Selecting and Sharing Multidimensional Projection Algorithms: A Practical View (original) (raw)

Toward a Quantitative Survey of Dimension Reduction Techniques

IEEE Transactions on Visualization and Computer Graphics, 2019

Dimensionality reduction methods, also known as projections, are frequently used in multidimensional data exploration in machine learning, data science, and information visualization. Tens of such techniques have been proposed, aiming to address a wide set of requirements, such as ability to show the high-dimensional data structure, distance or neighborhood preservation, computational scalability, stability to data noise and/or outliers, and practical ease of use. However, it is far from clear for practitioners how to choose the best technique for a given use context. We present a survey of a wide body of projection techniques that helps answering this question. For this, we characterize the input data space, projection techniques, and the quality of projections, by several quantitative metrics. We sample these three spaces according to these metrics, aiming at good coverage with bounded effort. We describe our measurements and outline observed dependencies of the measured variables. Based on these results, we draw several conclusions that help comparing projection techniques, explain their results for different types of data, and ultimately help practitioners when choosing a projection for a given context. Our methodology, datasets, projection implementations, metrics, visualizations, and results are publicly open, so interested stakeholders can examine and/or extend this benchmark.

Visual analysis of dimensionality reduction quality for parameterized projections

Computers & Graphics, 2014

In recent years, many dimensionality reduction (DR) algorithms have been proposed for visual analysis of multidimensional data. Given a set of n-dimensional observations, such algorithms create a 2D or 3D projection thereof that preserves relative distances or neighborhoods. The quality of resulting projections is strongly influenced by many choices, such as the DR techniques used and their various parameter settings. Users find it challenging to judge the effectiveness of a projection in maintaining features from the original space and to understand the effect of parameter settings on these results, as well as performing related tasks such as comparing two projections. We present a set of interactive visualizations that aim to help users with these tasks by revealing the quality of a projection and thus allowing inspection of parameter choices for DR algorithms, by observing the effects of these choices on the resulting projection. Our visualizations target questions regarding neighborhoods, such as finding false and missing neighbors and showing how such projection errors depend on algorithm or parameter choices. By using several space-filling techniques, our visualizations scale to large datasets. We apply our visualizations on several recent DR techniques and high-dimensional datasets, showing how they easily offer local detail on point and group neighborhood preservation while relieving users from having to understand technical details of projections.

On improved projection techniques to support visual exploration of multi-dimensional data sets

2003

Abstract Projection (or dimensionionality reduction) techniques have been used as a means to handling the growing dimensionality of data sets as well as providing a way to visualize information coded into point relationships. Their role is essential in data interpretation and simultaneous use of different projections and their visualizations improve data understanding and increase the level of confidence in the result. For that purpose projections should be fast to allow multiple views of the same data set.

Quantitative Evaluation of Time‐Dependent Multidimensional Projection Techniques

Computer Graphics Forum, 2020

Dimensionality reduction methods are an essential tool for multidimensional data analysis, and many interesting processes can be studied as time-dependent multivariate datasets. There are, however, few studies and proposals that leverage on the concise power of expression of projections in the context of dynamic/temporal data. In this paper, we aim at providing an approach to assess projection techniques for dynamic data and understand the relationship between visual quality and stability. Our approach relies on an experimental setup that consists of existing techniques designed for time-dependent data and new variations of static methods. To support the evaluation of these techniques, we provide a collection of datasets that has a wide variety of traits that encode dynamic patterns, as well as a set of spatial and temporal stability metrics that assess the quality of the layouts. We present an evaluation of 11 methods, 10 datasets, and 12 quality metrics, and elect the best-suited methods for projecting time-dependent multivariate data, exploring the design choices and characteristics of each method. All our results are documented and made available in a public repository to allow reproducibility of results. CCS Concepts • Human-centered computing → Visualization techniques; • Computing methodologies → Dimensionality reduction and manifold learning;

