Tasks for multivariate network analysis

In Chap. 1, a multivariate network was defined as having two important characteristics. First, nodes are connected to each other via links; there is topological structure. Second, being multivariate, nodes and links have attributes associated with them, with these attributes having a value. In this chapter, we describe tasks associated with multivariate networks. We consider a task to be an activity that a user wishes to accomplish by interacting with a visual representation of a multivariate network. This implies that there is user intent [13], and that the network has been presented visually. At the highest level, this intent is usually described as the goal of obtaining insight about the data being studied [6]

Seeing more than the graph: evaluation of multivariate graph visualization methods.

Many real-world networks are multivariate, i.e., they have attributes associated with nodes and/or edges. Examples include social networks whose nodes represent people and edges represent relationships. There is usually information about each person (such as name, age, and gender) and the relationship (such type, duration, and strength). Besides common graph analysis tasks (such as identifying the most influential or structurally important nodes), there are more complex analyses for multivariate networks. One of these is the multivariate graph clustering, i.e., identifying clusters formed by nodes that have similar attributes and are close to each other in terms of graph distance. For instance, in social network analysis, it is interesting to sociologists whether or not people with similar characteristics (node attributes) are also connected to each other. Currently there are very few visualization methods available for such analysis. Graph and multivariate visualization have been well studied separately in the literature. Herman et al. summarized the recent work on graph visualization [3], and Wong and Bergeron covered the development in multivariate visualization [4]. However, there is relatively less work available on multivariate network visualization. Two types of approaches are commonly used. The first one is the mapping approach, which maps attributes to visual elements of a node or edge. A simple example is to map one attribute to node size and another to node color [2]. A more advanced mapping approach uses glyphs to represent node or edge attributes. One such example is to use the length and width of a rectangle node glyph to represent two node attributes [1]. The second one is the 2.5D approach: it uses the third dimension to present the multivariate information, while the graph is shown on a 2D plane. Examples include the recently proposed "GraphScape" [5], which adopts a landscape metaphor: each attribute is represented by a two-and-a-half- dimensional surface, whose height indicates its value. Each approach has its strength and weakness. The mapping approach is effective of showing numerical value using visual element such as size, but it can be difficult to compare the value of attributes represented by different elements such as size and color. The problem is alleviated by a carefully designed glyph, but visual complexity increases quickly as the number of attributes that a glyph needs to represent grows. The 2.5D approach is good at showing the distribution of attribute values over the network, but the attribute surface could introduce occlusion and affect the visibility of underlying network. In this paper, we present a study evaluating the effectiveness of these two approaches for different analysis tasks. We compare the performance of mapping and 2.5D approach in a controlled lab environment. We included both simple tasks (such as identifying nodes with the largest attribute value) and complex tasks (such as multivariate graph clustering). The performance is measured both in terms of accuracy and completion time. The results indicate that statistically mapping approach performs better for the simple tasks, while the 2.5D approach is favored in the complex task. The outcomes from this study provide some guidelines for the design of effective multivariate graph visualization for different analysis tasks

Monitoring of Complex Processes with Bayesian Networks

This chapter is about the multivariate process monitoring (detection and diagnosis) with Bayesian networks. It allows to unify in a same tool (a Bayesian network) some monitoring dedicated methods like multivariate control charts or discriminant analysis. After the context introduction, we develop in section 2, principles of process monitoring, namely fault detection and fault diagnosis. We presents classical statistical techniques to achieve these tasks. In section 3, after a presentation of Bayesian networks (with discrete and Gaussian nodes), we propose the modeling of the two tasks (detection and diagnosis) in the Bayesian network framework, unifying the two steps of the process monitoring in a sole tool, the Bayesian network. An application is given in section 4 in order to demonstrate the effectiveness of the proposed approach. This application is a benchmark problem in process monitoring: the Tennessee Eastman Process. Efficiency of the network is evaluated for detection and for diagnosis. Finally, we give conclusions on the proposed approach and outlooks concerning the use of Bayesian network for the process monitoring

Outcome contingency selectively affects the neural coding of outcomes but not of tasks

Value-based decision-making is ubiquitous in every-day life, and critically depends on the contingency between choices and their outcomes. Only if outcomes are contingent on our choices can we make meaningful value-based decisions. Here, we investigate the effect of outcome contingency on the neural coding of rewards and tasks. Participants performed a reversal-learning paradigm in which reward outcomes were contingent on trial-by-trial choices, and performed a ‘free choice’ paradigm in which rewards were random and not contingent on choices. We hypothesized that contingent outcomes enhance the neural coding of rewards and tasks, which was tested using multivariate pattern analysis of fMRI data. Reward outcomes were encoded in a large network including the striatum, dmPFC and parietal cortex, and these representations were indeed amplified for contingent rewards. Tasks were encoded in the dmPFC at the time of decision-making, and in parietal cortex in a subsequent maintenance phase. We found no evidence for contingency-dependent modulations of task signals, demonstrating highly similar coding across contingency conditions. Our findings suggest selective effects of contingency on reward coding only, and further highlight the role of dmPFC and parietal cortex in value-based decision-making, as these were the only regions strongly involved in both reward and task coding