While language models (LMs) have demonstrated remarkable general-purpose capabilities across domains, including molecule generation using line notations such as SMILES and SELFIES, their direct application to 3D structure design remains constrained by two interdependent challenges. First, the difficulty in designing a 3D line notation that ensures SE(3)-invariant atomic coordinates and supports autoregressive generation. Second, the incompatibility between continuous spatial coordinates and the discrete token inputs required by LMs. To address this, we propose Mol-StrucTok, a unified framework for tokenizing 3D molecular structures. Our approach comprises two key innovations: (1) a 3D line notation—Spherical Coordinate Notation—that encodes local atomic environments in spherical coordinates, agnostic to 2D notations and inherently SE(3)-invariant; and (2) a structure-aware Vector Quantized Variational Autoencoder (VQ-VAE) for discretizing these coordinates into chemically valid tokens suitable for language model processing. Leveraging this tokenization framework, we train a GPT-2 style model for end-to-end 3D molecular generation. Empirical results demonstrate strong, task-dependent performance: in unconditional generation, Mol-StrucTok achieves diffusion-level stability with ~28× faster inference; in conditional generation, it reduces property-matching mean absolute error (MAE) by 5–8× compared to diffusion-based methods, highlighting the advantage of autoregressive contextual modeling for precise control of molecular attributes. Our code is available at https://github.com/KyGao/Mol-StrucTok.

Node tokenized graph Transformers (GTs) have shown promising performance in node classification. The generation of token sequences is the key module in existing tokenized GTs which transforms the input graph into token sequences, facilitating the node representation learning via Transformer. In this paper, we observe that the generations of token sequences in existing GTs only focus on the first-order neighbors on the constructed similarity graphs, which leads to the limited usage of nodes to generate diverse token sequences, further restricting the potential of tokenized GTs for node classification. To this end, we propose a new method termed SwapGT. SwapGT first introduces a novel token swapping operation based on the characteristics of token sequences that fully leverages the semantic relevance of nodes to generate more informative token sequences. Then, SwapGT leverages a Transformer-based backbone to learn node representations from the generated token sequences. Moreover, SwapGT develops a center alignment loss to constrain the representation learning from multiple token sequences, further enhancing the model performance. Extensive empirical results on various datasets showcase the superiority of SwapGT for node classification. Code is available at https://github.com/JHL-HUST/SwapGT.

Though deep neural networks exhibit superior performance on various tasks, they are still plagued by adversarial examples. Adversarial training has been demonstrated to be the most effective method to defend against adversarial attacks. However, existing adversarial training methods show that the model robustness has apparent oscillations and overfitting issues in the training process, degrading the defense efficacy. To address these issues, we propose a novel framework called Parameter Interpolation Adversarial Training (PIAT). PIAT tunes the model parameters between each epoch by interpolating the parameters of the previous and current epochs. It makes the decision boundary of model change more moderate and alleviates the overfitting issue, helping the model converge better and achieving higher model robustness. In addition, we suggest using the Normalized Mean Square Error (NMSE) to further improve the robustness by aligning the relative magnitude of logits between clean and adversarial examples rather than the absolute magnitude. Extensive experiments conducted on several benchmark datasets demonstrate that our framework could prominently improve the robustness of both Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs).

Much of the complexity of social, biological, and engineering systems arises from the complicated interactions among the entities in the corresponding networks. A number of network analysis tools have been successfully used to discover latent structures termed communities in such networks. However, some communities with relatively weak structures can be difficult to uncover because they are obscured by other stronger connections. To cope with this situation, our previous work proposes an algorithm called HICODE to detect and amplify the dominant and hidden community structures. In this work, we conduct a comprehensive and systematic theoretical analysis on the impact of hidden community structure and the efficacy of the HICODE algorithm, as well as provide illustrations of the detection process and results. Specifically, we define a multi-layer stochastic block model and use this model to explain why the existence of hidden structure makes the detection of dominant structure harder than equivalent random noises, which can also explain why many community detection algorithms only focusing on the dominant structure do not work well as expected. We then provide theoretical analysis that the iterative reducing methods could help to enhance the discovery of hidden structure as well as the dominant structure in the multi-layer stochastic block model for the two cases of accurate and inaccurate detection. Finally, visual simulations and experimental results are presented to show the process of HICODE algorithm and the impact of different number of layers on the detection quality.

While tokenized graph Transformers have demonstrated strong performance in node classification tasks, their reliance on a limited subset of nodes with high similarity scores for constructing token sequences overlooks valuable information from other nodes, hindering their ability to fully harness graph information for learning optimal node representations. To address this limitation, we propose a novel graph Transformer called GCFormer. Unlike previous approaches, GCFormer develops a hybrid token generator to create two types of token sequences, positive and negative, to capture diverse graph information. And a tailored Transformer-based backbone is adopted to learn meaningful node representations from these generated token sequences. Additionally, GCFormer introduces contrastive learning to extract valuable information from both positive and negative token sequences, enhancing the quality of learned node representations. Extensive experimental results across various datasets, including homophily and heterophily graphs, demonstrate the superiority of GCFormer in node classification, when compared to representative graph neural networks (GNNs) and graph Transformers.

We examine concept generalization at a large scale in the natural visual spectrum. Established computational modes (*i.e.*, rule-based or similarity-based) are primarily studied isolated, focusing on confined and abstract problem spaces. In this work, we study these two modes when the *problem space* scales up and when the *complexity* of concepts becomes diverse. At the **representational level**, we investigate how the complexity varies when a visual concept is mapped to the representation space. Prior literature has shown that two types of complexities (Griffiths & Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun & Firestone, 2021). Leveraging *Representativeness of Attribute* (RoA), we computationally confirm: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the **computational level**, we examine how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in rule-based generalization, while the trend is the opposite in similarity-based generalization.

