallow buried tunnel section suggested an excellent performance of the proposed WSN system. The transformer model shows the best performance in terms of the model prediction results, which can extract more information from the time sequence data than the attention-enhanced LSTM and LSTM models. The proposed system has great value as guidance and reference for the construction of rock tunnel projects in complex and unfavourable geological conditions.

AbstractMany 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.

User interfaces (UI) of desktop, web, and mobile applications involve a hierarchy of objects (e.g., applications, screens, view class, and other types of design objects) with multimodal (e.g., textual, visual) and positional (e.g., spatial location, sequence order and hierarchy level) attributes. We can therefore represent a set of application UIs as a heterogeneous network with multimodal and positional attributes. Such a network not only represents how users understand the visual layout of UIs, but also influences how users would interact with applications through these UIs. To model the UI semantics well for different UI annotation, search, and evaluation tasks, this paper proposes the novel Heterogeneous Attention-based Multimodal Positional (HAMP) graph neural network model. HAMP combines graph neural networks with the scaled dot-product attention used in transformers to learn the embeddings of heterogeneous nodes and associated multimodal and positional attributes in a unified manner. HAMP is evaluated with classification and regression tasks conducted on three distinct real-world datasets. Our experiments demonstrate that HAMP significantly out-performs other state-of-the-art models on such tasks. To further provide interpretations of the contribution of heterogeneous network information for understanding the relationships between the UI structure and prediction tasks, we propose Adaptive HAMP (AHAMP), which adaptively learns the importance of different edges linking different UI objects. Our experiments demonstrate AHAMP’s superior performance over HAMP on a number of tasks, and its ability to provide interpretations of the contribution of multimodal and positional attributes, as well as heterogeneous network information to different tasks.

Protein–protein interaction (PPI) is the basis of the whole molecular mechanisms of living cells. Although traditional experiments are able to detect PPIs accurately, they often encounter high cost and require more time. As a result, computational methods have been used to predict PPIs to avoid these problems. Graph structure, as the important and pervasive data carriers, is considered as the most suitable structure to present biomedical entities and relationships. Although graph embedding is the most popular approach for graph representation learning, it usually suffers from high computational and space cost, especially in large-scale graphs. Therefore, developing a framework, which can accelerate graph embedding and improve the accuracy of embedding results, is important to large-scale PPIs prediction. In this paper, we propose a multi-level model LPPI to improve both the quality and speed of large-scale PPIs prediction. Firstly, protein basic information is collected as its attribute, including positional gene sets, motif gene sets, and immunological signatures. Secondly, we construct a weighted graph by using protein attributes to calculate node similarity. Then GraphZoom is used to accelerate the embedding process by reducing the size of the weighted graph. Next, graph embedding methods are used to learn graph topology features from the reconstructed graph. Finally, the linear Logistic Regression (LR) model is used to predict the probability of interactions of two proteins. LPPI achieved a high accuracy of 0.99997 and 0.9979 on the PPI network dataset and GraphSAGE-PPI dataset, respectively. Our further results show that the LPPI is promising for large-scale PPI prediction in both accuracy and efficiency, which is beneficial to other large-scale biomedical molecules interactions detection.

