3rd Workshop in Symbolic Data Analysis: book of abstracts

This workshop is the third regular meeting of researchers interested in Symbolic Data Analysis. The main aim of the event is to favor the meeting of people and the exchange of ideas from different fields - Mathematics, Statistics, Computer Science, Engineering, Economics, among others - that contribute to Symbolic Data Analysis

Exploratory Likert Scaling as an Alternative to Exploratory Factor Analysis: Methodological Foundation and a Comparative Example Using an Innovative Scaling Procedure

Identifying the dimensional structure of a set of items (e.g., when studying attitudes) is an important and intricate task in empirical social research. In research practice, exploratory factor analysis is usually employed for this purpose. Factor analysis, however, has known problems that may lead to distorted results. One of its central methodological challenges is to select an adequate multidimensional factor space. Purely statistical decision heuristics to determine the number of factors to be extracted are of only limited value. As I will illus­trate using an example from lifestyle research, there is a considerable risk of fragmenting a complex unidimensional construct by extracting too many factors (overextraction) and splitting it across several factors. As an alternative to exploratory factor analysis, this paper presents an innovative scaling procedure called exploratory Likert scaling. This method­ologically based technique is designed to identify multiple unidimensional scales. It reli­ably finds even extensive latent dimensions without fragmenting them. To demonstrate this benefit, this paper takes up an example from lifestyle research and analyzes it using a novel R package for exploratory Likert scaling. The unidimensional scales are constructed se­quentially by means of bottom-up item selection. Exploratory Likert scaling owes its high analytical potential to the principle of multiple scaling, which is adopted from Mokken scale analysis and transferred to classical test theory

Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

International audienceBackground: In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions. Methods: Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 “High-dimensional data” of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD. Results: The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided. Conclusions: This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses

Doctor of Philosophy

dissertationWith the ever-increasing amount of available computing resources and sensing devices, a wide variety of high-dimensional datasets are being produced in numerous fields. The complexity and increasing popularity of these data have led to new challenges and opportunities in visualization. Since most display devices are limited to communication through two-dimensional (2D) images, many visualization methods rely on 2D projections to express high-dimensional information. Such a reduction of dimension leads to an explosion in the number of 2D representations required to visualize high-dimensional spaces, each giving a glimpse of the high-dimensional information. As a result, one of the most important challenges in visualizing high-dimensional datasets is the automatic filtration and summarization of the large exploration space consisting of all 2D projections. In this dissertation, a new type of algorithm is introduced to reduce the exploration space that identifies a small set of projections that capture the intrinsic structure of high-dimensional data. In addition, a general framework for summarizing the structure of quality measures in the space of all linear 2D projections is presented. However, identifying the representative or informative projections is only part of the challenge. Due to the high-dimensional nature of these datasets, obtaining insights and arriving at conclusions based solely on 2D representations are limited and prone to error. How to interpret the inaccuracies and resolve the ambiguity in the 2D projections is the other half of the puzzle. This dissertation introduces projection distortion error measures and interactive manipulation schemes that allow the understanding of high-dimensional structures via data manipulation in 2D projections