Timeslices are often used to draw and visualize dynamic graphs. While timeslices are a natural way to think about dynamic graphs, they are routinely imposed on continuous data. Often, it is unclear how many timeslices to select: too few timeslices can miss temporal features such as causality or even graph structure while too many timeslices slows the drawing computation. We present a model for dynamic graphs which is not based on timeslices, and a dynamic graph drawing algorithm, DynNoSlice, to draw graphs in this model. In our evaluation, we demonstrate the advantages of this approach over timeslicing on continuous data sets.
Time-to-space mapping approaches @cite_27 use one dimension for space and one dimension for time in order to visualize the network @cite_2 @cite_23 @cite_5 @cite_28 . Recent scalable approaches use dimensionality reduction to show time as a curve in the plane 15Bach,15Elzen . By using spatial dimensions to represent time, these visualizations are substantially different from classic dynamic node-link diagrams.
@cite_28 @cite_27 @cite_23 @cite_2 @cite_5
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We present a new visual representation for 3D action recognition from sequences of depth maps. In this new representation, space and time axes are divided into multiple segments to define a 4D grid for each depth map sequences. Each cell in the grid is associated with an occupancy value which is a function of the number of space-time points falling into this cell. The occupancy values of all the cells form a high dimensional feature vector, called Space-Time Occupancy Pattern (STOP). We then perform dimensionality reduction to obtain lower-dimensional feature vectors. The advantage of STOP is that it preserves spatial and temporal contextual information between space and time cells while being flexible enough to accommodate intra-action variations. Furthermore, we combine depth maps with skeletons in order to obtain view invariance and present an automatic segmentation and time alignment method for on-line recognition of depth sequences. Our visual representation is validated with experiments on a public 3D human action dataset. We describe a data structure, a rectangular complex, that can be used represent hyperconvex metric spaces that have the same topology (although not necessarily the same distance function) as subsets of the plane. We show how to use this data structure to construct the tight span of a metric space given as an n × n distance matrix, when the tight span is homeomorphic to a subset of the plane, in time O ( n 2 ), and to add a single point to a planar tight span in time O ( n ). As an application of this construction, we show how to test whether a given ﬁnite metric space embeds isometrically into the Manhattan plane in time O( n 2 ), and add a single point to the space and re-test whether it has such an embedding in time O ( n ). Visualization plays a crucial role in understanding dynamic social networks at many different levels (i.e., group, subgroup, and individual). Node-link-based visualization techniques are currently widely used for these tasks and have been demonstrated to be effective, but it was found that they also have limitations in representing temporal changes, particularly at the individual and subgroup levels. To overcome these limitations, this article presents a new network visualization technique, called “TimeMatrix,” based on a matrix representation. Interaction techniques, such as overlay controls, a temporal range slider, semantic zooming, and integrated network statistical measures, support analysts in studying temporal social networks. To validate the design, the article presents a user study involving three social scientists analyzing inter-organizational collaboration data. The study demonstrates how TimeMatrix may help analysts gain insights about the temporal aspects of network data that can be subseque... This paper describes a generalized axiomatic scale-space theory that makes it possible to derive the notions of linear scale-space, affine Gaussian scale-space and linear spatio-temporal scale-space using a similar set of assumptions (scale-space axioms). The notion of non-enhancement of local extrema is generalized from previous application over discrete and rotationally symmetric kernels to continuous and more general non-isotropic kernels over both spatial and spatio-temporal image domains. It is shown how a complete classification can be given of the linear (Gaussian) scale-space concepts that satisfy these conditions on isotropic spatial, non-isotropic spatial and spatio-temporal domains, which results in a general taxonomy of Gaussian scale-spaces for continuous image data. The resulting theory allows filter shapes to be tuned from specific context information and provides a theoretical foundation for the recently exploited mechanisms of shape adaptation and velocity adaptation, with highly useful applications in computer vision. It is also shown how time-causal spatio-temporal scale-spaces can be derived from similar assumptions. The mathematical structure of these scale-spaces is analyzed in detail concerning transformation properties over space and time, the temporal cascade structure they satisfy over time as well as properties of the resulting multi-scale spatio-temporal derivative operators. It is also shown how temporal derivatives with respect to transformed time can be defined, leading to the formulation of a novel analogue of scale normalized derivatives for time-causal scale-spaces. The kernels generated from these two types of theories have interesting relations to biological vision. We show how filter kernels generated from the Gaussian spatio-temporal scale-space as well as the time-causal spatio-temporal scale-space relate to spatio-temporal receptive field profiles registered from mammalian vision. Specifically, we show that there are close analogies to space-time separable cells in the LGN as well as to both space-time separable and non-separable cells in the striate cortex. We do also present a set of plausible models for complex cells using extended quasi-quadrature measures expressed in terms of scale normalized spatio-temporal derivatives. The theories presented as well as their relations to biological vision show that it is possible to describe a general set of Gaussian and or time-causal scale-spaces using a unified framework, which generalizes and complements previously presented scale-space formulations in this area.