The Creative City Unlike the terms ‘creative industries’, which nobody ever quite understood, and ‘creative class’, about which actual ‘creatives’ were always ambiguous, the ‘creative city’ has been an incredibly successful global policy meme, to which cities across the world continue to aspire. From the early 1990s, faced with de-industrialisation, rising unemployment, and the increased global mobility of capital, professionals, and consumer-tourists, the ‘creative city’ became an essential part of the new urban imaginary for politicians, planners, local growth coalitions, and advocates and practitioners in art and culture. In the later 1980s and early 1990s, much of this policy and practice work had progressive intent; as decaying parts of the city acquired new artistic and cultural uses, and neo-bohemian lifestyles and pop-cultural aspirations seemed to provide the grounds for future-oriented urban identities. Whilst investment in iconic cultural buildings and refurbished heritage sites repositioned cities as destinations for global tourism and finance (Peck et al.), new forms of creative production would provide employment and catalyse the wider urban economy. The creative city was to be a benign economy of innovative small businesses, working in projects and acting in symbiosis with the transformed urban landscape of the city (Pratt; Scott). If at first such a “creativity fix” (Peck, Creativity) was permeable to new actors and radical visions, it rapidly became a codified “cookie cutter” approach (Oakley), primarily concerned with revalorising decaying urban built stock as ‘vibrant’ spaces for upmarket urban consumption. This has stretched from visual arts to popular music (Bennett; O’Connor Music). The “creative imaginary” of entrepreneurial subjects—working in flat networks clustered around zones or milieux of intensified creativity (O’Connor and Shaw; O’Connor and Gu)—was quickly localised in spaces of real estate-led consumption, with production corralled into the ‘managed workspace’ whose image value—a shiny ‘creative hub’—was usually worth far more than any actual production taking place inside of it (O’Connor, Art). From the turn of the millennium, this global “fast policy” flowed through elite circuits of ‘policy transfer’ (Peck, Scale): unevenly distributed nodes assembling politicians, public administrators, planners, ‘cool’ developers, cultural consultants, branded arts institutions, and creative ‘thought-leaders’ (De Beukelaer and O’Connor). Global agencies such as UNESCO, through its Creative Cities Network, or consultancies such as Charles Landry and BOP, have attempted to frame this in a benign narrative of ‘hands across the ocean’ cultural globalisation. But we now know from two decades of creative economy proselytising that culture is a “driver and enabler” of development, not a normative standard against which it might be judged. And however inclusive ‘culture’ is made to sound, the creative city agenda remains firmly in the hands of local elites attempting to harness global flows of finance, media images, tourists, and ‘creatives’ for local development opportunities (Novy and Colomb; Courage and McKeown). By 2008 the creative city was already in trouble, as an increasingly brutal wave of gentrification came to be seen as the necessary corollary of the gleaming images of creative clusters, hipster hangouts, and iconic arts infrastructure. Predicated on a “spatial fix” (Harvey) for the decaying landscapes of the industrial city, the creative city was already producing its own ruins, as culture-led investment projects failed (Brodie). Since 2008, as the paper-thin walls between art, creativity, and real estate capital dissolved, it became increasingly clear that, though the script remained, the utopian moment was dead and buried. For many critics, both inside the cultural sector and out, it was time to roughly bundle it into the catch-all of neoliberalism and ‘gentrification’ and throw it overboard. Creative City RIP. The Ordinary City This critical take was performed early on by geographers such as Ash Amin and others (Amin and Graham; Amin, Massey, and Thrift), who suggested we re-centre the ordinary city—the one in which most people live—rather than fetishise some high-growth, hi-tech, gleaming Creative City. It was reiterated more recently by the Foundational Economy Collective, who argue that it is the everyday infrastructures and services of our towns and cities—and their mundane local economies of nail bars, cafes, and auto-repair shops—that should form the basis of our urban economic thinking (FEC). Jamie Peck, an early critic of the Creative City, had already cast doubt on the real economic weight of ‘creative industries’ and saw the whole thing as cover for the ‘entrepreneurial (read: neoliberal) city’, and a new kind of culturally-inflected growth coalition (Peck and Ward; Peck, Struggling). Similar dissent could be found amongst those writing within the cultural field. For every new city on the global creative smorgasbord, there were local artists and community activists who could show you a whole other side, excluded from the glass boxes and white cubes, from the funding and the hyped-up narratives lavished on the creative city. This mostly targeted the big iconic developments, led by global brands sucking the funding and the imagination from the surrounding city—what we might call ‘the Bilbao effect’. This cynicism toward the Creative City overlapped with a rejection of a ‘high art’ establishment and its elitist forms of culture. The ‘ordinary city’ here did not set the mundane against art and culture but reframed these as part of an everyday creativity. This could mean small-scale, neighbourhood-embedded art and culture, proposed by those in favour of ‘community arts’ and indeed those seeking localised popular culture such as music scenes. But