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.
Bertifier @cite_1 is a table-visualization technique inspired by Jacques Bertin's matrix analysis methods. It uses various visual encodings for cells , ) that can be interactively re-ordered based on similarities between rows and columns. Other features, such as styling options for the table grid, indicate that the technique is intended mainly for presenting small or medium-sized tables. Bertifier does not support aggregation ) or grouping ) and is limited to numerical data.
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2018614013 2013172302 2951815872 1977580401
We present BERTIFIER, a web app for rapidly creating tabular visualizations from spreadsheets. BERTIFIER draws from Jacques Bertin's matrix analysis method, whose goal was to "simplify without destroying" by encoding cell values visually and grouping similar rows and columns. Although there were several attempts to bring this method to computers, no implementation exists today that is both exhaustive and accessible to a large audience. BERTIFIER remains faithful to Bertin's method while leveraging the power of today's interactive computers. Tables are formatted and manipulated through crossets, a new interaction technique for rapidly applying operations on rows and columns. We also introduce visual reordering, a semi-interactive reordering approach that lets users apply and tune automatic reordering algorithms in a WYSIWYG manner. Sessions with eight users from different backgrounds suggest that BERTIFIER has the potential to bring Bertin's method to a wider audience of both technical and non-technical users, and empower them with data analysis and communication tools that were so far only accessible to a handful of specialists. Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset. Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called rank-revealing QR , which seeks a well-conditioned collection of columns that spans the (numerical) range of the matrix. The functional analysis literature contains another strand of work on column selection whose algorithmic implications have not been explored. In particular, a celebrated result of Bourgain and Tzafriri demonstrates that each matrix with normalized columns contains a large column submatrix that is exceptionally well conditioned. Unfortunately, standard proofs of this result cannot be regarded as algorithmic. This paper presents a randomized, polynomial-time algorithm that produces the submatrix promised by Bourgain and Tzafriri. The method involves random sampling of columns, followed by a matrix factorization that exposes the well-conditioned subset of columns. This factorization, which is due to Grothendieck, is regarded as a central tool in modern functional analysis. The primary novelty in this work is an algorithm, based on eigenvalue minimization, for constructing the Grothendieck factorization. These ideas also result in a novel approximation algorithm for the @math norm of a matrix, which is generally NP -hard to compute exactly. As an added bonus, this work reveals a surprising connection between matrix factorization and the famous maxcut semidefinite program. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.