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.
We presented initial versions of , , and earlier as part of Clustrophile, an exploratory visual clustering analysis tool @cite_35 . We give here a focused discussion of our revised interaction and visualization techniques, introduce Praxis, a new visualization tool that implements our techniques for exploratory data analysis using DR, and provide a thorough computational and user-performance evaluation. The current work also introduces , a new visualization technique to facilitate interactions.
@cite_35
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While clustering is one of the most popular methods for data mining, analysts lack adequate tools for quick, iterative clustering analysis, which is essential for hypothesis generation and data reasoning. We introduce Clustrophile, an interactive tool for iteratively computing discrete and continuous data clusters, rapidly exploring different choices of clustering parameters, and reasoning about clustering instances in relation to data dimensions. Clustrophile combines three basic visualizations -- a table of raw datasets, a scatter plot of planar projections, and a matrix diagram (heatmap) of discrete clusterings -- through interaction and intermediate visual encoding. Clustrophile also contributes two spatial interaction techniques, @math and @math , and a visualization method, @math , for reasoning about two-dimensional projections obtained through dimensionality reductions. General purpose graphical interfaces for data exploration are typically based on manual visualization and interaction specifications. While designing manual specification can be very expressive, it demands high efforts to make effective decisions, therefore reducing exploratory speed. Instead, principled automated designs can increase exploratory speed, decrease learning efforts, help avoid ineffective decisions, and therefore better support data analytics novices. Towards these goals, we present Keshif, a new systematic design for tabular data exploration. To summarize a given dataset, Keshif aggregates records by value within attribute summaries, and visualizes aggregate characteristics using a consistent design based on data types. To reveal data distribution details, Keshif features three complementary linked selections: highlighting, filtering, and comparison. Keshif further increases expressiveness through aggregate metrics, absolute part-of scale modes, calculated attributes, and saved selections, all working in synchrony. Its automated design approach also simplifies authoring of dashboards composed of summaries and individual records from raw data using fluid interaction. We show examples selected from @math datasets from diverse domains. Our study with novices shows that after exploring raw data for 15 minutes, our participants reached close to 30 data insights on average, comparable to other studies with skilled users using more complex tools. A first line of attack in exploratory data analysis is data visualization, i.e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable. Standard Johnson-Lindenstrauss dimensionality reduction does not produce data visualizations. The t-SNE heuristic of van der Maaten and Hinton, which is based on non-convex optimization, has become the de facto standard for visualization in a wide range of applications. This work gives a formal framework for the problem of data visualization - finding a 2-dimensional embedding of clusterable data that correctly separates individual clusters to make them visually identifiable. We then give a rigorous analysis of the performance of t-SNE under a natural, deterministic condition on the "ground-truth" clusters (similar to conditions assumed in earlier analyses of clustering) in the underlying data. These are the first provable guarantees on t-SNE for constructing good data visualizations. We show that our deterministic condition is satisfied by considerably general probabilistic generative models for clusterable data such as mixtures of well-separated log-concave distributions. Finally, we give theoretical evidence that t-SNE provably succeeds in partially recovering cluster structure even when the above deterministic condition is not met. Exploratory data analysis aims to discover and generate multiple views of the structure within a dataset. Conventional clustering techniques, however, are designed to only provide a single grouping or clustering of a dataset. In this paper, we introduce a novel algorithm called CAMI, that can uncover alternative clusterings from a dataset. CAMI takes a mathematically appealing approach, combining the use of mutual information to distinguish between alternative clusterings, coupled with an expectation maximization framework to ensure clustering quality. We experimentally test CAMI on both synthetic and real-world datasets, comparing it against a variety of state-of-the-art algorithms. We demonstrate that CAMI’s performance is high and that its formulation provides a number of advantages compared to existing techniques.