it could also mean a valorisation of creativity writ large; a generalised urban creativity in which imagination and experimentation, but also subversion and contestation permeate the everyday. Following the Global Financial Crisis (GFC), critiques of the creative city concept became increasingly common. Oli Mould’s 2015 book Urban Subversion and the Creative City captures much of this, providing a distinction between the capitalised Creative City and the lower-case creative city. Mould distinguishes between the ‘Creative City’ ideology as extractive, and the ‘creative city’ as enabling citizenship. For Mould, the Creative City is “the antithesis of urban creativity” (Urban 4), and “shorthand for the capitalistic, paradigmatic (bordering on dogmatic) and meta-narrative view of how creativity can be used to economically stimulate and develop the city” (5). It is top-down creative planning at its worst. Against this, Mould evokes the lower-case concept of creative city, seeing some hope for it as a descriptor of urban spaces where “being creative is the very act of citizenship” (5). The Creative City imposed itself as a requirement of urban economic competitiveness (successful or not) and needs to be implacably opposed. Alternatively, the creative city persists in various forms of ‘urban subversion’, though whether the actual term—like creativity itself (Mould, Against)—can be freed from an association with its capitalised nemesis is, for Mould, still moot. Whilst Mould’s distinction allows us to evoke an urban creativity distinct from the commodified, extractive forms of the Creative City—one rooted in the ordinary, everyday creative practices of the city still open to themes of subversion and contestation centring cultural labour over cultural infrastructure—we also have some reservations. The C/creative couplet recalls de Certeau’s opposition of strategy and tactics, skyscraper and street, and has some of its problems. Baldly, this gives control of the city over to the powerful and condemns the rest of us to a game of endless evasion and subversion. For whilst the contemporary Creative City agenda may be largely as Mould describes it, its provenance is more complex than the extractive agenda which currently animates it. Understanding this provenance might give us some pointers beyond this binary impasse. Roots of the Creative City Although the Creative City eventually became integrated into the neoliberal urban script, the policy imaginary that birthed it emerged from the post-1960s rise of urban social movements, anti-development coalitions, new cultural practices (especially around popular music), artist co-ops, squats, and alternative cultures. Across the 1970s and 1980s one might say the C/creative City was an aspect of growing claims for cultural citizenship, the more explicit acknowledgement of a cultural dimension within T.H. Marshall’s ‘social citizenship’ (Marshall). The Greater London Council (GLC) of 1979-86 is exemplary here (Bianchini; Hatherley), but this was only the most visible case in which de-industrialising cities acquired aspirations to a different kind of city living. The utopian-romantic vision of a new kind of urban culture in which the transformative powers of art would abandon the ethereal world of the museum-gallery and take carnal form in the grotesque ruins of an industrial city was most literal in Wim Wenders’s 1987 film Wings of Desire. It was there in Berlin and New York as it was in Melbourne and Manchester, and a hundred other such cities (Whitney). As an industrial urban civilisation no longer seemed viable in the Global North, ‘culture’ became a central stake in anticipating what might come next. What new forms of working and living might be possible? What new identities, pleasures, desires might it accommodate? A new generation, immersed in what Mark Fisher called ‘popular modernism’ (Fisher), sought new forms of artistic expression within popular culture, making demands on the formal cultural system, on the infrastructure of the city, and on how the city could be re-imagined. In short, the C/creative City was not simply an invention of neoliberalism. It carried within it a utopian promise that should not be discounted. Perhaps we can see this in that most vilified of concepts, the ‘creative class’. The (Not-So) Creative Class By the 2008 GFC, the concept of the ‘creative class’—positioned as the primary driver and beneficiary of the creative city—was already coming apart. Unaffordable housing, rent hikes, rising debts, welfare cuts, reducing returns to ‘educational capital’ and the dominance of asset economies, precarious employment, culture budget cuts, and the integration of large sections of creative production into new platform economies have accelerated since that time. Global development capital has now built high-end leisure, entertainment, accommodation, and amenities into its core business model, one that does not require a prior process of valorisation by local creatives. Mould suggests the Creative City was a Trojan Horse and the creative class the Greeks inside (Urban 8). But whilst policymakers and city marketers embraced this term, it was never a class for-itself, with the clear strategic focus of soldiers waiting to pounce. Florida’s statistical fantasy netted a massive chunk of the population—almost 40 percent—as ‘professional, managerial and scientific’ (Florida, Rise). Meanwhile actual ‘creatives’ were always a poor relation and lived very differently to those others, most of whom preferred the suburbs and ex-burbs to the bustling city. Artists were not the storm-troopers of gentrification but its dupes, eventually evicted from the city they helped conquer. Meanwhile, since the advent of Florida and Landry, developers didn’t even need to use these ‘storm-troopers’ to soften up places for gentrification. They could now