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 graphtopologyfromagivensetofnoisymeasurementsofsignals. It is assumed that the graph signals are generated from GaussianMarkovRandomFieldprocesses. First,usingafactor 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 Maximization (EM) procedure, a filter is proposed to recover the signal from noisy measurements and an optimization problem is formulated to estimatetheunderlyinggraphtopology. Theexperimentalresults show that the proposed method has better performance whencomparedtothecurrentstate-of-the-artalgorithmswith different performance measures.
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Bayesian Topology Learning and noise removal from network data
Abstract Learning the topology of a graph from available data is of great interest in many emerging applications. Some examples are social networks, internet of things networks (intelligent IoT and industrial IoT), biological connection networks, sensor networks and traffic network patterns. In this paper, a graph topology inference approach is proposed to learn the underlying graph structure from a given set of noisy multi-variate observations, which are modeled as graph signals generated from a Gaussian Markov Random Field (GMRF) process. A factor analysis model is applied to represent the graph signals in a latent space where the basis is related to the underlying graph structure. An optimal graph filter is also developed to recover the graph signals from noisy observations. In the final step, an optimization problem is proposed to learn the underlying graph topology from the recovered signals. Moreover, a fast algorithm employing the proximal point method has been proposed to solve the problem efficiently. Experimental results employing both synthetic and real data show the effectiveness of the proposed method in recovering the signals and inferring the underlying graph.
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- NSF-PAR ID:
- 10276757
- Date Published:
- Journal Name:
- Discover Internet of Things
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2730-7239
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Background Characterizing the topology of gene regulatory networks (GRNs) is a fundamental problem in systems biology. The advent of single cell technologies has made it possible to construct GRNs at finer resolutions than bulk and microarray datasets. However, cellular heterogeneity and sparsity of the single cell datasets render void the application of regular Gaussian assumptions for constructing GRNs. Additionally, most GRN reconstruction approaches estimate a single network for the entire data. This could cause potential loss of information when single cell datasets are generated from multiple treatment conditions/disease states.
Results To better characterize single cell GRNs under different but related conditions, we propose the joint estimation of multiple networks using multiple signed graph learning (scMSGL). The proposed method is based on recently developed graph signal processing (GSP) based graph learning, where GRNs and gene expressions are modeled as signed graphs and graph signals, respectively. scMSGL learns multiple GRNs by optimizing the total variation of gene expressions with respect to GRNs while ensuring that the learned GRNs are similar to each other through regularization with respect to a learned signed consensus graph. We further kernelize scMSGL with the kernel selected to suit the structure of single cell data.
Conclusions scMSGL is shown to have superior performance over existing state of the art methods in GRN recovery on simulated datasets. Furthermore, scMSGL successfully identifies well-established regulators in a mouse embryonic stem cell differentiation study and a cancer clinical study of medulloblastoma.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s43926-021-00011-w
