Distributed Adaptive Learning with Multiple Kernels in Diffusion Networks

We propose an adaptive scheme for distributed learning of nonlinear functions by a network of nodes. The proposed algorithm consists of a local adaptation stage utilizing multiple kernels with projections onto hyperslabs and a diffusion stage to achieve consensus on the estimates over the whole network. Multiple kernels are incorporated to enhance the approximation of functions with several high and low frequency components common in practical scenarios. We provide a thorough convergence analysis of the proposed scheme based on the metric of the Cartesian product of multiple reproducing kernel Hilbert spaces. To this end, we introduce a modified consensus matrix considering this specific metric and prove its equivalence to the ordinary consensus matrix. Besides, the use of hyperslabs enables a significant reduction of the computational demand with only a minor loss in the performance. Numerical evaluations with synthetic and real data are conducted showing the efficacy of the proposed algorithm compared to the state of the art schemes.Comment: Double-column 15 pages, 10 figures, submitted to IEEE Trans. Signal Processin

A Distributed Algorithm for Identifying Information Hubs in Social Networks

Abstract—This paper addresses the problem of identifying the top-k information hubs in a social network. Identifying topk information hubs is crucial for many applications such as advertising in social networks where advertisers are interested in identifying hubs to whom free samples can be given. Existing solutions are centralized and require time stamped information about pair-wise user interactions and can only be used by social network owners as only they have access to such data. Existing distributed algorithms suffer from poor accuracy. In this paper, we propose a new algorithm to identify information hubs that preserves user privacy. Our method can identify hubs without requiring a central entity to access the complete friendship graph. We achieve this by fully distributing the computation using the Kempe-McSherry algorithm, while addressing user privacy concerns. We evaluate the effectiveness of our proposed technique using three real-world data set; The first two are Facebook data sets containing about 6 million users and more than 40 million friendship links. The third data set is from Twitter and comprises of a little over 2 million users. The results of our analysis show that our algorithm is up to 50 % more accurate than existing algorithms. Results also show that the proposed algorithm can estimate the rank of the top-k information hubs users more accurately than existing approaches. Index Terms—Social network analysis; spectral graph analysis; eigendecomposition; information hubs