work directly with compliant city authorities to do the work for them. Creative cities could be deployed by toolkit (Landry) and, of course, measured via economic impact studies and a variety of other econometrics weaponised by corporate consultancies for hire. This was the social and political landscape upon which the Global Financial Crisis dealt an especially severe form of austerity, disproportionately affecting the cultural sector, and exacerbating many of the problematic areas of ‘creative city’ policy that had previously been abated and ameliorated by a veneer of hipster cool. Nonetheless, the ‘creative class’ also articulated a utopian promise, especially in places outside of the ‘Global North’ where more traditional forms of political power, gender roles, and religion remain in play. In a period of rapid globalisation, as relatively insulated economies became integrated into global capital flows, and cities bore the brunt of disruptive social and cultural changes, the C/creative City could stand in for a global modernity with a future. It could make available a new set of aspirations and identities; for a younger, more educated few perhaps, yet still real despite this. De Beukelaer, in the Indonesian context, talks about the “productive friction” between the two C/creative Cities, where the gap between the universal abstract and the local reality can form a site of negotiation. The C/creative City licences an encounter between new aspirations and identities, and the more traditional elites; an unequal struggle to define or give further content to the neoliberal nostrums of creative modernity that emanate from the Creative City meme. Yet it is not clear just why this negotiation is only made possible by the ‘apolitical’ notion of ‘creative’, or what’s at stake in that term. Is it a merely a cypher—or McGuffin—for a more complex conflict of interests? In what form would the “re-politicisation” of the creative city, called for at the end of the article, consist? What Next? We are not then talking about The City & the City (Mieville), in which two cities occupy the same geographic space but codify their separation by routinely ignoring each other and that which is deemed to belong to the other city. They are always in some kind of negotiation and contestation, but around what? We would argue that the imaginary of the C/creative City was annexed by, but not necessarily created by, neoliberalism. If the C/creative City articulated a future beyond a Fordist industrial civilisation, then we must take care in rejecting it not to abandon at the same time the power to imagine a different future. So, too, in attempting to assert the ordinary everyday city, we must also keep hold of a sense of the creative imagination that art and culture articulates, rather than dismissing this as part of the shiny glass palace on the hill. The absence of art and culture from the new progressive social and economic agendas that are currently finding their way into the mainstream—green new deals, doughnuts, well-being, community and ecological economics, and so on—is telling (O’Connor, Reset). In part this reflects the capture of arts and cultural policy by neoliberalism. This is not just ‘economic rationalism’ or market fundamentalism, for in the ‘creative economy’ art and cultural policy fused with neoliberalism at a deep DNA level, and the creative city imaginary was part of this. Mould is right to doubt whether the notion of ‘creative’, so closely enmeshed, could ever be retrieved. But regardless of whether art and culture have been condemned by this close association, the collapse of its romantic-utopian promise into a consumer leisure economy has left a void. If Jameson’s contention that we cannot think the end of capitalism is no longer the case (Jameson; Morozov), then culture is not present at this new moment of transition. So much well-being, community, and ecological economics speaks of culture whilst barely naming it. For us, the rearticulation of the place of art and culture in the contemporary city is crucial. We would even suggest that without art and culture, a full transformation of the contemporary city would be impossible. But how to think this? Any democratic cultural policy would need to reclaim both the ordinary and the creative city. This would entail the creative city of dissent and subversion, so closely aligned with the broad social movements to which we must look, in large part, to transform the city. It would also mean the right to a full participation in the imaginary of the collective city in which we all dwell and where we can imagine different futures. For this to happen, art and culture needs to be taken out of the hands of real estate, tourism, and economic development, and reframed as part of public service and public value. Just as new movements seek to reframe economic growth in terms of sustainability, equity, and human flourishing (Raworth), a radical creative city would be one in which art and culture were constitutive of the social foundations and part of how we live together as citizens, not simply another engine of the consumption economy. This process of re-embedding art and culture in the everyday foundations of the ordinary city is certainly underway. The ‘new municipalism’ (Thompson) has begun to make space for culture, with cities such as Barcelona and organisations such as the UCLG making a lot of the running. Notions of cultural rights, both individual and collective, have returned to challenge the urban consumption model. Just as art and culture try to position themselves alongside other foundational services—health, education, welfare—they also need to engage with new approaches to urban design, where technologies and infrastructures have been repositioned as cultural rather than technological. This suggests both that art and culture engage with