Hidden community is a useful concept proposed recently for social network analysis. Hidden communities indicate some weak communities whose most members also belong to other stronger dominant communities. Dominant communities could form a layer that partitions all the individuals of a network, and hidden communities could form other layer(s) underneath. These layers could be natural structures in the real-world networks like students grouped by major, minor, hometown, and so on. To handle the rapid growth of network scale, in this work, we explore the detection of hidden communities from the local perspective, and propose a new method that detects and boosts each layer iteratively on a subgraph sampled from the original network. We first expand the seed set from a single seed node based on our modified local spectral method and detect an initial dominant local community. Then we temporarily remove the members of this community as well as their connections to other nodes, and detect all the neighborhood communities in the remaining subgraph, including some “broken communities” that only contain a fraction of members in the original network. The local community and neighborhood communities form a dominant layer, and by reducing the edge weights inside these communities, we weaken this layer’s structure to reveal the hidden layers. Eventually, we repeat the whole process, and all communities containing the seed node can be detected and boosted iteratively. We theoretically show that our method can avoid some situations that a broken community and the local community are regarded as one community in the subgraph, leading to the inaccuracy of detection which can be caused by global hidden community detection methods. Extensive experiments show that our method could significantly outperform the state-of-the-art baselines designed for either global hidden community detection or multiple local community detection.

The black-box adversarial attack has attracted impressive attention for its practical use in the field of deep learning security. Meanwhile, it is very challenging as there is no access to the network architecture or internal weights of the target model. Based on the hypothesis that if an example remains adversarial for multiple models, then it is more likely to transfer the attack capability to other models, the ensemble-based adversarial attack methods are efficient and widely used for black-box attacks. However, ways of ensemble attack are rather less investigated, and existing ensemble attacks simply fuse the outputs of all the models evenly. In this work, we treat the iterative ensemble attack as a stochastic gradient descent optimization process, in which the variance of the gradients on different models may lead to poor local optima. To this end, we propose a novel attack method called the stochastic variance reduced ensemble (SVRE) attack, which could reduce the gradient variance of the ensemble models and take full advantage of the ensemble attack. Empirical results on the standard ImageNet dataset demonstrate that the proposed method could boost the adversarial transferability and outperforms existing ensemble attacks significantly. Code is available at https://github.com/JHL-HUST/SVRE.

It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust training error can be near zero via some methods, all existing algorithms lead to a high robust generalization error. In this paper, we provide a theoretical understanding of this puzzling phenomenon from the perspective of expressive power for deep neural networks. Specifically, for binary classification problems with well-separated data, we show that, for ReLU networks, while mild over-parameterization is sufficient for high robust training accuracy, there exists a constant robust generalization gap unless the size of the neural network is exponential in the data dimension $d$. This result holds even if the data is linear separable (which means achieving standard generalization is easy), and more generally for any parameterized function classes as long as their VC dimension is at most polynomial in the number of parameters. Moreover, we establish an improved upper bound of $\exp({\mathcal{O}}(k))$ for the network size to achieve low robust generalization error when the data lies on a manifold with intrinsic dimension $k$ ($k \ll d$). Nonetheless, we also have a lower bound that grows exponentially with respect to $k$ --- the curse of dimensionality is inevitable. By demonstrating an exponential separation between the network size for achieving low robust training and generalization error, our results reveal that the hardness of robust generalization may stem from the expressive power of practical models.

While community detection has been one of the cornerstones in network analysis and data science, its opposite, community obfuscation, has received little attention in recent years. With the increasing awareness of data security and privacy protection, the need to understand the impact of such attacks on traditional community detection algorithms emerges. To this end, we investigate the community obfuscation problem which aims to hide a target set of communities from being detected by perturbing the network structure. We identify and analyze the Matthew effect incurred by the classical quality function based methods, which essentially results in the imbalanced allocation of perturbation resources. To mitigate such effect, we propose a probabilistic framework named as ProHiCo to hide communities. The key idea of ProHiCo is to first allocate the resource of perturbations randomly and fairly and then choose the appropriate edges to perturb via likelihood minimization. Our ProHiCo framework provides the additional freedom to choose the generative graph model with community structure. By incorporating the stochastic block model and its degree-corrected variant into the ProHiCo framework, we develop two scalable and effective algorithms called SBM and DCSBM. Via extensive experiments on 8 real-world networks and 5 community detection algorithms, we show that both SBM and DCSBM are about 30x faster than the prominent baselines in the literature when there are around 500 target communities, while their performance is comparable to the baselines.

We address the problem of removing undesirable reflections from a single image captured through a glass surface, which is an ill-posed, challenging but practically important problem for photo enhancement. Inspired by iterative structure reduction for hidden community detection in social networks, we propose an Iterative Boost Convolutional LSTM Network (IBCLN) that enables cascaded prediction for reflection removal. IBCLN is a cascaded network that iteratively refines the estimates of transmission and reflection layers in a manner that they can boost the prediction quality to each other, and information across steps of the cascade is transferred using an LSTM. The intuition is that the transmission is the strong, dominant structure while the reflection is the weak, hidden structure. They are complementary to each other in a single image and thus a better estimate and reduction on one side from the original image leads to a more accurate estimate on the other side. To facilitate training over multiple cascade steps, we employ LSTM to address the vanishing gradient problem, and propose residual reconstruction loss as further training guidance. Besides, we create a dataset of real-world images with reflection and ground-truth transmission layers to mitigate the problem of insufficient data. Comprehensive experiments demonstrate that the proposed method can effectively remove reflections in real and synthetic images compared with state-of-the-art reflection removal methods.

