Analysis of high dimensional data is a common task. Often, small multiples are used to visualize 1 or 2 dimensions at a time, such as in a scatterplot matrix. Associating data points between different views can be difficult though, as the points are not fixed. Other times, dimensional reduction techniques are employed to summarize the whole dataset in one image, but individual dimensions are lost in this view. In this paper, we present a means of augmenting a dimensional reduction plot with isocontours to reintroduce the original dimensions. By applying this to each dimension in the original data, we create multiple views where the points are consistent, which facilitates their comparison. Our approach employs a combination of a novel, graph-based projection technique with a GPU accelerated implementation of moving least squares to interpolate space between the points. We also present evaluations of this approach both with a case study and with a user study.
Many data projection and representation techniques can result in a high degree of overplot, where many data points map to the same area of the screen. Data reduction techniques, such as sampling @cite_44 @cite_38 or clustering @cite_33 @cite_8 , can be used to address the issue of overplot by creating an abstracted overview, but in doing so, they do not show the entire dataset. In order to explore the entire dataset from such an overview, semantic zooming such as fisheye lensing @cite_21 with user interaction is necessary. Several works @cite_27 @cite_10 @cite_13 @cite_16 employ such fisheye lensing. Many of them do so purely geometrically without the need for semantic abstraction. However, they do not account for points that are precisely collocated. @cite_6 address this issue by displacing overplotted points to the nearest free pixel. While this method does allow for all points to be drawn with minimum overplot, there is no visual indication of this displacement having occurred. Also, all of these methods use rectilinear distortion, which substantially limits their flexibility.
@cite_13 @cite_38 @cite_33 @cite_8 @cite_21 @cite_6 @cite_44 @cite_27 @cite_16 @cite_10
2020141201 2158378644 2762085884 2169504875
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. Existing information-visualization techniques that target small screens are usually limited to exploring a few hundred items. In this article we present a scatterplot tool for personal digital assistants that allows the handling of many thousands of items. The application's scalability is achieved by incorporating two alternative interaction techniques: a geometric-semantic zoom that provides smooth transition between overview and detail, and a fisheye distortion that displays the focus and context regions of the scatterplot in a single view. A user study with 24 participants was conducted to compare the usability and efficiency of both techniques when searching a book database containing 7500 items. The study was run on a pen-driven Wacom board simulating a PDA interface. While the results showed no significant difference in task-completion times, a clear majority of 20 users preferred the fisheye view over the zoom interaction. In addition, other dependent variables such as user satisfaction and subjective rating of orientation and navigation support revealed a preference for the fisheye distortion. These findings partly contradict related research and indicate that, when using a small screen, users place higher value on the ability to preserve navigational context than they do on the ease of use of a simplistic, metaphor-based interaction style Sufficient training examples are the fundamental requirement for most of the learning tasks. However, collecting well-labelled training examples is costly. Inspired by Zero-shot Learning (ZSL) that can make use of visual attributes or natural language semantics as an intermediate level clue to associate low-level features with high-level classes, in a novel extension of this idea, we aim to synthesise training data for novel classes using only semantic attributes. Despite the simplicity of this idea, there are several challenges. First, how to prevent the synthesised data from over-fitting to training classes? Second, how to guarantee the synthesised data is discriminative for ZSL tasks? Third, we observe that only a few dimensions of the learnt features gain high variances whereas most of the remaining dimensions are not informative. Thus, the question is how to make the concentrated information diffuse to most of the dimensions of synthesised data. To address the above issues, we propose a novel embedding algorithm named Unseen Visual Data Synthesis (UVDS) that projects semantic features to the high-dimensional visual feature space. Two main techniques are introduced in our proposed algorithm. (1) We introduce a latent embedding space which aims to reconcile the structural difference between the visual and semantic spaces, meanwhile preserve the local structure. (2) We propose a novel Diffusion Regularisation (DR) that explicitly forces the variances to diffuse over most dimensions of the synthesised data. By an orthogonal rotation (more precisely, an orthogonal transformation), DR can remove the redundant correlated attributes and further alleviate the over-fitting problem. On four benchmark datasets, we demonstrate the benefit of using synthesised unseen data for zero-shot learning. Extensive experimental results suggest that our proposed approach significantly outperforms the state-of-the-art methods. We propose a novel projection based visualization method for high-dimensional datasets by combining concepts from MDS and the geometry of the hyperbolic spaces. Our approach Hyperbolic Multi-Dimensional Scaling (H-MDS) extends earlier work [7] using hyperbolic spaces for visualization of tree structures data ( "hyperbolic tree browser" ).By borrowing concepts from multi-dimensional scaling we map proximity data directly into the 2-dimensional hyperbolic space (H2). This removes the restriction to "quasihierarchical", graph-based data -- limiting previous work. 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 used the circular Poincare model of the H2 which allows effective human-computer interaction: by moving the "focus" via mouse 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.We present several high-dimensional mapping examples including synthetic and real world data and a successful application for unstructured text. By analyzing and integrating multiple film critiques from news:rec.art.movies.reviews and the internet movie database, each movie becomes placed within the H2. Here the idea is, that related films share more words in their reviews than unrelated. Their semantic proximity leads to a closer arrangement. The result is a kind of high-level content structured display allowing the user to explore the "space of movies".