Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBatch kernel SOM and related Laplacian methods for social network analysis
112
0
0.0
(
0
)
Added by
Nathalie Villa
Publication date
2008
fields
Mathematical Statistics
and research's language is
English
Authors
Romain Boulet
Ask ChatGPT about the research
No Arabic abstract
Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts.
rate research
Read More
Let $X:=(X_1, ldots, X_p)$ be random objects (the inputs), defined on some probability space $(Omega,{mathcal{F}}, mathbb P)$ and valued in some measurable space $E=E_1timesldots times E_p$. Further, let $Y:=Y = f(X_1, ldots, X_p)$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $mathbb{H}$ ($mathbb{H}$ could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when $Yinmathbb R$ ), when the output belongs to $mathbb{H}$. These indices have very nice properties. First, they are invariant. under isometry and scaling. Further they can be, as in dimension $1$, easily estimated by using the so-called Pick and Freeze method. We investigate the asymptotic behaviour of such estimation scheme.
Network tomography has been regarded as one of the most promising methodologies for performance evaluation and diagnosis of the massive and decentralized Internet. This paper proposes a new estimation approach for solving a class of inverse problems in network tomography, based on marginal distributions of a sequence of one-dimensional linear projections of the observed data. We give a general identifiability result for the proposed method and study the design issue of these one dimensional projections in terms of statistical efficiency. We show that for a simple Gaussian tomography model, there is an optimal set of one-dimensional projections such that the estimator obtained from these projections is asymptotically as efficient as the maximum likelihood estimator based on the joint distribution of the observed data. For practical applications, we carry out simulation studies of the proposed method for two instances of network tomography. The first is for traffic demand tomography using a Gaussian Origin-Destination traffic model with a power relation between its mean and variance, and the second is for network delay tomography where the link delays are to be estimated from the end-to-end path delays. We compare estimators obtained from our method and that obtained from using the joint distribution and other lower dimensional projections, and show that in both cases, the proposed method yields satisfactory results.
Although social neuroscience is concerned with understanding how the brain interacts with its social environment, prevailing research in the field has primarily considered the human brain in isolation, deprived of its rich social context. Emerging work in social neuroscience that leverages tools from network analysis has begun to pursue this issue, advancing knowledge of how the human brain influences and is influenced by the structures of its social environment. In this paper, we provide an overview of key theory and methods in network analysis (especially for social systems) as an introduction for social neuroscientists who are interested in relating individual cognition to the structures of an individuals social environments. We also highlight some exciting new work as examples of how to productively use these tools to investigate questions of relevance to social neuroscientists. We include tutorials to help with practical implementation of the concepts that we discuss. We conclude by highlighting a broad range of exciting research opportunities for social neuroscientists who are interested in using network analysis to study social systems.
Several statistics-based detectors, based on unimodal matrix models, for determining the number of sources in a field are designed. A new variance ratio statistic is proposed, and its asymptotic distribution is analyzed. The variance ratio detector is shown to outperform the alternatives. It is shown that further improvements are achievable via optimally selected rotations. Numerical experiments demonstrate the performance gains of our detection methods over the baseline approach.
In order to maintain consistent quality of service, computer network engineers face the task of monitoring the traffic fluctuations on the individual links making up the network. However, due to resource constraints and limited access, it is not possible to directly measure all the links. Starting with a physically interpretable probabilistic model of network-wide traffic, we demonstrate how an expensively obtained set of measurements may be used to develop a network-specific model of the traffic across the network. This model may then be used in conjunction with easily obtainable measurements to provide more accurate prediction than is possible with only the inexpensive measurements. We show that the model, once learned may be used for the same network for many different periods of traffic. Finally, we show an application of the prediction technique to create relevant control charts for detection and isolation of shifts in network traffic.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