In this paper we make progress on the unsupervised task of mining arbitrarily shaped clusters in highly noisy datasets, which is a task present in many real-world applications. Based on the fundamental work that first applies a wavelet transform to data clustering, we propose an adaptive clustering algorithm, denoted as AdaWave, which exhibits favorable characteristics for clustering. By a self-adaptive thresholding technique, AdaWave is parameter free and can handle data in various situations. It is deterministic, fast in linear time, order-insensitive, shape-insensitive, robust to highly noisy data, and requires no pre-knowledge on data models. Moreover, AdaWave inherits the ability from the wavelet transform to cluster data in different resolutions. We adopt the "grid labeling" data structure to drastically reduce the memory consumption of the wavelet transform so that AdaWave can be used for relatively high dimensional data. Experiments on synthetic as well as natural datasets demonstrate the effectiveness and efficiency of our proposed method.

Community detection is an important information mining task to uncover modular structures in large networks. For increasingly common large network datasets, global community detection is prohibitively expensive, and attention has shifted to methods that mine local communities, i.e., identifying all latent members of a particular community from a few labeled seed members. To address such semi-supervised mining task, we systematically develop a local spectral (LOSP) subspace-based community detection method, called LOSP. We define a family of LOSP subspaces based on Krylov subspaces, and seek a sparse indicator for the target community via an ℓ 1 norm minimization over the Krylov subspace. Variants of LOSP depend on type of random walks with different diffusion speeds, type of random walks, dimension of the LOSP subspace, and step of diffusions. The effectiveness of the proposed LOSP approach is theoretically analyzed based on Rayleigh quotients, and it is experimentally verified on a wide variety of real-world networks across social, production, and biological domains, as well as on an extensive set of synthetic LFR benchmark datasets.

In this paper we show the similarities and differences of two deep neural networks by comparing the manifolds composed of activation vectors in each fully connected layer of them. The main contribution of this paper includes (1) a new data generating algorithm which is crucial for determining the dimension of manifolds; (2) a systematic strategy to compare manifolds. Especially, we take Riemann curvature and sectional curvature as part of criterion, which can reflect the intrinsic geometric properties of manifolds. Some interesting results and phenomenon are given, which help in specifying the similarities and differences between the features extracted by two networks and demystifying the intrinsic mechanism of deep neural networks.

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what representations do deep neural networks learn. In this work, we move a tiny step towards a theory and better understanding of the representations. Specifically, we study a simpler problem: How similar are the representations learned by two networks with identical architecture but trained from different initializations. We develop a rigorous theory based on the neuron activation subspace match model. The theory gives a complete characterization of the structure of neuron activation subspace matches, where the core concepts are maximum match and simple match which describe the overall and the finest similarity between sets of neurons in two networks respectively. We also propose efficient algorithms to find the maximum match and simple matches. Finally, we conduct extensive experiments using our algorithms. Experimental results suggest that, surprisingly, representations learned by the same convolutional layers of networks trained from different initializations are not as similar as prevalently expected, at least in terms of subspace match.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms for mining communities have focused on global graph structure, and often run in time proportional to the size of the entire graph. As we explore networks with millions of vertices and find communities of size in the hundreds, it becomes important to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify communities from a few exemplary seed members. In this article, we propose a novel approach for finding overlapping communities called L emon ( L ocal E xpansion via M inimum O ne N orm). Provided with a few known seeds , the algorithm finds the community by performing a local spectral diffusion. The core idea of L emon is to use short random walks to approximate an invariant subspace near a seed set, which we refer to as local spectra . Local spectra can be viewed as the low-dimensional embedding that captures the nodes’ closeness in the local network structure. We show that L emon ’s performance in detecting communities is competitive with state-of-the-art methods. Moreover, the running time scales with the size of the community rather than that of the entire graph. The algorithm is easy to implement and is highly parallelizable. We further provide theoretical analysis of the local spectral properties, bounding the measure of tightness of extracted community using the eigenvalues of graph Laplacian. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

In this paper, we propose a novel generative model named Stacked Generative Adversarial Networks (SGAN), which is trained to invert the hierarchical representations of a bottom-up discriminative network. Our model consists of a top-down stack of GANs, each learned to generate lower-level representations conditioned on higher-level representations. A representation discriminator is introduced at each feature hierarchy to encourage the representation manifold of the generator to align with that of the bottom-up discriminative network, leveraging the powerful discriminative representations to guide the generative model. In addition, we introduce a conditional loss that encourages the use of conditional information from the layer above, and a novel entropy loss that maximizes a variational lower bound on the conditional entropy of generator outputs. We first train each stack independently, and then train the whole model end-to-end. Unlike the original GAN that uses a single noise vector to represent all the variations, our SGAN decomposes variations into multiple levels and gradually resolves uncertainties in the top-down generative process. Based on visual inspection, Inception scores and visual Turing test, we demonstrate that SGAN is able to generate images of much higher quality than GANs without stacking.

