Smooth Graphs for Visual Exploration of Higher-Order State Transitions

Abstract

Fig. 1. A smooth graph representation of a labeled biological time-series. Each ring represents a state, and the edges between states visualize the state transitions. This graph uses smooth curves to explicitly visualize third order transitions, so that each curved edge represents a unique sequence of four successive states. The orange node is part of a selection set, and all transitions matching the current selection are highlighted in orange.Abstract-In this paper, we present a new visual way of exploring state sequences in large observational time-series. A key advantage of our method is that it can directly visualize higher-order state transitions. A standard first order state transition is a sequence of two states that are linked by a transition. A higher-order state transition is a sequence of three or more states where the sequence of participating states are linked together by consecutive first order state transitions. Our method extends the current state-graph exploration methods by employing a two dimensional graph, in which higher-order state transitions are visualized as curved lines. All transitions are bundled into thick splines, so that the thickness of an edge represents the frequency of instances. The bundling between two states takes into account the state transitions before and after the transition. This is done in such a way that it forms a continuous representation in which any subsequence of the timeseries is represented by a continuous smooth line. The edge bundles in these graphs can be explored interactively through our incremental selection algorithm. We demonstrate our method with an application in exploring labeled time-series data from a biological survey, where a clustering has assigned a single label to the data at each time-point. In these sequences, a large number of cyclic patterns occur, which in turn are linked to specific activities. We demonstrate how our method helps to find these cycles, and how the interactive selection process helps to find and investigate activities.

HoNVis: Visualizing and exploring higher-order networks

“…HoN visualization is sporadic in the literature. Blaas et al [6] proposed to visualize higher-order transitions by connecting nodes using higher-order curves. By following a smooth curve from one end to the other, one can identify which nodes are associated with higher-order transitions and what are the orders of the nodes.…”

“…We display the previous ports as circles to the left side of the higher-order nodes, as shown in Figure 3 (b). For each higher-order node, we draw a smooth high-order CatmullRom spline to connect its corresponding ports in the visit order for clear observation, as suggested by Blaas et al [6]. The curves exhibit color transition from red to blue, indicating the visit order of ports (i.e., red indicates the port visited first and blue indicates the current port).…”

TimeClassifier: a visual analytic system for the classification of multi-dimensional time series data

“…Spherical coordinates have been applied to show common behavioural cycles [14] and extended to show them in relation to other sensor channels by combining with parallel coordinates [36]. Further attributes have been derived to abstract from the raw sensor values, including animal movement via reconstructed pseudo-tracks using a dead reckoning approach [37], and labelled behaviour to show higher-order state transitions between behaviours [5]. Unlike previous work which assists in understanding and exploring sensor data, we introduce a system for the analysis of animal behaviour through classification.…”

Exploring agent-based simulations in political science using Aggregate Temporal Graphs

“…Our work is also informed by contributions in the area of state space visualization, such as those made by Van Ham et al [30,31], Pretorius et al [24,23], and Blaas et al [5]. Recent work in this area explored the visualization of large state spaces, where traditional node-link diagrams become quickly over-cluttered and fail to support the analyst in generating insight.…”