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.
Spielman and Teng @cite_16 use degree-normalized, personalized PageRank (DN PageRank) with respect to the start seed and do truncation on small values, leading to the PageRank Nibble method @cite_18 . And the DN PageRank is adopted by several PageRank-based clustering algorithms @cite_22 @cite_8 , which are competitive with a sophisticated and popular algorithm METIS @cite_3 . Kloumann and Kleinberg @cite_1 evaluate different variations of PageRank, and find that the standard PageRank yields better performance than the DN PageRank.
@cite_18 @cite_22 @cite_8 @cite_1 @cite_3 @cite_16
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In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks. We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter. For global PageRank, we assume that the social network has n nodes, and m adversarially chosen edges arrive in a random order. We show that with a reset probability of e, the expected total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is [EQUATION]. This is significantly better than all known bounds for incremental PageRank. For instance, if we naively recompute the PageRanks as each edge arrives, the simple power iteration method needs [EQUATION] total time and the Monte Carlo method needs O(mn e) total time; both are prohibitively expensive. We also show that we can handle deletions equally efficiently. We then study the computation of the top k personalized PageRanks starting from a seed node, assuming that personalized PageRanks follow a power-law with exponent α q ln n random walks starting from every node for large enough constant q (using the approach outlined for global PageRank), then the expected number of calls made to the distributed social network database is O(k (R(1-α) α)). We also present experimental results from the social networking site, Twitter, verifying our assumptions and analyses. The overall result is that this algorithm is fast enough for real-time queries over a dynamic social network. In a network, identifying all vertices whose PageRank is more than a given threshold value Δ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem. When given a directed network G=(V,E), a threshold value Δ, and a positive constant c>3, with probability 1−o(1), our algorithm will return a subset S⊆V with the property that S contains all vertices of PageRank at least Δ and no vertex with PageRank less than Δ c. The running time of our algorithm is always @math . In addition, our algorithm can be efficiently implemented in various network access models including the Jump and Crawl query model recently studied by [6], making it suitable for dealing with large social and information networks. As part of our analysis, we show that any algorithm for solving this problem must have expected time complexity of @math . Thus, our algorithm is optimal up to logarithmic factors. Our algorithm (for identifying vertices with significant PageRank) applies a multi-scale sampling scheme that uses a fast personalized PageRank estimator as its main subroutine. For that, we develop a new local randomized algorithm for approximating personalized PageRank which is more robust than the earlier ones developed by Jeh and Widom [9] and by Andersen, Chung, and Lang [2]. Since the publication of Brin and Page's paper on PageRank, many in the Web community have depended on PageRank for the static (query-independent) ordering of Web pages. We show that we can significantly outperform PageRank using features that are independent of the link structure of the Web. We gain a further boost in accuracy by using data on the frequency at which users visit Web pages. We use RankNet, a ranking machine learning algorithm, to combine these and other static features based on anchor text and domain characteristics. The resulting model achieves a static ranking pairwise accuracy of 67.3 (vs. 56.7 for PageRank or 50 for random). Recently, DNN model compression based on network architecture design, e.g., SqueezeNet, attracted a lot attention. No accuracy drop on image classification is observed on these extremely compact networks, compared to well-known models. An emerging question, however, is whether these model compression techniques hurt DNNs learning ability other than classifying images on a single dataset. Our preliminary experiment shows that these compression methods could degrade domain adaptation (DA) ability, though the classification performance is preserved. Therefore, we propose a new compact network architecture and unsupervised DA method in this paper. The DNN is built on a new basic module Conv-M which provides more diverse feature extractors without significantly increasing parameters. The unified framework of our DA method will simultaneously learn invariance across domains, reduce divergence of feature representations, and adapt label prediction. Our DNN has 4.1M parameters, which is only 6.7 of AlexNet or 59 of GoogLeNet. Experiments show that our DNN obtains GoogLeNet-level accuracy both on classification and DA, and our DA method slightly outperforms previous competitive ones. Put all together, our DA strategy based on our DNN achieves state-of-the-art on sixteen of total eighteen DA tasks on popular Office-31 and Office-Caltech datasets.