To what extent is the success of deep visualization due to the training? Could we do deep visualization using untrained, random weight networks? To address this issue, we explore new and powerful generative models for three popular deep visualization tasks using untrained, random weight convolutional neural networks. First we invert representations in feature spaces and reconstruct images from white noise inputs. The reconstruction quality is statistically higher than that of the same method applied on well trained networks with the same architecture. Next we synthesize textures using scaled correlations of representations in multiple layers and our results are almost indistinguishable with the original natural texture and the synthesized textures based on the trained network. Third, by recasting the content of an image in the style of various artworks, we create artistic images with high perceptual quality, highly competitive to the prior work of Gatys et al. on pretrained networks. To our knowledge this is the first demonstration of image representations using untrained deep neural networks. Our work provides a new and fascinating tool to study the representation of deep network architecture and sheds light on new understandings on deep visualization. It may possibly lead to a way to compare network architectures without training.

How can web services that depend on user generated content discern fake social engagement activities by spammers from legitimate ones? In this paper, we focus on the social site of YouTube and the problem of identifying bad actors posting inorganic contents and inflating the count of social engagement metrics. We propose an effective method, Leas (Local Expansion at Scale), and show how the fake engagement activities on YouTube can be tracked over time by analyzing the temporal graph based on the engagement behavior pattern between users and YouTube videos. With the domain knowledge of spammer seeds, we formulate and tackle the problem in a semi-supervised manner --- with the objective of searching for individuals that have similar pattern of behavior as the known seeds --- based on a graph diffusion process via local spectral subspace. We offer a fast, scalable MapReduce deployment adapted from the localized spectral clustering algorithm. We demonstrate the effectiveness of our deployment at Google by achieving a manual review accuracy of 98% on YouTube Comments graph in practice. Comparing with the state-of-the-art algorithm CopyCatch, Leas achieves 10 times faster running time on average. Leas is now actively in use at Google, searching for daily deceptive practices on YouTube's engagement graph spanning over a billion users.

Social instant messaging services are emerging as a transformative form with which people connect, communicate with friends in their daily life they catalyze the formation of social groups, and they bring people stronger sense of community and connection. However, research community still knows little about the formation and evolution of groups in the context of social messaging their lifecycles, the change in their underlying structures over time, and the diffusion processes by which they develop new members. In this paper, we analyze the daily usage logs from WeChat group messaging platform the largest standalone messaging communication service in China with the goal of understanding the processes by which social messaging groups come together, grow new members, and evolve over time. Specifically, we discover a strong dichotomy among groups in terms of their lifecycle, and develop a separability model by taking into account a broad range of group-level features, showing that long-term and short-term groups are inherently distinct. We also found that the lifecycle of messaging groups is largely dependent on their social roles and functions in users' daily social experiences and specific purposes. Given the strong separability between the long-term and short-term groups, we further address the problem concerning the early prediction of successful communities. In addition to modeling the growth and evolution from group-level perspective, we investigate the individual-level attributes of group members and study the diffusion process by which groups gain new members. By considering members' historical engagement behavior as well as the local social network structure that they embedded in, we develop a membership cascade model and demonstrate the effectiveness by achieving AUC of 95.31% in predicting inviter, and an AUC of 98.66% in predicting invitee.

Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Using the power method for a few steps, LOSP finds an approximate invariant subspace, which depicts the embedding of the local neighborhood structure around the seeds of interest. LOSP then identifies the local community expanded from the given seeds by seeking a sparse indicator vector in the subspace where the seeds are in its support. We provide a systematic investigation on LOSP, and thoroughly evaluate it on large real world networks across multiple domains. With the prior information of very few seed members, LOSP can detect the remaining members of a target community with high accuracy. Experiments demonstrate that LOSP outperforms the Heat Kernel and PageRank diffusions. Using LOSP as a subroutine, we further address the problem of multiple membership identification, which aims to find all the communities a single vertex belongs to. High F1 scores are achieved in detecting multiple local communities with respect to arbitrary single seed for various large real world networks.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. %Very few approaches can systematically demonstrate both high efficiency and effectiveness that significantly stands out amongst the divergent approaches in finding communities.

The recent interest in networks has inspired a broad range of work on algorithms and techniques to characterize, identify, and extract communities from networks. Such efforts are complicated by a lack of consensus on what a “community” truly is, and these disagreements have led to a wide variety of mathematical formulations for describing communities. Often, these mathematical formulations, such as modularity and conductance, have been founded in the general principle that communities, like a G ( n , p ) graph, are “round,” with connections throughout the entire community, and so algorithms were developed to optimize such mathematical measures. More recently, a variety of algorithms have been developed that, rather than expecting connectivity through the entire community, seek out very small groups of well-connected nodes and then connect these groups into larger communities. In this article, we examine seven real networks, each containing external annotation that allows us to identify “annotated communities.” A study of these annotated communities gives insight into why the second category of community detection algorithms may be more successful than the first category. We then present a flexible algorithm template that is based on the idea of joining together small sets of nodes. In this template, we first identify very small, tightly connected “subcommunities” of nodes, each corresponding to a single node’s “perception” of the network around it. We then create a new network in which each node represents such a subcommunity, and then identify communities in this new network. Because each node can appear in multiple subcommunities, this method allows us to detect overlapping communities. When evaluated on real data, we show that our template outperforms many other state-of-the-art algorithms.

