Fast, asymptotically efficient, recursive estimation in a Riemannian manifold

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a statistical parameter which belongs to a Riemannian manifold. Roughly, this task amounts to stochastic minimisation of a statistical divergence function. The following problem is considered : how to obtain fast, asymptotically efficient, recursive estimates, using a Riemannian stochastic optimisation algorithm with decreasing step sizes? In solving this problem, several original results are introduced. First, without any convexity assumptions on the divergence function, it is proved that, with an adequate choice of step sizes, the algorithm computes recursive estimates which achieve a fast non-asymptotic rate of convergence. Second, the asymptotic normality of these recursive estimates is proved, by employing a novel linearisation technique. Third, it is proved that, when the Fisher information metric is used to guide the algorithm, these recursive estimates achieve an optimal asymptotic rate of convergence, in the sense that they become asymptotically efficient. These results, while relatively familiar in the Euclidean context, are here formulated and proved for the first time, in the Riemannian context. In addition, they are illustrated with a numerical application to the recursive estimation of elliptically contoured distributions.Comment: updated version of draft submitted for publication, currently under revie

Holographic Schwinger Effect in Anisotropic Media

Using the guage/gravity correspondence, we discuss the holographic Schwinger effect in anisotropic backgrond. First of all, we compute the separating length of the particle-antiparticle pairs at different anisotropic background which is specified by dynamical exponent $\nu$ with the isotropic case is $\nu= 1$. Then it is found that the maximum separating length $x$ decreases with the increasing of dynamical exponent $\nu$. This can be regarded as the virtual particles become real ones more easily. Subsequently, we find that the potential barrier is reduced by dynamical exponent $\nu$, warp factor coefficient $c$ and chemical potential $\mu$ at small distance. Moreover, we also find the critical electric field is reduced by the chemical potential and dynamical exponent, but enhanced by the warp factor coefficient

Building domain-specific web collections for scientific digital libraries: A meta-search enhanced focused crawling method

Collecting domain-specific documents from the Web using focused crawlers has been considered one of the most important strategies to build digital libraries that serve the scientific community. However, because most focused crawlers use local search algorithms to traverse the Web space, they could be easily trapped within a limited sub-graph of the Web that surrounds the starting URLs and build domain-specific collections that are not comprehensive and diverse enough to scientists and researchers. In this study, we investigated the problems of traditional focused crawlers caused by local search algorithms and proposed a new crawling approach, meta-search enhanced focused crawling, to address the problems. We conducted two user evaluation experiments to examine the performance of our proposed approach and the results showed that our approach could build domain-specific collections with higher quality than traditional focused crawling techniques

Studying the Structure of Terrorist Networks: A Web Structural Mining Approach

Because terrorist organizations often operate in network forms where individual terrorists collaborate with each other to carry out attacks, we could gain valuable knowledge about the terrorist organizations by studying structural properties of such terrorist networks. However, previous studies of terrorist network structure have generated little actionable results. This is due to the difficulty in collecting and accessing reliable data and the lack of advanced network analysis methodologies in the field. To address these problems, we introduced the Web structural mining technique into the terrorist network analysis field which, to the best our knowledge, has never been done before. We employed the proposed technique on a Global Salafi Jihad network dataset collected through a large scale empirical study. Results from our analysis not only provide insights for terrorism research community but also support decision making in law-reinforcement, intelligence, and security domains to make our nation safer

SpidersRUs: Automated development of vertical search engines in different domains and languages

In this paper we discuss the architecture of a tool designed to help users develop vertical search engines in different domains and different languages. The design of the tool is presented and an evaluation study was conducted, showing that the system is easier to use than other existing tools. Categories and Subject Descriptor

Building Knowledge Management System for Researching Terrorist Groups on the Web

Nowadays, terrorist organizations have found a cost-effective resource to advance their courses by posting high-impact Web sites on the Internet. This alternate side of the Web is referred to as the “Dark Web.” While counterterrorism researchers seek to obtain and analyze information from the Dark Web, several problems prevent effective and efficient knowledge discovery: the dynamic and hidden character of terrorist Web sites, information overload, and language barrier problems. This study proposes an intelligent knowledge management system to support the discovery and analysis of multilingual terrorist-created Web data. We developed a systematic approach to identify, collect and store up-to-date multilingual terrorist Web data. We also propose to build an intelligent Web-based knowledge portal integrated with advanced text and Web mining techniques such as summarization, categorization and cross-lingual retrieval to facilitate the knowledge discovery from Dark Web resources. We believe our knowledge portal provide counterterrorism research communities with valuable datasets and tools in knowledge discovery and sharing