On the effectiveness of user manipulation in multidimensional projections

2015

With the advent of interactive techniques for multidimensional data visualization using dimensionality reduction, new possibilities of dealing with data complexity were introduced. The idea behind those methods is to allow the user to manually modify the mapping of a subset of the data, steering the mapping of the whole data set. Previous studies suggest that user manipulation is beneficial to the visualization as a means of effectively modifying the final result. Still, those studies focus only on the grouping of instances, such as group separation and compactness. This paper proposes a new view on effectiveness of user manipulation based on well-known evaluation measures. In addition, it provides initial experimental evidence on the effectiveness of user manipulation on state of the art interactive methods. Although the manipulation does affect results, we conclude that it does not lead to definitive improvements. Keywords-interactive techniques; dimensionality reduction; data vis...

Projection inspector: Assessment and synthesis of multidimensional projections

Neurocomputing, 2015

As the number and complexity of visualization techniques have grown, it has become progressively more difficult to make a decision as to which technique to employ for any given situation or application. A particular case is that of multidimensional data visualization utilizing projections, which have gained much attention lately and are being utilized in a growing number of applications. With their popularity, many new variations of multidimensional projections have been proposed in the literature. Numerical evaluations are varied and are useful, but do not reflect visual properties of projections accurately. In this paper we present Projection Inspector, an approach that contributes to the problem of understanding the difference amongst projections. It is an interactive assessment method that allows a user to explore a "space" of known projection techniques and view their results, as well as to identify the differences between them. In addition, it generates "on-the-fly" new projection techniques via interpolations of existing techniques as the user explores the projection space. We present the theoretical foundations of the projection exploration space and an interactive tool that implements a view of this space. We demonstrate the approach with case studies that demonstrate the need for projection assessment and the value of combining projections into new, better suited, projection alternatives.

Understanding High Dimensional Spaces through Visual Means Employing Multidimensional Projections

International Journal on Engineering, Science and Technology

Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called multidimensional spaces. A large set of mathematical tools, named frequently as multidimensional projections, aim to map such large spaces into 'visual spaces', that is, to 2 or 3 dimensions, where the aspect of that space can be visualised. While the final product is intuitive in that proximity between points - or iconic representation of points - indicate similarity relationships in the original space, understanding the formulation of the projection methods many times escapes researchers. In this paper, we illustrate ways of employing the visual results of multidimensional projection algorithms to understand and fine-tune the parameters of their mathematical framework. Some of the common mathematical common to these approaches are Lapla...

A Framework for Exploring Multidimensional Data with 3D Projections

Computer Graphics Forum, 2011

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the Least-Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework's applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

Multidimensional projections for the visual exploration of multimedia data

Brazilian group, thanks for the relaxing and enjoyable time playing together. My research group in Brazil VICG (and ICMC in general), thank you for discussing useful (or not) ideas while drinking coffee, and moments of making fun of each others inside the office. Thanks go to the SVCG research group in Groningen, that treat me kindly and helped me to improve my research skills. Many thanks to the 5 th floor JBI friends, for exploring the city, countries and restaurants, and spending great moments together. Also, I would like to acknowledge the research funding provided by the Brazilian agencies FAPESP (grant 2011/17925-1), CNPq (grant 156580/2011-0), and the research project CAPES/NUFFIC 028/11. Carol, for believing in me more than I usually do, giving me support in hard times and sharing so many great moments together: Thanks a lot. God: No matter who, what or where are You. No matter if You are only one or many. No matter which religion You really belong (if You, in fact, belong to some). What matters is that you are providing me wonderful moments, in wonderful places, with wonderful people. Thanks! Palavr as-chave: visualização de informação, projeção multidimensional, visualização multimídia, visualização explicativa. ABST RACT COIMBRA, D. B.. M ultidimensional proj ections for the visual explor ation of multimedia data. 2016. 236 f. Thesis (Doctorate Candidate Program in Computer Science and Computational Mathematics (ICMC-USP) and of PhD (RUG), in accordance with the international academic agreement for PhD double degree agreement for PhD double degree signed between