Visibility graph for time series prediction and image classification: a review

Abstract

The analysis of time series and images is significant across different fields due to their widespread applications. In the past few decades, many approaches have been developed, including data-driven artificial intelligence methods, mechanism-driven physical methods, and hybrid mechanism and data-driven models. Complex networks have been used to model numerous complex systems due to its characteristics, including time series prediction and image classification. In order to map time series and images into complex networks, many visibility graph algorithms have been developed, such as horizontal visibility graph, limited penetrable visibility graph, multiplex visibility graph, and image visibility graph. The family of visibility graph algorithms will construct different types of complex networks, including (un-) weighted, (un-) directed, and (single-) multi-layered networks, thereby focusing on different kinds of properties. Different types of visibility graph algorithms will be reviewed in this paper. Through exploring the topological structure and information in the network based on statistical physics, the property of time series and images can be discovered. In order to forecast (multivariate) time series, several variations of local random walk algorithms and different information fusion approaches are applied to measure the similarity between nodes in the network. Different forecasting frameworks are also proposed to consider the information in the time series based on the similarity. In order to classify the image, several machine learning models (such as support vector machine and linear discriminant) are used to classify images based on global features, local features, and multiplex features. Through various simulations on a variety of datasets, researchers have found that the visibility graph algorithm outperformed existing algorithms, both in time series prediction and image classification. Clearly, complex networks are closely connected with time series and images by visibility graph algorithms, rendering complex networks to be an important tool for understanding the characteristics of time series and images. Finally, we conclude in the last section with future outlooks for the visibility graph.

Automatic snoring detection using a hybrid 1D–2D convolutional neural network

“…Therefore, in future work, we will improve further the robustness and generalization of the current snore detection algorithm by adding more expiration snore sounds and considering more snore events due to distinct places of pharyngeal constriction. Furthermore, the original VG method could be replaced by other methods in VG family, which includes HVG, limited penetrable visibility graph (LPVG) and so on, for improvement of noise resistance and computation efficiency 57 . In addition, the VG map used in this study only contains the 0 and 1 elements representing whether the features in different points are visible.…”

Topological data analysis and image visibility graph for texture classification

“…Several visibility graph approaches map time series and images into graphs. These methods include horizontal, natural, multiplex, image natural, and image horizontal visibility graphs [38]. The visibility graph algorithm [39] is a significant method used in the conversion of time series and images into graph representation.…”

“…The INVG and IHVG can obtain topological plots, global and local features, and multiplex features from a graph [16]. Local properties look at small parts of the graph, while global properties give information about the topology of the whole graph [38]. Horizontal visibility graph with N vertices is in bijection with degree distribution, hence degree distribution is significant for global characteristics [40].…”

Graph- and Machine-Learning-Based Texture Classification

“…This is because the visibility graph technique establishes strong links between complex networks, time series, and images. There are different types of visibility graphs, like horizontal visibility graphs, natural visibility graphs, multiplex visibility graphs, image horizontal visibility graphs, and image natural visibility graphs, that can be used to map time series and images into complex networks [34].…”