Four major factors govern the intricacies of community extraction in networks: (1) the literature offers a multitude of disparate community detection algorithms whose output exhibits high structural variability across the collection, (2) communities identified by algorithms may differ structurally from real communities that arise in practice, (3) there is no consensus characterizing how to discriminate communities from noncommunities, and (4) the application domain includes a wide variety of networks of fundamentally different natures. In this article, we present a class separability framework to tackle these challenges through a comprehensive analysis of community properties. Our approach enables the assessment of the structural dissimilarity among the output of multiple community detection algorithms and between the output of algorithms and communities that arise in practice. In addition, our method provides us with a way to organize the vast collection of community detection algorithms by grouping those that behave similarly. Finally, we identify the most discriminative graph-theoretical properties of community signature and the small subset of properties that account for most of the biases of the different community detection algorithms. We illustrate our approach with an experimental analysis, which reveals nuances of the structure of real and extracted communities. In our experiments, we furnish our framework with the output of 10 different community detection procedures, representative of categories of popular algorithms available in the literature, applied to a diverse collection of large-scale real network datasets whose domains span biology, online shopping, and social systems. We also analyze communities identified by annotations that accompany the data, which reflect exemplar communities in various domain. We characterize these communities using a broad spectrum of community properties to produce the different structural classes. As our experiments show that community structure is not a universal concept, our framework enables an informed choice of the most suitable community detection method for identifying communities of a specific type in a given network and allows for a comparison of existing community detection algorithms while guiding the design of new ones.

The method of Cauchy random projections is popular for computing the $l_1$ distance in high dimension. In this paper, we propose to use only the signs of the projected data and show that the probability of collision (i.e., when the two signs differ) can be accurately approximated as a function of the chi-square ($\chi^2$) similarity, which is a popular measure for nonnegative data (e.g., when features are generated from histograms as common in text and vision applications). Our experiments confirm that this method of sign Cauchy random projections is promising for large-scale learning applications. Furthermore, we extend the idea to sign $\alpha$-stable random projections and derive a bound of the collision probability.

We study how links are formed in social networks. In particular, we focus on investigating how a reciprocal (two-way) link, the basic relationship in social networks, is developed from a parasocial (one-way) relationship and how the relationships further develop into triadic closure, one of the fundamental processes of link formation. We first investigate how geographic distance and interactions between users influence the formation of link structure among users. Then we study how social theories including homophily, social balance, and social status are satisfied over networks with parasocial and reciprocal relationships. The study unveils several interesting phenomena. For example, “friend's friend is a friend” indeed exists in the reciprocal relationship network, but does not hold in the parasocial relationship network. We propose a learning framework to formulate the problems of predicting reciprocity and triadic closure into a graphical model. We demonstrate that it is possible to accurately infer 90% of reciprocal relationships in a Twitter network. The proposed model also achieves better performance (+20--30% in terms of F1-measure) than several alternative methods for predicting the triadic closure formation.

Three major factors govern the intricacies of community extraction in networks: (1) the application domain includes a wide variety of networks of fundamentally different natures, (2) the literature offers a multitude of disparate community detection algorithms, and (3) there is no consensus characterizing how to discriminate communities from non-communities. In this paper, we present a comprehensive analysis of community properties through a class separability framework. Our approach enables the assessement of the structural dissimilarity among the output of multiple community detection algorithms and between the output of algorithms and communities that arise in practice. To demostrate this concept, we furnish our method with a large set of structural properties and multiple community detection algorithms. Applied to a diverse collection of large scale network datasets, the analysis reveals that (1) the different detection algorithms extract fundamentally different structures; (2) the structure of communities that arise in practice is closest to that of communities that random-walk-based algorithms extract, although still siginificantly different from that of the output of all the algorithms; and (3) a small subset of the properties are nearly as discriminative as the full set, while making explicit the ways in which the algorithms produce biases. Our framework enables an informed choice of the most suitable community detection method for a given purpose and network and allows for a comparison of existing community detection algorithms while guiding the design of new ones.

We study the extent to which the formation of a two-way relationship can be predicted in a dynamic social network. A two-way (called reciprocal) relationship, usually developed from a one-way (parasocial) relationship, represents a more trustful relationship between people. Understanding the formation of two-way relationships can provide us insights into the micro-level dynamics of the social network, such as what is the underlying community structure and how users influence each other. Employing Twitter as a source for our experimental data, we propose a learning framework to formulate the problem of reciprocal relationship prediction into a graphical model. The framework incorporates social theories into a machine learning model. We demonstrate that it is possible to accurately infer 90% of reciprocal relationships in a dynamic network. Our study provides strong evidence of the existence of the structural balance among reciprocal relationships. In addition, we have some interesting findings, e.g., the likelihood of two "elite" users creating a reciprocal relationships is nearly 8 times higher than the likelihood of two ordinary users. More importantly, our findings have potential implications such as how social structures can be inferred from individuals' behaviors.

In many social networks, there exist two types of users that exhibit different influence and different behavior. For instance, statistics have shown that less than 1% of the Twitter users (e.g. entertainers, politicians, writers) produce 50% of its content, while the others (e.g. fans, followers, readers) have much less influence and completely different social behavior. In this paper, we define and explore a novel problem called community kernel detection in order to uncover the hidden community structure in large social networks. We discover that influential users pay closer attention to those who are more similar to them, which leads to a natural partition into different community kernels. We propose Greedy and We BA, two efficient algorithms for finding community kernels in large social networks. Greedy is based on maximum cardinality search, while We BA formalizes the problem in an optimization framework. We conduct experiments on three large social networks: Twitter, Wikipedia, and Coauthor, which show that We BA achieves an average 15%-50% performance improvement over the other state-of-the-art algorithms, and We BA is on average 6-2,000 times faster in detecting community kernels.

In this paper we study how to discover the evolution of topics over time in a time-stamped document collection. Our approach is uniquely designed to capture the rich topology of topic evolution inherent in the corpus. Instead of characterizing the evolving topics at fixed time points, we conceptually define a topic as a quantized unit of evolutionary change in content and discover topics with the time of their appearance in the corpus. Discovered topics are then connected to form a topic evolution graph using a measure derived from the underlying document network. Our approach allows inhomogeneous distribution of topics over time and does not impose any topological restriction in topic evolution graphs. We evaluate our algorithm on the ACM corpus.

