arXiv subjects

Meng Ma

Publications and source records attributed to Meng Ma.

21 records · Page 2Linked to original sources

arXiv2018

Kernel-based Inference of Functions over Graphs

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.

stat.ML↗

arXiv2016

Kernel-based Reconstruction of Graph Signals

A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data. Estimating such signals in all vertices given noisy observations of their values on a subset of vertices has been extensively analyzed in the literature of signal processing on graphs (SPoG). This paper advocates kernel regression as a framework generalizing popular SPoG modeling and reconstruction and expanding their capabilities. Formulating signal reconstruction as a regression task on reproducing kernel Hilbert spaces of graph signals permeates benefits from statistical learning, offers fresh insights, and allows for estimators to leverage richer forms of prior information than existing alternatives. A number of SPoG notions such as bandlimitedness, graph filters, and the graph Fourier transform are naturally accommodated in the kernel framework. Additionally, this paper capitalizes on the so-called representer theorem to devise simpler versions of existing Thikhonov regularized estimators, and offers a novel probabilistic interpretation of kernel methods on graphs based on graphical models. Motivated by the challenges of selecting the bandwidth parameter in SPoG estimators or the kernel map in kernel-based methods, the present paper further proposes two multi-kernel approaches with complementary strengths. Whereas the first enables estimation of the unknown bandwidth of bandlimited signals, the second allows for efficient graph filter selection. Numerical tests with synthetic as well as real data demonstrate the merits of the proposed methods relative to state-of-the-art alternatives.

stat.ML↗

arXiv2014

Study on Downlink Spectral Efficiency in Orthogonal Frequency Division Multiple Access Systems

In previous studies on the capacity of orthogonal frequency division multiple access (OFDMA) systems, it is usually assumed that co-channel interference (CCI) from adjacent cells is a Gaussian-distributed random variable. However, very-little work shows that the Gaussian assumption does not hold true in OFDMA systems. In this paper, the statistical property of CCI in downlink OFDMA systems is studied, and spectral efficiency of downlink OFDMA system is analyzed based on the derived statistical model. First, the probability density function (PDF) of CCI in downlink OFDMA cellular systems is studied with the considerations of path loss, multipath fading and Gaussian-like transmit signals. Moreover, some closed-form expressions of the PDF are obtained for special cases. The derived results show that the PDFs of CCI are with a heavy tail, and significantly deviate from the Gaussian distribution. Then, based on the derived statistical properties of CCI, the downlink spectral efficiency is derived. Numerical and simulation results justify the derived statistical CCI model and spectral efficiency.

cs.IT↗