Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms generally lack clear relation to the initial data dimensions. Therefore, interpreting and reasoning about dimensionality reductions can be difficult. In this work, we introduce two interaction techniques, and , for reasoning dynamically about scatter plots of dimensionally reduced data. We also contribute two related visualization techniques, and to facilitate and enrich the effective use of the proposed interactions, which we integrate in a new tool called . To evaluate our techniques, we first analyze their time and accuracy performance across varying sample and dimension sizes. We then conduct a user study in which twelve data scientists use so as to assess the usefulness of the techniques in performing exploratory data analysis tasks. Results suggest that our visual interactions are intuitive and effective for exploring dimensionality reductions and generating hypotheses about the underlying data.
Principle Component Analysis (PCA) is a widely used mathematical technique in many fields for factor and trend analysis, dimension reduction, etc. However, it is often considered to be a "black box" operation whose results are difficult to interpret and sometimes counter-intuitive to the user. In order to assist the user in better understanding and utilizing PCA, we have developed a system that visualizes the results of principal component analysis using multiple coordinated views and a rich set of user interactions. Our design philosophy is to support analysis of multivariate datasets through extensive interaction with the PCA output. To demonstrate the usefulness of our system, we performed a comparative user study with a known commercial system, SAS INSIGHT's Interactive Data Exploration. Participants in our study solved a number of high-level analysis tasks with each interface and rated the systems on ease of learning and usefulness. Based on the participants' accuracy, speed, and qualitative feedback, we observe that our system helps users to better understand relationships between the data and the calculated eigenspace, which allows the participants to more accurately analyze the data. User feedback suggests that the interactivity and transparency of our system are the key strengths of our approach. Dimensionality Reduction (DR) is a core building block in visualizing multidimensional data. For DR techniques to be useful in exploratory data analysis, they need to be adapted to human needs and domain-specific problems, ideally, interactively, and on-the-fly. Many visual analytics systems have already demonstrated the benefits of tightly integrating DR with interactive visualizations. Nevertheless, a general, structured understanding of this integration is missing. To address this, we systematically studied the visual analytics and visualization literature to investigate how analysts interact with automatic DR techniques. The results reveal seven common interaction scenarios that are amenable to interactive control such as specifying algorithmic constraints, selecting relevant features, or choosing among several DR algorithms. We investigate specific implementations of visual analysis systems integrating DR, and analyze ways that other machine learning methods have been combined with DR. Summarizing the results in a “human in the loop” process model provides a general lens for the evaluation of visual interactive DR systems. We apply the proposed model to study and classify several systems previously described in the literature, and to derive future research opportunities. Visual-interactive cluster analysis provides valuable tools for effectively analyzing large and complex data sets. Due to desirable properties and an inherent predisposition for visualization, the Kohonen Feature Map (or self-organizing map, or SOM) algorithm is among the most popular and widely used visual clustering techniques. However, the unsupervised nature of the algorithm may be disadvantageous in certain applications. Depending on initialization and data characteristics, cluster maps (cluster layouts) may emerge that do not comply with user preferences, expectations, or the application context. Considering SOM-based analysis of trajectory data, we propose a comprehensive visual-interactive monitoring and control framework extending the basic SOM algorithm. The framework implements the general Visual Analytics idea to effectively combine automatic data analysis with human expert supervision. It provides simple, yet effective facilities for visually monitoring and interactively controlling the trajectory clustering process at arbitrary levels of detail. The approach allows the user to leverage existing domain knowledge and user preferences, arriving at improved cluster maps. We apply the framework on a trajectory clustering problem, demonstrating its potential in combining both unsupervised (machine) and supervised (human expert) processing, in producing appropriate cluster results.  The increasing availability of motion sensors and video cameras in living spaces has made possible the analysis of motion patterns and collective behavior in a number of situations. The visualization of this movement data, however, remains a challenge. Although maintaining the actual layout of the data space is often desirable, direct visualization of movement traces becomes cluttered and confusing as the spatial distribution of traces may be disparate and uneven. We present proximity-based visualization as a novel approach to the visualization of movement traces in an abstract space rather than the given spatial layout. This abstract space is obtained by considering proximity data, which is computed as the distance between entities and some number of important locations. These important locations can range from a single fixed point, to a moving point, several points, or even the proximities between the entities themselves. This creates a continuum of proximity spaces, ranging from the fixed absolute reference frame to completely relative reference frames. By combining these abstracted views with the concrete spatial views, we provide a way to mentally map the abstract spaces back to the real space. We demonstrate the effectiveness of this approach, and its applicability to visual analytics problems such as hazard prevention, migration patterns, and behavioral studies. 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.