We consider the problem of learning mixtures of arbitrary symmetric distributions. We formulate sufficient separation conditions and present a learning algorithm with provable guarantees for mixtures of distributions that satisfy these separation conditions. Our bounds are independent of the variances of the distributions; to the best of our knowledge, there were no previous algorithms known with provable learning guarantees for distributions having infinite variance and/or expectation. For Gaussians and log-concave distributions, our results match the best known sufficient separation conditions by D. Achlioptas and F. McSherry (2005) and S. Vempala and G. Wang (2004). Our algorithm requires a sample of size O/spl tilde/(dk), where d is the number of dimensions and k is the number of distributions in the mixture. We also show that for isotropic power-laws, exponential, and Gaussian distributions, our separation condition is optimal up to a constant factor.

This paper presents a learning theoretical analysis of correlation clustering (Bansal et al., 2002). In particular, we give bounds on the error with which correlation clustering recovers the correct partition in a planted partition model (Condon & Karp, 2001; Mc-Sherry, 2001). Using these bounds, we analyze how the accuracy of correlation clustering scales with the number of clusters and the sparsity of the graph. We also propose a statistical test that analyzes the significance of the clustering found by correlation clustering.

The importance of scalability and fault-tolerance in modern distributed systems has led to considerable research in multicast protocols using gossip. In a gossip protocol, each node forwards messages to a small set of “gossip partners ” chosen at random from the entire group membership. By discarding the strong reliability guarantees of traditional protocols in favour of probabilistic guarantees, gossip protocols can deliver greater scalability and fault tolerance. In early gossip algorithms, partners were chosen uniformly at random from the entire membership, limiting scalability because of the resources required to store and maintain complete membership views at each node. Later protocols avoided this issue by storing much smaller random subsets of the membership at each node, and choosing gossip partners only from these local views. Such protocols are subtle: at least some local views must change in response to group membership changes in order to preserve connectivity and performance guarantees. While these protocols have been the subject of much simulation and analysis, formal proofs of key properties – in particular the probability of partitioning – have remained elusive. In this paper we give a new scalable gossip-based algorithm for local view maintenance, together with a proof that the expected time until a network partition is at least exponential in the square of the view size. We also develop probabilistic bounds on the in-degree (hence the load) of individual nodes, and argue that protocols lacking our reinforcement component eventually converge to star-like networks, whose connectivity depends on a small set of overloaded nodes. We also argue that the undirected connectivity graph is an expander, for which application-level gossip multi-cast protocols will converge rapidly. Our theoretical results are supported by simulations.

We extend spectral methods to random graphs with skewed degree distributions through a degree based normalization closely connected to the normalized Laplacian. The normalization is based on intuition drawn from perturbation theory of random matrices, and has the effect of boosting the expectation of the random adjacency matrix without increasing the variances of its entries, leading to better perturbation bounds. The primary implication of this result lies in the realm of spectral analysis of random graphs with skewed degree distributions, such as the ubiquitous "power law graphs". Mihail and Papadimitriou (2002) argued that for randomly generated graphs satisfying a power law degree distribution, spectral analysis of the adjacency matrix simply produces the neighborhoods of the high degree nodes as its eigenvectors, and thus miss any embedded structure. We present a generalization of their model, incorporating latent structure, and prove that after applying our transformation, spectral analysis succeeds in recovering the latent structure with high probability.

We are interested in finding natural communities in large-scale linked networks. Our ultimate goal is to track changes over time in such communities. For such temporal tracking, we require a clustering algorithm that is relatively stable under small perturbations of the input data. We have developed an efficient, scalable agglomerative strategy and applied it to the citation graph of the NEC CiteSeer database (250,000 papers; 4.5 million citations). Agglomerative clustering techniques are known to be unstable on data in which the community structure is not strong. We find that some communities are essentially random and thus unstable while others are natural and will appear in most clusterings. These natural communities will enable us to track the evolution of communities over time.

The design of an extensible system is discussed in which the behavior of physical objects is simulated from their models. Complex objects can be defined in a multiplicity of domains, including their geometric shape, their dynamic response to applied forces, and their controlled behavior. In response to unforeseen changes, e.g., for unexpected collisions, the object models are modified automatically during the simulation.

The motion planning problem for multiple objects is studied where an object is a 2-dimensional region whose sides are line segments parallel to the axes of ${\bf R}^2 $ and translations are the only motions allowed. Towards this end we analyze the structure of configuration space, the space of points that correspond to positions of the objects. In particular, we consider CONNECTED, the set of all points in configuration space that correspond to configurations of the objects where the objects form one connected component. We show that CONNECTED consists of faces of various dimensions such that if there is a path in CONNECTED between two 0-dimensional faces (vertices) of CONNECTED then there is a path between them along 1-dimensional faces (edges) of CONNECTED. It is known that if there is a motion between two configurations of CONNECTED then there is a path in CONNECTED between the configurations. Thus the existence of a motion between two vertices of CONNECTED implies a motion corresponding to a path along edges of CONNECTED. Hence the motion planning problem is reduced from a search of a high dimensional space to a graph searching problem. From this result it is shown that motion planning for rectangles in a rectangular boundary is in PSPACE. Since it is known that the problem is PSPACE-hard, we conclude it is a PSPACE-complete problem.

