Daniel Engel

A Survey of Dimension Reduction Methods for High-dimensional Data Analysis and Visualization

Dimension reduction is commonly defined as the process of mapping high-dimensional data to a lower-dimensional embedding. Applications of dimension reduction include, but are not limited to, filtering, compression, regression, classification, feature analysis, and visualization. We review methods that compute a point-based visual representation of high-dimensional data sets to aid in exploratory data analysis. The aim is not to be exhaustive but to provide an overview of basic approaches, as well as to review select state-of-the-art methods. Our survey paper is an introduction to dimension reduction from a visualization point of view. Subsequently, a comparison of state-of-the-art methods outlines relations and shared research foci. 1998 ACM Subject Classification G.3 Multivariate Statistics, I.2.6 Learning, G.1.2 Approximation

Structural decomposition trees

Researchers and analysts in modern industrial and academic environments are faced with a daunting amount of multi‐dimensional data. While there has been significant development in the areas of data mining and knowledge discovery, there is still the need for improved visualizations and generic solutions. The state‐of‐the‐art in visual analytics and exploratory data visualization is to incorporate more profound analysis methods while focusing on fast interactive abilities. The common trend in these scenarios is to either visualize an abstraction of the data set or to better utilize screen‐space.

Neighborhood relation diagrams for local comparison of carbon footprints in urban planning

The dreaded effects of climate change have led to a new research focus in many applications. In urban planning, the visualization of carbon footprints has become one of the most sought after aspects. Urban planning data of carbon footprints contains spatial (location) and abstract (statistical indicators) information. Although many techniques for the visualization of such partially spatial data have been successfully applied in the area of geovisualization, the core focus has been on a global depiction of non-spatial information. However, conducting local comparisons, as in the case of comparing neighborhood districts and households, is of particular importance in investigative tasks. Additionally, representing different carbon footprint indicators (multiple non-spatial parameters) and unstructured parameter values (resulting in scaling issues) in a static representation provides an interesting challenge for visualization. This paper describes a novel and generic solution to the above-mentioned issues: a neighborhood relation diagram for the local comparison of non-spatial information in partial spatial data. The technique is based on the geometric computation of Voronoi diagrams according to a weighted neighborhood metric. The shape of spatial regions (e.g. city districts) within this diagram is characterized by a directed and constrained deformation according to the non-spatial (i.e. carbon footprint) relations to neighboring regions. The effectiveness of our method is highlighted in a preliminary study of carbon footprint patterns in downtown Phoenix (Arizona, USA). In this study, neighborhood relation diagrams enable city planners to detect local effects on carbon emissions and their relation to planning projects.

Visual Steering and Verification of Mass Spectrometry Data Factorization in Air Quality Research

The study of aerosol composition for air quality research involves the analysis of high-dimensional single particle mass spectrometry data. We describe, apply, and evaluate a novel interactive visual framework for dimensionality reduction of such data. Our framework is based on non-negative matrix factorization with specifically defined regularization terms that aid in resolving mass spectrum ambiguity. Thereby, visualization assumes a key role in providing insight into and allowing to actively control a heretofore elusive data processing step, and thus enabling rapid analysis meaningful to domain scientists. In extending existing black box schemes, we explore design choices for visualizing, interacting with, and steering the factorization process to produce physically meaningful results. A domain-expert evaluation of our system performed by the air quality research experts involved in this effort has shown that our method and prototype admits the finding of unambiguous and physically correct lower-dimensional basis transformations of mass spectrometry data at significantly increased speed and a higher degree of ease.

Visualization of Building Performance Simulation Results: State-of-the-Art and Future Directions

Performance attributes such as energy use or natural ventilation are becoming rapidly more important in the design of modern buildings. As a basis for the improvement of existing visualization techniques in this application domain, we provide a detailed tasks and requirements analysis using feedback from an architect. State-of-the-art visualization strategies used for building performance simulation results are then evaluated by comparing them to the quality aspects derived before. This assessment specifically reveals shortcomings with respect to the applied techniques for visualizing spatiotemporal data. Therefore, we discuss the potential of utilizing other visualization techniques to meet the identified prerequisites and reveal future directions based on these findings.

Visual exploration of Location-Based Social Networks data in urban planning

The increasing amount of data generated by Location Based Social Networks (LBSN) such as Twitter, Flickr, or Foursquare, is currently drawing the attention of urban planners, as it is a new source of data that contains valuable information about the behavior of the inhabitants of a city. Making this data accessible to the urban planning domain can add value to the decision making processes. However, the analysis of the spatial and temporal characteristics of this data in the context of urban planning is an ongoing research problem. This paper describes ongoing work in the design and development of a visual exploration tool to facilitate this task. The proposed design provides an approach towards the integration of a visual exploration tool and the capabilities of a visual query system from a multilevel perspective (e.g., multiple spatial scales and temporal resolutions implicit in LBSN data). A preliminary discussion about the design and the potential insights that can be gained from the exploration and analysis of this data with the proposed tool is presented, along with the conclusions and future work for the continuation of this work.

Towards high-dimensional data analysis in air quality research

Analysis of chemical constituents from mass spectrometry of aerosols involves non‐negative matrix factorization, an approximation of high‐dimensional data in lower‐dimensional space. The associated optimization problem is non‐convex, resulting in crude approximation errors that are not accessible to scientists. To address this shortcoming, we introduce a new methodology for user‐guided error‐aware data factorization that entails an assessment of the amount of information contributed by each dimension of the approximation, an effective combination of visualization techniques to highlight, filter, and analyze error features, as well as a novel means to interactively refine factorizations. A case study and the domain‐expert feedback provided by the collaborating atmospheric scientists illustrate that our method effectively communicates errors of such numerical optimization results and facilitates the computation of high‐quality data factorizations in a simple and intuitive manner.

Structural Decomposition Trees: Semantic and Practical Implications

The visualization of high-dimensional data is a challenging research topic. Existing approaches can usually be assigned to either relation or value visualizations. Merging approaches from both classes into a single integrated strategy, Structural Decomposition Trees (SDTs) represent a completely novel visualization approach for high-dimensional data. Although this method is new and promising, statements on how to use and apply the technique in the context of real-world applications are still missing. This paper discusses how SDTs can be interpreted and interacted with to gain insights about the data more effectively. First, it is discussed what properties about the data can be obtained by an interpretation of the initial projection. These statements are also valid for other projections based on principal components analysis, addressing a frequent problem when applying this technique. Further, a detailed and task-oriented interaction guideline shows how provided interaction methods can be utilized effectively for data exploration. The results obtained by an application of these guidelines in air quality research indicate that much insight can be gained even for large and complex data sets. This justifies and further motivates the usefulness and wide applicability of SDTs as a novel visualization approach for high-dimensional data.