Abstract-Similarity-based layouts generated by multidimensional projections or other dimension reduction techniques are commonly used to visualize high-dimensional data. Many projection techniques have been recently proposed addressing different objectives and application domains. Nonetheless, very little is known about the effectiveness of the generated layouts from a user's perspective, how distinct layouts from the same data compare regarding the typical visualization tasks they support, or how domain-specific issues affect the outcome of the techniques. Learning more about projection usage is an important step towards both consolidating their role in high-dimensional data analysis and taking informed decisions when choosing techniques. This work provides a contribution towards this goal. We describe the results of an investigation on the performance of layouts generated by projection techniques as perceived by their users. We conducted a controlled user study to test against the following hypotheses: (1) projection performance is task-dependent; (2) certain projections perform better on certain types of tasks; (3) projection performance depends on the nature of the data; and (4) subjects prefer projections with good segregation capability. We generated layouts of high-dimensional data with five techniques representative of different projection approaches. As application domains we investigated image and document data. We identified eight typical tasks, three of them related to segregation capability of the projection, three related to projection precision, and two related to incurred visual cluttering. Answers to questions were compared for correctness against 'ground truth' computed directly from the data. We also looked at subject confidence and task completion times. Statistical analysis of the collected data resulted in Hypotheses 1 and 3 being confirmed, Hypothesis 2 being confirmed partially and Hypotheses 4 could not be confirmed. We discuss our findings in comparison with some numerical measures of projection layout quality. Our results offer interesting insight on the use of projection layouts in data visualization tasks and provide a departing point for further systematic investigations.

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the LeastSquare Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework's applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

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Understanding the academic performance of students in colleges is an essential topic in Education research field. Educators, program coordinators and professors are interested in understanding how students are learning specific topics, how specific topics may influence the learning of other topics, how students' grades/attendances in each course may represent important indicators to measure their performance, among other tasks. The use of data visualization and analytics is expanding in education institutions to perform a variety of tasks related to data processing and gaining into data-informed insights. In this paper, we present a visual analytic tool that combines data visualization and machine learning techniques to perform some visual analysis of students' data from program courses. Two educational data collections were used to guide the creation of i) predictive models employing a variety of well known machine learning strategies, attempting to predict students' future grade based on grade and attendance previous semesters and ii) a set interactive layouts that highlight the relationship between grades and attendance, also including additional variables such as gender, parents education level, among others. We performed several experiments, also using these data collections, to evaluate the layouts ability of highlighting interesting patterns, and we obtained promising results, demonstrating that such analysis may help the education experts to understand deficiencies on course structures.

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A common strategy for encoding multidimensional data for visual analysis is to use dimensionality reduction techniques that project data from higher dimensions onto a lower-dimensional space. This article examines the use of motion to retain an accurate representation of the point density of clusters that might otherwise be lost when a multidimensional dataset is projected into a two-dimensional space. Specifically, we consider different types of density-based motion, where the magnitude of the motion is directly related to the density of the clusters. We investigate how users interpret motion in two-dimensional scatterplots and whether or not they are able to effectively interpret the point density of the clusters through motion. We conducted a series of user studies with both synthetic and real-world datasets to explore how motion can help users in completing various multidimensional data analysis tasks. Our findings indicate that for some tasks, motion outperforms the static scatterplots; circular path motions in particular give significantly better results compared to the other motions. We also found that users were easily able to distinguish clusters with different densities as long the magnitudes of motion were above a particular threshold. Our results indicate that incorporating density-based motion into visualization analytics systems effectively enables the exploration and analysis of multidimensional datasets.

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