Understanding large amounts of spatiotemporal data from particle-based simulations, such as molecular dynamics, often relies on the computation and analysis of aggregate measures. These, however, by virtue of aggregation, hide structural information about the space time localization of the studied phenomena. This leads to degenerate cases where the measures fail to capture distinct behaviour. In order to drill into these aggregate values, we propose a multi-scale visual exploration technique. Our novel representation, based on partial domain aggregation, enables the construction of a continuous scale-space for discrete datasets and the simultaneous exploration of scales in both space and time. We link these two scale-spaces in a scale-space space-time cube and model linked views as orthogonal slices through this cube, thus enabling the rapid identification of spatio-temporal patterns at multiple scales. To demonstrate the effectiveness of our approach, we showcase an advanced exploration of a protein-ligand simulation.
This paper contributes to the analysis of data that usually would be treated as a time series of spatially aggregated values. A good overview of visualization techniques for time-dependent data can be found in a book by @cite_57 . They focus primarily on time-dependent data in general, without specifically addressing spatial localization or scale-space approaches. @cite_28 proposed an analysis based on multivariate trend identification in time dependent data without spatial dependence. @cite_9 explore the use of parallel coordinates for the visualization of trajectories in multi-dimensional dynamical systems.
@cite_57 @cite_9 @cite_28
2020141201 2141859737 1925915230 2145646037
We introduce a novel projection-based visualization method for high-dimensional data sets by combining concepts from MDS and the geometry of the hyperbolic spaces. This approach hyperbolic multi-dimensional scaling (H-MDS) is a synthesis of two important concepts for explorative data analysis and visualization: (i) multi-dimensional scaling uses proximity or pair distance data to generate a low-dimensional, spatial presentation of the data; (ii) previous work on the "hyperbolic tree browser" demonstrated the extraordinary advantages for an interactive display of graph-like data in the two-dimensional hyperbolic space (H2).In the new approach, H-MDS maps proximity data directly into the H2. This removes the restriction to "quasihierarchical", graph-based data--a major limitation of (ii). Since a suitable distance function can convert all kinds of data to proximity (or distance-based) data, this type of data can be considered the most general.We review important properties of the hyperbolic space and, in particular, the circular Poincare model of the H2. It enables effective human-computer interaction: by mouse dragging the "focus", the user can navigate in the data without loosing the context. In H2 the "fish-eye" behavior originates not simply by a non-linear view transformation but rather by extraordinary, non-Euclidean properties of the H2. Especially, the exponential growth of length and area of the underlying space makes the H2 a prime target for mapping hierarchical and (now also) high-dimensional data.Several high-dimensional mapping examples including synthetic and real-world data are presented. Since high-dimensional data produce "ring"-shaped displays, we present methods to enhance the display by modulating the dissimilarity contrast. This is demonstrated for an application for unstructured text: i.e., by using multiple film critiques from news:rec.art.movies.reviews and www.imdb.com, each movie is placed within the H2--creating a "space of movies" for interactive exploration. This paper is concerned with the representation and recognition of the observed dynamics (i.e., excluding purely spatial appearance cues) of spacetime texture based on a spatiotemporal orientation analysis. The term “spacetime texture” is taken to refer to patterns in visual spacetime, (x,y,t), that primarily are characterized by the aggregate dynamic properties of elements or local measurements accumulated over a region of spatiotemporal support, rather than in terms of the dynamics of individual constituents. Examples include image sequences of natural processes that exhibit stochastic dynamics (e.g., fire, water, and windblown vegetation) as well as images of simpler dynamics when analyzed in terms of aggregate region properties (e.g., uniform motion of elements in imagery, such as pedestrians and vehicular traffic). Spacetime texture representation and recognition is important as it provides an early means of capturing the structure of an ensuing image stream in a meaningful fashion. Toward such ends, a novel approach to spacetime texture representation and an associated recognition method are described based on distributions (histograms) of spacetime orientation structure. Empirical evaluation on both standard and original image data sets shows the promise of the approach, including significant improvement over alternative state-of-the-art approaches in recognizing the same pattern from different viewpoints. Many scientific and economic problems involve the analysis of highdimensional time series datasets. However, theoretical studies in highdimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of � 1-regularized estimates in two important statistical problems in the context of high-dimensional time series: (a) stochastic regression with serially correlated errors and (b) transition matrix estimation in vector autoregressive (VAR) models. We derive nonasymptotic upper bounds on the estimation errors of the regularized estimates and establish that consistent estimation under high-dimensional scaling is possible via � 1-regularization for a large class of stable processes under sparsity constraints. A key technical contribution of the work is to introduce a measure of stability for stationary processes using their spectral properties that provides insight into the effect of dependence on the accuracy of the regularized estimates. With this proposed stability measure, we establish some useful deviation bounds for dependent data, which can be used to study several important regularized estimates in a time series setting. Our ability to accumulate large, complex (multivariate) data sets has far exceeded our ability to effectively process them in searching for patterns, anomalies and other interesting features. Conventional multivariate visualization techniques generally do not scale well with respect to the size of the data set. The focus of this paper is on the interactive visualization of large multivariate data sets based on a number of novel extensions to the parallel coordinates display technique. We develop a multi-resolution view of the data via hierarchical clustering, and use a variation of parallel coordinates to convey aggregation information for the resulting clusters. Users can then navigate the resulting structure until the desired focus region and level of detail is reached, using our suite of navigational and filtering tools. We describe the design and implementation of our hierarchical parallel coordinates system which is based on extending the XmdvTool system. Lastly, we show examples of the tools and techniques applied to large (hundreds of thousands of records) multivariate data sets.