New insights into the suitability of the third dimension for visualizing multivariate/multidimensional data: a study based on loss of quality quantification

Most visualization techniques have traditionally used two-dimensional, instead of three-dimensional representations to visualize multidimensional and multivariate data. In this article, a way to demonstrate the underlying superiority of three-dimensional, with respect to two-dimensional, representation is proposed. Specifically, it is based on the inevitable quality degradation produced when reducing the data dimensionality. The problem is tackled from two different approaches: a visual and an analytical approach. First, a set of statistical tests (point classification, distance perception, and outlier identification) using the two-dimensional and three-dimensional visualization are carried out on a group of 40 users. The results indicate that there is an improvement in the accuracy introduced by the inclusion of a third dimension; however, these results do not allow to obtain definitive conclusions on the superiority of three-dimensional representation. Therefore, in order to draw further conclusions, a deeper study based on an analytical approach is proposed. The aim is to quantify the real loss of quality produced when the data are visualized in two-dimensional and three-dimensional spaces, in relation to the original data dimensionality, to analyze the difference between them. To achieve this, a recently proposed methodology is used. The results obtained by the analytical approach reported that the loss of quality reaches significantly high values only when switching from three-dimensional to two-dimensional representation. The considerable quality degradation suffered in the two-dimensional visualization strongly suggests the suitability of the third dimension to visualize data

HyperNP: Interactive Visual Exploration of Multidimensional Projection Hyperparameters

Projection algorithms such as t-SNE or UMAP are useful for the visualization of high dimensional data, but depend on hyperparameters which must be tuned carefully. Unfortunately, iteratively recomputing projections to find the optimal hyperparameter value is computationally intensive and unintuitive due to the stochastic nature of these methods. In this paper we propose HyperNP, a scalable method that allows for real-time interactive hyperparameter exploration of projection methods by training neural network approximations. HyperNP can be trained on a fraction of the total data instances and hyperparameter configurations and can compute projections for new data and hyperparameters at interactive speeds. HyperNP is compact in size and fast to compute, thus allowing it to be embedded in lightweight visualization systems such as web browsers. We evaluate the performance of the HyperNP across three datasets in terms of performance and speed. The results suggest that HyperNP is accurate, scalable, interactive, and appropriate for use in real-world settings

Deep Learning Multidimensional Projections

Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very popular for their ability to visually separate distinct data clusters. However, such methods are computationally expensive for large datasets, suffer from stability problems, and cannot directly handle out-of-sample data. We propose a learning approach to construct such projections. We train a deep neural network based on a collection of samples from a given data universe, and their corresponding projections, and next use the network to infer projections of data from the same, or similar, universes. Our approach generates projections with similar characteristics as the learned ones, is computationally two to three orders of magnitude faster than SNE-class methods, has no complex-to-set user parameters, handles out-of-sample data in a stable manner, and can be used to learn any projection technique. We demonstrate our proposal on several real-world high dimensional datasets from machine learning

Visualization of dynamic multidimensional and hierarchical datasets

When it comes to tools and techniques designed to help understanding complex abstract data, visualization methods play a prominent role. They enable human operators to lever age their pattern finding, outlier detection, and questioning abilities to visually reason about a given dataset. Many methods exist that create suitable and useful visual represen tations of static abstract, non-spatial, data. However, for temporal abstract, non-spatial, datasets, in which the data changes and evolves through time, far fewer visualization tech niques exist. This thesis focuses on the particular cases of temporal hierarchical data representation via dynamic treemaps, and temporal high-dimensional data visualization via dynamic projec tions. We tackle the joint question of how to extend projections and treemaps to stably, accurately, and scalably handle temporal multivariate and hierarchical data. The literature for static visualization techniques is rich and the state-of-the-art methods have proven to be valuable tools in data analysis. Their temporal/dynamic counterparts, however, are not as well studied, and, until recently, there were few hierarchical and high-dimensional methods that explicitly took into consideration the temporal aspect of the data. In addi tion, there are few or no metrics to assess the quality of these temporal mappings, and even fewer comprehensive benchmarks to compare these methods. This thesis addresses the abovementioned shortcomings. For both dynamic treemaps and dynamic projections, we propose ways to accurately measure temporal stability; we eval uate existing methods considering the tradeoff between stability and visual quality; and we propose new methods that strike a better balance between stability and visual quality than existing state-of-the-art techniques. We demonstrate our methods with a wide range of real-world data, including an application of our new dynamic projection methods to support the analysis and classification of hyperkinetic movement disorder data.Quando se trata de ferramentas e técnicas projetadas para ajudar na compreensão dados abstratos complexos, métodos de visualização desempenham um papel proeminente. Eles permitem que os operadores humanos alavanquem suas habilidades de descoberta de padrões, detecção de valores discrepantes, e questionamento visual para a raciocinar sobre um determinado conjunto de dados. Existem muitos métodos que criam representações visuais adequadas e úteis de para dados estáticos, abstratos, e não-espaciais. No entanto, para dados temporais, abstratos, e não-espaciais, isto é, dados que mudam e evoluem no tempo, existem poucas técnicas apropriadas. Esta tese concentra-se nos casos específicos de representação temporal de dados hierárquicos por meio de treemaps dinâmicos, e visualização temporal de dados de alta dimen sionalidade via projeções dinâmicas. Nós abordar a questão conjunta de como estender projeções e treemaps de forma estável, precisa e escalável para lidar com conjuntos de dados hierárquico-temporais e multivariado-temporais. Em ambos os casos, a literatura para técnicas estáticas é rica e os métodos estado da arte provam ser ferramentas valiosas em análise de dados. Suas contrapartes temporais/dinâmicas, no entanto, não são tão bem estudadas e, até recentemente, existiam poucos métodos hierárquicos e de alta dimensão que explicitamente levavam em consideração o aspecto temporal dos dados. Além disso, existiam poucas métricas para avaliar a qualidade desses mapeamentos visuais temporais, e ainda menos benchmarks abrangentes para comparação esses métodos. Esta tese aborda as deficiências acima mencionadas para treemaps dinâmicos e projeções dinâmicas. Propomos maneiras de medir com precisão a estabilidade temporal; avalia mos os métodos existentes, considerando o compromisso entre estabilidade e qualidade visual; e propomos novos métodos que atingem um melhor equilíbrio entre estabilidade e a qualidade visual do que as técnicas estado da arte atuais. Demonstramos nossos mé todos com uma ampla gama de dados do mundo real, incluindo uma aplicação de nossos novos métodos de projeção dinâmica para apoiar a análise e classificação dos dados de transtorno de movimentos