Visual Detection of Structural Changes in Time-Varying Graphs Using Persistent Homology

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into metric spaces, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data. To validate our approach, we conduct several case studies on real world data sets and show how our method can find cyclic patterns, deviations from those patterns, and one-time events in time-varying graphs. We also examine whether persistence-based similarity measure as a graph metric satisfies a set of well-established, desirable properties for graph metrics

Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets

Runaway Feedback Loops in Predictive Policing

Predictive policing systems are increasingly used to determine how to allocate police across a city in order to best prevent crime. Discovered crime data (e.g., arrest counts) are used to help update the model, and the process is repeated. Such systems have been empirically shown to be susceptible to runaway feedback loops, where police are repeatedly sent back to the same neighborhoods regardless of the true crime rate. In response, we develop a mathematical model of predictive policing that proves why this feedback loop occurs, show empirically that this model exhibits such problems, and demonstrate how to change the inputs to a predictive policing system (in a black-box manner) so the runaway feedback loop does not occur, allowing the true crime rate to be learned. Our results are quantitative: we can establish a link (in our model) between the degree to which runaway feedback causes problems and the disparity in crime rates between areas. Moreover, we can also demonstrate the way in which \emph{reported} incidents of crime (those reported by residents) and \emph{discovered} incidents of crime (i.e. those directly observed by police officers dispatched as a result of the predictive policing algorithm) interact: in brief, while reported incidents can attenuate the degree of runaway feedback, they cannot entirely remove it without the interventions we suggest.Comment: Extended version accepted to the 1st Conference on Fairness, Accountability and Transparency, 2018. Adds further treatment of reported as well as discovered incident

Querying and creating visualizations by analogy

Journal ArticleWhile there have been advances in visualization systems, particularly in multi-view visualizations and visual exploration, the process of building visualizations remains a major bottleneck in data exploration. We show that provenance metadata collected during the creation of pipelines can be reused to suggest similar content in related visualizations and guide semi-automated changes. We introduce the idea of query-by-example in the context of an ensemble of visualizations, and the use of analogies as first-class operations in a system to guide scalable interactions. We describe an implementation of these techniques in VisTrails, a publicly-available, open-source system

A Vector Field Design Approach to Animated Transitions

Animated transitions can be effective in explaining and exploring a small number of visualizations where there are drastic changes in the scene over a short interval of time. This is especially true if data elements cannot be visually distinguished by other means. Current research in animated transitions has mainly focused on linear transitions (all elements follow straight line paths) or enhancing coordinated motion through bundling of linear trajectories. In this paper, we introduce animated transition design, a technique to build smooth, non-linear transitions for clustered data with either minimal or no user involvement. The technique is flexible and simple to implement, and has the additional advantage that it explicitly enhances coordinated motion and can avoid crowding, which are both important factors to support object tracking in a scene. We investigate its usability, provide preliminary evidence for the effectiveness of this technique through metric evaluations and user study and discuss limitations and future directions

Problems with Shapley-value-based explanations as feature importance measures

Game-theoretic formulations of feature importance have become popular as a way to "explain" machine learning models. These methods define a cooperative game between the features of a model and distribute influence among these input elements using some form of the game's unique Shapley values. Justification for these methods rests on two pillars: their desirable mathematical properties, and their applicability to specific motivations for explanations. We show that mathematical problems arise when Shapley values are used for feature importance and that the solutions to mitigate these necessarily induce further complexity, such as the need for causal reasoning. We also draw on additional literature to argue that Shapley values do not provide explanations which suit human-centric goals of explainability.Comment: Accepted to ICML 202