The mover’s problem is the following: can an object in 3-dimensional space be moved from one given position to another while avoiding obstacles? It is known that the general version of this problem involving objects with movable joints is PSPACE hard, even for a simple tree-like structure moving in a 3-dimensional region. In this paper, we investigate a 2-dimensional mover’s problem in which the object is a robot arm with an arbitrary number of joints. In particular, we give a polynomial time algorithm for moving an arm confined within a circle from one given configuration to another. We also give a polynomial time algorithm for moving the arm from its initial position to a position in which the end of the arm reaches a given point within the circle. Finally, we show that 148 circles suffice to cover the boundary of the reachable region of a joint in an arm enclosed in a circle and that the boundary can be computed in polynomial time.

This paper is motivated by questions concerning the planning of motion in robotics. In particular, it is concerned with the motion of planar linkages from the complexity point of view. There are two main results. First, a planar linkage can be constrained to stay inside a bounded region whose boundary consists of straight lines by the addition of a polynomial number of new links. Second, the question of whether a planar linkage in some initial configuration can be moved so that a designated joint reaches a given point in the plane is PSPACE-hard.

We present parallel algorithms to compute the determinant and characteristic polynomial of n×n-matrices and the gcd of polynomials of degree ≤n. The algorithms use parallel time O(log2n) and a polynomial number of processors. We also give a fast parallel Las Vegas algorithm for the rank of matrices. All algorithms work over arbitrary fields.

The classical mover's problem is the following: can a rigid object in 3-dimensional space be moved from one given position to another while avoiding obstacles? It is known that a more general version of this problem involving objects with movable joints is PSPACE-complete, even for a simple tree-like structure. In this paper, we investigate a 2-dimensional mover's problem in which the object being moved is a robot arm with an arbitrary number of joints. We reduce the mover's problem for arms constrained to move within bounded regions whose boundaries are made up of straight lines to the mover's problem for a more complex linkage that is not constrained. We prove that the latter problem is PSPACE-hard even in 2-dimensional space and then turn to special cases of the mover's problem for arms. In particular, we give a polynomial time algorithm for moving an arm confined within a circle from one given configuration to another. We also give a polynomial time algorithm for moving the arm from its initial position to a position in which the end of the arm reaches a given point within the circle.

A variety of models have been proposed for the study of synchronous parallel computation. We review these models and study further some prototype problems. We distinguish two classes of models, fixed connection networks and models based on a shared memory. Routing is the prototype problem for the networks. In particular, routing provides the basis for simulating the more powerful shared memory models. We show that a simple but important class of deterministic strategies (oblivious routing) is necessarily inefficient with respect to worst case analysis. Routing can be viewed as a special case of sorting and the existence of a deterministic O(logn) routing or sorting algorithm for an n processor fixed connection network remains open. However, if we consider the more powerful class of shared memory models, we are “almost” able to achieve such an efficient sort via Valiant's parallel merging algorithm. Within a spectrum of models, we show that log log n - log log r is asymptotically optimal for rn processors to merge two sorted lists of n elements.

The present paper shows how to find a minimal edge coloring of a bipartite graph with E edges and V vertices in time $O(E\log V)$.

A permutation group on n letters may always be represented by a small set of generators, even though its size may be exponential in n. We show that it is practical to use such a representation since many problems such as membership testing, equality testing, and inclusion testing are decidable in polynomial time. In addition, we demonstrate that the normal closure of a subgroup can be computed in polynomial time, and that this proceaure can be used to test a group for solvability. We also describe an approach to computing the intersection of two groups. The procedures and techniques have wide applicability and have recently been used to improve many graph isomorphism algorithms.

It is shown that every deterministic multitape Turing machine of time complexity t ( n ) can be simulated by a deterministic Turing machine of tape complexity t ( n )/log t ( n ). Consequently, for tape constructable t ( n ), the class of languages recognizable by multitape Turing machines of time complexity t ( n ) is strictly contained in the class of languages recognized by Turing machines of tape complexity t ( n ). In particular the context-sensitive languages cannot be recognized in linear time by deterministic multitape Turing machines.

Trees in an n-node forest are merged according to instructions in a given sequence, while other instructions in the sequence ask for the lowest common ancestor of pairs of nodes. We show that any sequence of $O(n)$ such instructions can be processed “on-line” in $O(n\log n)$ steps on a random access computer. If we can accept our answer “off-line”, that is, no answers need to be produced until the entire sequence of instructions has been seen, then we may perform the task in $O(n\alpha (n))$ steps, where $\alpha (n)$ is the very slowly growing inverse Ackermann function defined in [14]. A third algorithm solves a problem of intermediate complexity. We require the answers on-line, but we assume that all tree merging instructions precede the information requests. This algorithm requires $O(n \log \log n)$ time. We apply the first on-line algorithm to a problem in code optimization, that of computing immediate dominators in a reducible flow graph. We show how this computation can be performed in $O(n\log n)$ steps.

The isomorphism problem for graphs G1 and G2 is to determine if there exists a one-to-one mapping of the vertices of G1 onto the vertices of G2 such that two vertices of G1 are adjacent if and only if their images in G2 are adjacent. In addition to determining the existence of such an isomorphism, it is useful to be able to produce an isomorphism-inducing mapping in the case where one exists.

This paper describes an efficient algorithm to determine whether an arbitrary graph G can be embedded in the plane. The algorithm may be viewed as an iterative version of a method originally proposed by Auslander and Parter and correctly formulated by Goldstein. The algorithm used depth-first search and has O ( V ) time and space bounds, where V is the number of vertices in G . An ALGOL implementation of the algorithm succesfully tested graphs with as many as 900 vertices in less than 12 seconds.

Trees in an n node forest are to be merged according to instructions in a given sequence, while other instructions in the sequence ask for the lowest common ancestor of pairs of nodes. We show that any sequence of O(n) instructions can be processed “on line” in O(n log n) steps on a random access computer.

