0000000000139725
AUTHOR
Karl Skretting
Graph Topology Learning and Signal Recovery Via Bayesian Inference
The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…
Robust Graph Topology Learning and Application in Stock Market Inference
In many applications, there are multiple interacting entities, generating time series of data over the space. To describe the relation within the set of data, the underlying topology may be used. In many real applications, not only the signal/data of interest is measured in noise, but it is also contaminated with outliers. The proposed method, called RGTL, infers the graph topology from noisy measurements and removes these outliers simultaneously. Here, it is assumed that we have no information about the space graph topology, while we know that graph signal are sampled consecutively in time and thus the graph in time domain is given. The simulation results show that the proposed algorithm h…
Topology Inference and Signal Representation Using Dictionary Learning
This paper presents a Joint Graph Learning and Signal Representation algorithm, called JGLSR, for simultaneous topology learning and graph signal representation via a learned over-complete dictionary. The proposed algorithm alternates between three main steps: sparse coding, dictionary learning, and graph topology inference. We introduce the “transformed graph” which can be considered as a projected graph in the transform domain spanned by the dictionary atoms. Simulation results via synthetic and real data show that the proposed approach has a higher performance when compared to the well-known algorithms for joint undirected graph topology inference and signal representation, when there is…