Most tabular data visualization techniques focus on overviews, yet many practical analysis tasks are concerned with investigating individual items of interest. At the same time, relating an item to the rest of a potentially large table is important. In this work we present Taggle, a tabular visualization technique for exploring and presenting large and complex tables. Taggle takes an item-centric, spreadsheet-like approach, visualizing each row in the source data individually using visual encodings for the cells. At the same time, Taggle introduces data-driven aggregation of data subsets. The aggregation strategy is complemented by interaction methods tailored to answer specific analysis questions, such as sorting based on multiple columns and rich data selection and filtering capabilities. We demonstrate Taggle using a case study conducted by a domain expert on complex genomics data analysis for the purpose of drug discovery.
Pivot tables are another way of dealing with the analysis of large multidimensional data. They enable rotation, that is, pivoting of various data dimensions, and with use of data aggregation, such as sum, average, or count, they provide a quick data overview. Pivot tables are widely available in spreadsheet tools such as Excel and Google Sheets, and similar operations are available as part of libraries and programming languages used to create static tabular figures. Tableau @cite_24 employs pivot table principles for constructing nested matrices, where each matrix can then be represented visually in different ways. While pivot tables are well suited to, for instance, summing up the sales figures of multiple departments, they do not commonly support more nuanced aggregations, such as histograms and box plots.
@cite_24
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In the last several years, large multidimensional databases have become common in a variety of applications, such as data warehousing and scientific computing. Analysis and exploration tasks place significant demands on the interfaces to these databases. Because of the size of the data sets, dense graphical representations are more effective for exploration than spreadsheets and charts. Furthermore, because of the exploratory nature of the analysis, it must be possible for the analysts to change visualizations rapidly as they pursue a cycle involving first hypothesis and then experimentation. In this paper, we present Polaris, an interface for exploring large multidimensional databases that extends the well-known pivot table interface. The novel features of Polaris include an interface for constructing visual specifications of table-based graphical displays and the ability to generate a precise set of relational queries from the visual specifications. The visual specifications can be rapidly and incrementally developed, giving the analyst visual feedback as he constructs complex queries and visualizations. Scatterplot matrices (SPLOMs), parallel coordinates, and glyphs can all be used to visualize the multiple continuous variables (i.e., dependent variables or measures) in multidimensional multivariate data. However, these techniques are not well suited to visualizing many categorical variables (i.e., independent variables or dimensions). To visualize multiple categorical variables, 'hierarchical axes' that 'stack dimensions' have been used in systems like Polaris and Tableau. However, this approach does not scale well beyond a small number of categorical variables. [8] extend the matrix paradigm of the SPLOM to simultaneously visualize several categorical and continuous variables, displaying many kinds of charts in the matrix depending on the kinds of variables involved. We propose a variant of their technique, called the Generalized Plot Matrix (GPLOM). The GPLOM restricts 's technique to only three kinds of charts (scatterplots for pairs of continuous variables, heatmaps for pairs of categorical variables, and barcharts for pairings of categorical and continuous variable), in an effort to make it easier to understand. At the same time, the GPLOM extends 's work by demonstrating interactive techniques suited to the matrix of charts. We discuss the visual design and interactive features of our GPLOM prototype, including a textual search feature allowing users to quickly locate values or variables by name. We also present a user study that compared performance with Tableau and our GPLOM prototype, that found that GPLOM is significantly faster in certain cases, and not significantly slower in other cases. We introduce a method for organizing multivariate displays and for guiding interactive exploration through high-dimensional data. The method is based on nine characterizations of the 2D distributions of orthogonal pairwise projections on a set of points in multidimensional Euclidean space. These characterizations include such measures as density, skewness, shape, outliers, and texture. Statistical analysis of these measures leads to ways for 1) organizing 2D scatterplots of points for coherent viewing, 2) locating unusual (outlying) marginal 2D distributions of points for anomaly detection and 3) sorting multivariate displays based on high-dimensional data, such as trees, parallel coordinates, and glyphs Many data sets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a multiscale description of the homological features within a data set. A useful representation of this homological information is a persistence diagram (PD). Efforts have been made to map PDs into spaces with additional structure valuable to machine learning tasks. We convert a PD to a finite-dimensional vector representation which we call a persistence image (PI), and prove the stability of this transformation with respect to small perturbations in the inputs. The discriminatory power of PIs is compared against existing methods, showing significant performance gains. We explore the use of PIs with vector-based machine learning tools, such as linear sparse support vector machines, which identify features containing discriminating topological information. Finally, high accuracy inference of parameter values from the dynamic output of a discrete dynamical system (the linked twist map) and a partial differential equation (the anisotropic Kuramoto-Sivashinsky equation) provide a novel application of the discriminatory power of PIs.