the wider ‘cultural’—as in the anthropological, ‘whole way of life’—but that it no longer ‘owns’ this culture. Art and culture are not to be seen, as in the 1980s, as the ‘key’ to a total social transformation, but as one element only, however crucial. So too ‘creative’ needs to be unpicked and reframed, away from its association with ‘progress’ and absolute self-creation towards ‘slowdown’ (Dorling), sustainability, custodianship, care, incrementalism, and restoration – the kinds of values we now associate with First Nations. The shared DNA between creativity and capitalist modernity runs deep. Conclusion The COVID-19 pandemic has devastated large areas of art and culture, putting a question mark next to the urban use patterns that underpinned so much of the creative city model (Banks and O’Connor; de Peuter et al.; Tanghetti et al.; Whiting and Roberts). The Creative City of consumption, commuting, tourism, and entertainment stopped. Though some construction continued, the very purpose of the city centre—which over three decades had been rebranded as the Central Business District—was called into question. But the creative city was devastated too. Not just the collapse in income for cultural workers and business owners, but so too the filigrees of creative connection, the rhizomic mica that underpin the ecosystem of the city. Creatives already made no money, but at least they could go to openings and stay out late. Not anymore. This knockout blow was followed by the recognition that, for all the creative rhetoric, it was construction spending that counted most towards cultural funding budgets (Pacella et al.). Whilst talk quickly became one of getting artists and creatives to kickstart urban activity and animate deserted main street properties—‘build back better’—it is not at all clear where this endless supply of artists is going to come from. Now might be the time to explore how we might rethink art, culture, and the city rather than business as usual. As Arundhati Roy suggested, “nothing could be worse than a return to normality. Historically, pandemics have forced humans to break with the past and imagine their world anew. This one is no different. It is a portal, a gateway between one world and the next” (Roy). If art and culture don’t form part of that search for the new world, they will end up simply defending this one. 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Majority of the existing graph neural networks(GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings in those networks. This limitation prevents accurate performance in predictive tasks that rely on position information. In this paper, we develop GRAPHREACH , a position-aware inductive GNN that captures the global positions of nodes through reachability estimations with respect to a set of anchor nodes. The anchors are strategically selected so that reachability estimations across all the nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and, consequently, develop a greedy (1−1/e) approximation heuristic. Empirical evaluation against state-of-the-art GNN architectures reveal that GRAPHREACH provides up to 40% relative improvement in accuracy. In addition, it is more robust to adversarial attacks.

As a fundamental machine learning problem, graph clustering has facilitated various real-world applications, and tremendous efforts had been devoted to it in the past few decades. However, most of the existing methods like spectral clustering suffer from the sparsity, scalability, robustness and handling high dimensional raw information in clustering. To address this issue, we propose a deep probabilistic model, called Variational Graph Embedding and Clustering with Laplacian Eigenmaps (VGECLE), which learns node embeddings and assigns node clusters simultaneously. It represents each node as a Gaussian distribution to disentangle the true embedding position and the uncertainty from the graph. With a Mixture of Gaussian (MoG) prior, VGECLE is capable of learning an interpretable clustering by the variational inference and generative process. In order to learn the pairwise relationships better, we propose a Teacher-Student mechanism encouraging node to learn a better Gaussian from its instant neighbors in the stochastic gradient descent (SGD) training fashion. By optimizing the graph embedding and the graph clustering problem as a whole, our model can fully take the advantages in their correlation. To our best knowledge, we are the first to tackle graph clustering in a deep probabilistic viewpoint. We perform extensive experiments on both synthetic and real-world networks to corroborate the effectiveness and efficiency of the proposed framework.

The goal of network representation learning is to embed nodes so as to encode the proximity structures of a graph into a continuous low-dimensional feature space. In this paper, we propose a novel algorithm called node2hash based on feature hashing for generating node embeddings. This approach follows the encoder-decoder framework. There are two main mapping functions in this framework. The first is an encoder to map each node into high-dimensional vectors. The second is a decoder to hash these vectors into a lower dimensional feature space. More specifically, we firstly derive a proximity measurement called expected distance as target which combines position distribution and co-occurrence statistics of nodes over random walks so as to build a proximity matrix, then introduce a set of T different hash functions into feature hashing to generate uniformly distributed vector representations of nodes from the proximity matrix. Compared with the existing state-of-the-art network representation learning approaches, node2hash shows a competitive performance on multi-class node classification and link prediction tasks on three real-world networks from various domains.