Space-filling techniques seek to use as much as possible the visual space to represent a dataset, splitting it into regions that represent the data elements. Amongst those techniques, Treemaps have received wide attention due to its simplicity, reduced visual complexity, and compact use of the available space. Several different Treemap algorithms have been proposed, however the core idea is the same, to divide the visual space into rectangles with areas proportional to some data attribute or weight. Although pleasant layouts can be effectively produced by the existing techniques, most of them do not take into account relationships that might exist between different data elements when partitioning the visual space. This violates the distance-similarity metaphor, that is, close rectangles do not necessarily represent similar data elements. In this paper, we propose a novel approach, called Neighborhood Treemap (Nmap), that seeks to solve this limitation by employing a slice and scale strategy where the visual space is successively bisected on the horizontal or vertical directions and the bisections are scaled until one rectangle is defined per data element. Compared to the current techniques with the same similarity preservation goal, our approach presents the best results while being two to three orders of magnitude faster. The usefulness of Nmap is shown by two applications involving the organization of document collections and the construction of cartograms illustrating its effectiveness on different scenarios.
Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed.
Interactive visualization systems for exploring and manipulating high-dimensional feature spaces have experienced a substantial progress in the last few years. State-of-art methods rely on solid mathematical and computational foundations that enable sophisticated and flexible interactive tools. Current methods are even capable of modifying data attributes during interaction, highlighting regions of potential interest in the feature space, and building visualizations that bring out the relevance of attributes. However, those methodologies rely on complex and non-intuitive interfaces that hamper the free handling of the feature spaces. Moreover, visualizing how neighborhood structures are affected during the space manipulation is also an issue for existing methods. This paper presents a novel visualization-assisted methodology for interacting and transforming data attributes embedded in feature spaces. The proposed approach relies on a combination of multidimensional projections and local transformations to provide an interactive mechanism for modifying attributes. Besides enabling a simple and intuitive visual layout, our approach allows the user to easily observe the changes in neighborhood structures during interaction. The usefulness of our methodology is shown in an application geared to image retrieval.
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