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.
The seeding strategy is a key component for seed set expansion algorithms. GCE selects maximal cliques as the seeds @cite_27 . discover that an independent set of high-degree vertices, which they called spread hubs" outperforms Graclus centers, local egonets, and random seeding strategies @cite_10 . Kloumann and Kleinberg @cite_1 compare random seeds with high degree seeds, and discover that random seeds are superior to high degree seeds, and they suggest domain experts provide seeds with a diverse degree distribution.
@cite_1 @cite_27 @cite_10
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Seeding - the task of finding initial cluster centers - is critical in obtaining high-quality clusterings for k-Means. However, k-means++ seeding, the state of the art algorithm, does not scale well to massive datasets as it is inherently sequential and requires k full passes through the data. It was recently shown that Markov chain Monte Carlo sampling can be used to efficiently approximate the seeding step of k-means++. However, this result requires assumptions on the data generating distribution. We propose a simple yet fast seeding algorithm that produces *provably* good clusterings even *without assumptions* on the data. Our analysis shows that the algorithm allows for a favourable trade-off between solution quality and computational cost, speeding up k-means++ seeding by up to several orders of magnitude. We validate our theoretical results in extensive experiments on a variety of real-world data sets. Optimal spaced seeds were introduced by the theoretical computer science community to bioinformatics to effectively increase homology search sensitivity. They are now serving thousands of homology search queries daily. While dozens of papers have been published on optimal spaced seeds since their invention, many fundamental questions still remain unanswered. In this paper, we settle several open questions in this area. Specifically, we prove that when the length of a non-uniformly spaced seed is bounded by an exponential function of the seed weight, the seed outperforms strictly the traditional consecutive seed in both (i) the average number of non-overlapping hits and (ii) the asymptotic hit probability. Then, we study the computation of the hit probability of a spaced seed, solving three more open questions: (iii) hit probability computation in a uniform homologous region is NP-hard and (iv) it admits a PTAS; (v) the asymptotic hit probability is computable in exponential time in seed length, independent of the homologous region length. Clustering at multiple critical scales may be common for plants since many different factors and processes may cause clustering. This is especially true for tropical rain forests for which theories explaining species coexistence and community structure rest heavily on spatial patterns. We used point pattern analysis to analyze the spatial structure of Shorea congestiflora, a dominant species in a 25-ha forest dynamics plot in a rain forest at Sinharaja World Heritage Site (Sri Lanka), which apparently shows clustering at several scales. We developed cluster processes incorporating two critical scales of clustering for exploring the spatial structure of S. congestiflora and interpret it in relation to factors such as competition, dispersal limitation, recruitment limitation, and Janzen-Connell effects. All size classes showed consistent large-scale clustering with a cluster radius of ;25 m. Inside the larger clusters, small-scale clusters with a radius of 8 m were evident for recruits and saplings, weak for intermediates, and disappeared for adults. The pattern of all trees could be divided into two independent patterns: a random pattern (nearest neighbor distance . 8m ) comprising ;12 of the trees and a nested double-cluster pattern. This finding suggests two independent recruitment and or seed dispersal mechanisms. Saplings were several times as abundant as recruits and may accumulate several recruit generations. Recruits were only weakly associated with adults and occupied about half of the large-scale clusters, but saplings almost all. This is consistent with recruitment limitation. For ;70 (95 ) of all juveniles the nearest adult was less than 26 m away (53 m), suggesting a dispersal limitation that may also be related to the critical large-scale clustering. Our example illustrates the manner in which the use of a specific and complex null hypothesis of spatial structure in point pattern analysis can help us better understand the biology of a species and generate specific hypotheses to be further investigated in the field. Identifying the optimal set of individuals to first receive information ('seeds') in a social network is a widely-studied question in many settings, such as the diffusion of information, microfinance programs, and new technologies. Numerous studies have proposed various network-centrality based heuristics to choose seeds in a way that is likely to boost diffusion. Here we show that, for some frequently studied diffusion processes, randomly seeding s plus x individuals can prompt a larger cascade than optimally targeting the best s individuals, for a small x. We prove our results for large classes of random networks, but also show that they hold in simulations over several real-world networks. This suggests that the returns to collecting and analyzing network information to identify the optimal seeds may not be economically significant. Given these findings, practitioners interested in communicating a message to a large number of people may wish to compare the cost of network-based targeting to that of slightly expanding initial outreach.