Abstract The purpose of network representation is to learn a set of latent features by obtaining community information from network structures to provide knowledge for machine learning tasks. Recent research has driven significant progress in network representation by employing random walks as the network sampling strategy. Nevertheless, existing approaches rely on domain-specifically rich community structures and fail in the network that lack topological information in its own domain. In this paper, we propose a novel algorithm for cross-domain network representation, named as CDNR. By generating the random walks from a structural rich domain and transferring the knowledge on the random walks across domains, it enables a network representation for the structural scarce domain as well. To be specific, CDNR is realized by a cross-domain two-layer node-scale balance algorithm and a cross-domain two-layer knowledge transfer algorithm in the framework of cross-domain two-layer random walk learning. Experiments on various real-world datasets demonstrate the effectiveness of CDNR for universal networks in an unsupervised way.
In this article we propose new methods for computing the asymptotic value for the logarithm of the partition function (free energy) for certain statistical physics models on certain type of finite graphs, as the size of the underlying graph goes to infinity. The two models considered are the hard-core (independent set) model when the activity parameter λ is small, and also the Potts (q-coloring) model. We only consider the graphs with large girth. In particular, we prove that asymptotically the logarithm of the number of independent sets of any r-regular graph with large girth when rescaled is approximately constant if r ≤ 5. For example, we show that every 4-regular n-node graph with large girth has approximately (1.494…)n-many independent sets, for large n. Further, we prove that for every r-regular graph with r ≥ 2, with n nodes and large girth, the number of proper q ≥ r + 1 colorings is approximately @math n, for large n. We also show that these results hold for random regular graphs with high probability (w.h.p.) as well. As a byproduct of our method we obtain simple algorithms for the problem of computing approximately the logarithm of the number of independent sets and proper colorings, in low degree graphs with large girth. These algorithms are deterministic and use certain correlation decay properties for the corresponding Gibbs measures, and its implications to uniqueness of the Gibbs measures on the infinite trees, as well as some simple cavity trick which is well known in the physics and the Markov chain sampling literature.© 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008 Preliminary version of this paper appeared in Proceedings of the Seventeenth ACM-SIAM Symposium on Discrete Algorithms 2006. ArXive version. Identifying the same individual across different scenes is an important yet difficult task in intelligent video surveillance. Its main difficulty lies in how to preserve similarity of the same person against large appearance and structure variation while discriminating different individuals. In this paper, we present a scalable distance driven feature learning framework based on the deep neural network for person re-identification, and demonstrate its effectiveness to handle the existing challenges. Specifically, given the training images with the class labels (person IDs), we first produce a large number of triplet units, each of which contains three images, i.e. one person with a matched reference and a mismatched reference. Treating the units as the input, we build the convolutional neural network to generate the layered representations, and follow with the L 2 distance metric. By means of parameter optimization, our framework tends to maximize the relative distance between the matched pair and the mismatched pair for each triplet unit. Moreover, a nontrivial issue arising with the framework is that the triplet organization cubically enlarges the number of training triplets, as one image can be involved into several triplet units. To overcome this problem, we develop an effective triplet generation scheme and an optimized gradient descent algorithm, making the computational load mainly depend on the number of original images instead of the number of triplets. On several challenging databases, our approach achieves very promising results and outperforms other state-of-the-art approaches. HighlightsWe present a novel feature learning framework for person re-identification.Our framework is based on the maximum relative distance comparison.The learning algorithm is scalable to process large amount of data.We demonstrate superior performances over other state-of-the-arts. Representation learning has shown its effectiveness in many tasks such as image classification and text mining. Network representation learning aims at learning distributed vector representation for each vertex in a network, which is also increasingly recognized as an important aspect for network analysis. Most network representation learning methods investigate network structures for learning. In reality, network vertices contain rich information (such as text), which cannot be well applied with algorithmic frameworks of typical representation learning methods. By proving that DeepWalk, a state-of-the-art network representation method, is actually equivalent to matrix factorization (MF), we propose text-associated DeepWalk (TADW). TADW incorporates text features of vertices into network representation learning under the framework of matrix factorization. We evaluate our method and various baseline methods by applying them to the task of multi-class classification of vertices. The experimental results show that, our method outperforms other baselines on all three datasets, especially when networks are noisy and training ratio is small. The source code of this paper can be obtained from https: github.com albertyang33 TADW. This study promotes the use of statistical methods in specific classification tasks since statistical methods have certain advantages which advocate their use in pattern recognition. One central problem in statistical methods is estimation of class conditional probability density functions based on examples