The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal computation for a dual problem. An nxm by mxp matrix product is shown to be the dual of an nxp by pxm or an mxn by nxp matrix product implying that each of the matrix products requires the same number of multiplications to compute. Finally an algorithm for computing a single bilinear form over a noncommutative ring with a minimum number of multiplications is derived by considering a dual problem.

The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to $(m + n)\sqrt n $.

The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal computation for a dual problem. An $n \times m$ by $m \times p$ matrix product is shown to be the dual of an $n \times p$ by $p \times m$ or an $m \times n$ by $n \times p$ matrix product, implying that each of the matrix products requires the same number of multiplications to compute. Finally, an algorithm for computing a single bilinear form over a noncommutative ring with a minimum number of multiplications is derived by considering a dual problem.

An algorithm for dividing a graph into triconnected components is presented. When implemented on a random access computer, the algorithm requires $O(V + E)$ time and space to analyze a graph with V vertices and E edges. The algorithm is both theoretically optimal to within a constant factor and efficient in practice.

This paper considers the problem of merging sets formed from a total of n items in such a way that at any time, the name of a set containing a given item can be ascertained. Two algorithms using different data structures are discussed. The execution times of both algorithms are bounded by a constant times $nG(n)$, where $G(n)$ is a function whose asymptotic growth rate is less than that of any finite number of logarithms of n.

The purpose of this paper is to outline the theory of computational complexity which has emerged as a comprehensive theory during the last decade.This theory is concerned with the quantitative aspects of computations and its central theme is the measuring of the difficulty of computing functions.The paper concentrates on the study of computational complexity measures defined for all computable functions and makes no attempt to survey the whole field exhaustively nor to present the material in historical order.Rather it presents the basic concepts, results, and techniques of computational complexity from a new point of view from which the ideas are more easily understood and fit together as a coherent whole.

It is shown that if the family of languages accepted by a closed class of two-way balloon automata is closed under length-preserving homomorphism, then this family is an abstract family of languages (AFL) closed under intersection and e-free substitution.It is then proved that the family of languages accepted by the closed class of (nonerasing) (deterministic) stack acceptors is such a family.

A nested stack automaton is a generalization of the pushdown automaton. Basically, the nested stack automaton consists of an input tape, a finite control, and a single pushdown list. However, the nested stack automaton can access symbols in the interior of the stack in a read-only mode and create new stacks nested (to arbitrary depths) within the main stack, subject to the restriction that the stack head may not move up a stack without first having destroyed all stacks created at that level. The importance of the model is that the class of languages accepted is precisely the indexed languages. The indexed languages have most of the properties of the context- free languages, i.e., derivation trees, recursiveness, decidable emptiness problem, closed under concatenation, Kleene closure, homomorphisms, inverse homomorphisms, and intersection with regular sets. Furthermore, the indexed grammars are capable of exhibiting syntactic features in algorithmic programming languages not representable by context-free grammars.

Classes of tape-bounded Turing machines similar to the on-line and off-line Turing machines, but without the restrictions that each machine halt and be deterministic, are studied. It is shown that the lower bounds on tape complexity of [1] depend on neither the halting assumption nor determinism. The existence of a dense hierarchy of complexity classes likewise does not depend on the halting assumption, and it is shown that below log n tape complexity there exists a dense hierarchy of complexity classes for two-way nondeterministic devices. It is also shown that the complexity classes of one-way, nondeterministic machines below linear large complexity are not closed under complementation and are larger that the corresponding deterministic complexity class.

Four types of balloon automata (defined by one- or two-way input and deterministic or nondeterministic finite control) and closed classes of balloon automata were previously defined by the authors. A set of closed classes, one for each of the four types, is called a family if the classes use their infinite storage in the same way. The recursiveness and solvability of the emptiness problem for closed classes are investigated in the present paper. It is shown that in many cases the solvability of one of these questions for one closed class in a family implies that some other question are solvable for the closed classes of that family.

It is shown that if a language L is recognized by a (nondeterministic) single-tape Turing machine of time complexity T ( n ), then L is recognized by a (nondeterministic) offline Turing machine of tape complexity T 1/2 ( n ). If T ( n ) ≥ n 2 ;, L is recognized by a (nondeterministic) single-tape Turing machine of tape complexity T 1/2 ( n ). If a language L is recognized by a (nondeterministic) offline Turing machine of time complexity ( T ( n ), then L is recognized by a (nondeterministic) offline Turing machine of tape complexity ( T ( n ) log n ) 1/2 and by a (nondeterministic) single-tape Turing machine of that tape complexity if T ( n ) ≥ n 2 /log n .

Various encoding schemes are examined from the point of view of minimizing the mean magnitude error of a signal caused by transmission through a binary symmetric channel. A necessary property is developed for optimal codes for any binary symmetric channel and any set of quantization levels. The class of optimal codes is found for the case where the probability of error is small but realistic. This class of codes includes the natural numbering and some unit distance codes, among which are the Gray codes.

An algorithm is developed for synthesizing networks which realize Boolean switching functions through the use of a minimum number of threshold logic elements. A switching function is represented by a matrix and the algorithm is based on the principle that the removal of the positive linear dependences from the rows of this matrix results in a linearly separable function. The positive linear dependences are removed by adding columns to the matrix, each column representing the output of a threshold logic element in the network. The added columns in effect transform a nonseparable function into a sparable function a higher dimensional space. The algorithm is illustrated with examples of the synthesis of both single and multiple output networks. The technique is not restricted to completely specified functions.