in a training set. In this study maximum likelihood estimation methods for Gaussian mixture models are reviewed and discussed from a practical point of view. In addition, good practices for utilizing probability densities in feature classification and selection are discussed for Bayesian and, more importantly, for non-Bayesian tasks. As a result, the use of confidence information in the classification is proposed and a method for confidence estimation is presented. The propositions are tested experimentally. Breadth First Search (BFS) is a widely used approach for sampling large graphs. However, it has been empirically observed that BFS sampling is biased toward high-degree nodes, which may strongly affect the measurement results. In this paper, we quantify and correct the degree bias of BFS. First, we consider a random graph RG(pk) with an arbitrary degree distribution pk. For this model, we calculate the node degree distribution expected to be observed by BFS as a function of the fraction f of covered nodes. We also show that, for RG(pk), all commonly used graph traversal techniques (BFS, DFS, Forest Fire, Snowball Sampling, RDS) have exactly the same bias. Next, we propose a practical BFS-bias correction procedure that takes as input a collected BFS sample together with the fraction f. Our correction technique is exact (i.e., leads to unbiased estimation) for RG(pk). Furthermore, it performs well when applied to a broad range of Internet topologies and to two large BFS samples of Facebook and Orkut networks. By removing the irrelevant and redundant features, feature selection aims to find a compact representation of the original feature with good generalization ability. With the prevalence of unlabeled data, unsupervised feature selection has shown to be effective in alleviating the curse of dimensionality, and is essential for comprehensive analysis and understanding of myriads of unlabeled high dimensional data. Motivated by the success of low-rank representation in subspace clustering, we propose a regularized self-representation (RSR) model for unsupervised feature selection, where each feature can be represented as the linear combination of its relevant features. By using L 2 , 1 -norm to characterize the representation coefficient matrix and the representation residual matrix, RSR is effective to select representative features and ensure the robustness to outliers. If a feature is important, then it will participate in the representation of most of other features, leading to a significant row of representation coefficients, and vice versa. Experimental analysis on synthetic and real-world data demonstrates that the proposed method can effectively identify the representative features, outperforming many state-of-the-art unsupervised feature selection methods in terms of clustering accuracy, redundancy reduction and classification accuracy. HighlightsA regularized self-representation (RSR) model is proposed for unsupervised feature selection.An iterative reweighted least-squares algorithm is proposed to solve the RSR model.The proposed method shows superior performance to state-of-the-art. This paper provides algorithms for predicting the size of the Expanded Search Tree (EST) of Depth-first Branch and Bound algorithms (DFBnB) for optimization tasks. The prediction algorithm is implemented and evaluated in the context of solving combinatorial optimization problems over graphical models such as Bayesian and Markov networks. Our methods extend to DFBnB the approaches provided by Knuth-Chen schemes that were designed and applied for predicting the EST size of backtracking search algorithms. Our empirical results demonstrate good predictions which are superior to competing schemes. DeepWalk is a typical representation learning method that learns low-dimensional representations for vertices in social networks. Similar to other network representation learning (NRL) models, it encodes the network structure into vertex representations and is learnt in unsupervised form. However, the learnt representations usually lack the ability of discrimination when applied to machine learning tasks, such as vertex classification. In this paper, we overcome this challenge by proposing a novel semi-supervised model, max-margin Deep-Walk (MMDW). MMDW is a unified NRL framework that jointly optimizes the max-margin classifier and the aimed social representation learning model. Influenced by the max-margin classifier, the learnt representations not only contain the network structure, but also have the characteristic of discrimination. The visualizations of learnt representations indicate that our model is more discriminative than unsupervised ones, and the experimental results on vertex classification demonstrate that our method achieves a significant improvement than other state-of-the-art methods. The source code can be obtained from https: github.com thunlp MMDW. Information network mining often requires examination of linkage relationships between nodes for analysis. Recently, network representation has emerged to represent each node in a vector format, embedding network structure, so off-the-shelf machine learning methods can be directly applied for analysis. To date, existing methods only focus on one aspect of node information and cannot leverage node labels. In this paper, we propose TriDNR, a tri-party deep network representation model, using information from three parties: node structure, node content, and node labels (if available) to jointly learn optimal node representation. TriDNR is based on our new coupled deep natural language module, whose learning is enforced at three levels: (1) at the network structure level, TriDNR exploits inter-node relationship by maximizing the probability of observing surrounding nodes given a node in random walks; (2) at the node content level, TriDNR captures node-word correlation by maximizing the co-occurrence of word sequence given a node; and (3) at the node label level, TriDNR models label-word correspondence by maximizing the probability of word sequence given a class label. The tri-party information is jointly fed into the neural network model to mutually enhance each other to learn optimal representation, and results in up to 79 classification accuracy gain, compared to state-of-the-art methods.