Hervé Abdi

Similarity analyses between multiple correlation or covariance tables constitute the cornerstone of network neuroscience. Here, we introduce covSTATIS, a versatile, linear, unsupervised multi-table method designed to identify structured patterns in multi-table data, and allow for the simultaneous extraction and interpretation of both individual and group-level features. With covSTATIS, multiple similarity tables can now be easily integrated, without requiring a priori data simplification, complex black-box implementations, user-dependent specifications, or supervised frameworks. Applications of covSTATIS, a tutorial with Open Data and source code are provided. CovSTATIS offers a promising avenue for advancing the theoretical and analytic landscape of network neuroscience.

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing multivariate categorical data. In these methods, variables are integrated into optimal components computed as linear combinations whose weights are obtained from a generalized singular value decomposition (GSVD) that integrates specific metric constraints on the rows and columns of the original data matrix. The weights of the linear combinations are, in turn, used to interpret the components, and this interpretation is facilitated when components are 1) pairwise orthogonal and 2) when the values of the weights are either large or small but not intermediate-a pattern called a simple or a sparse structure. To obtain such simple configurations, the optimization problem solved by the GSVD is extended to include new constraints that implement component orthogonality and sparse weights. Because multiple correspondence analysis represents qualitative variables by a set of binary variables, an additional group constraint is added to the optimization problem in order to sparsify the whole set representing one qualitative variable. This new algorithm-called group-sparse GSVD (gsGSVD)-integrates these constraints via an iterative projection scheme onto the intersection of subspaces where each subspace implements a specific constraint. In this paper, we expose this new algorithm and show how it can be adapted to the sparsification of simple and multiple correspondence analysis, and illustrate its applications with the analysis of four different data sets-each illustrating the sparsification of a particular CA-based analysis.

Correspondence analysis, multiple correspondence analysis and their discriminant counterparts (i.e., discriminant simple correspondence analysis and discriminant multiple correspondence analysis) are methods of choice for analyzing multivariate categorical data. In these methods, variables are integrated into optimal components computed as linear combinations whose weights are obtained from a generalized singular value decomposition (GSVD) that integrates specific metric constraints on the rows and columns of the original data matrix. The weights of the linear combinations are, in turn, used to interpret the components, and this interpretation is facilitated when components are 1) pairwise orthogonal and 2) when the values of the weights are either large or small but not intermediate-a pattern called a simple or a sparse structure. To obtain such simple configurations, the optimization problem solved by the GSVD is extended to include new constraints that implement component orthogonality and sparse weights. Because multiple correspondence analysis represents qualitative variables by a set of binary variables, an additional group constraint is added to the optimization problem in order to sparsify the whole set representing one qualitative variable. This new algorithm-called group-sparse GSVD (gsGSVD)-integrates these constraints via an iterative projection scheme onto the intersection of subspaces where each subspace implements a specific constraint. In this paper, we expose this new algorithm and show how it can be adapted to the sparsification of simple and multiple correspondence analysis, and illustrate its applications with the analysis of four different data sets-each illustrating the sparsification of a particular CA-based analysis.

Occupations are typically characterized in nominal form, a format that limits options for hypothesis testing and data analysis. We drew upon ratings of knowledge, skills, and abilities for 966 occupations listed in the US Department of Labor’s Occupational Classification Network (O*NET) database to create an accessible, standardized multidimensional space in which occupations can be quantitatively localized and compared. Principal component analysis revealed that the occupation space comprises three main dimensions that correspond to (1) the required amount of education and training, (2) the degree to which an occupation falls within a science, technology, engineering, and mathematics (STEM) discipline versus social sciences and humanities, and (3) whether occupations are more mathematically or health related. Additional occupational spaces reflecting cognitive versus labor-oriented categories were created for finer-grained characterization of dimensions within occupational sets defined by higher or lower required educational preparation. Data-driven groupings of related occupations were obtained with hierarchical cluster analysis (HCA). Proof-of-principle was demonstrated with a real-world dataset (470 participants from the Nathan Kline Institute – Rockland Sample; NKI-RS), whereby verbal and non-verbal abilities—as assessed by standardized testing—were related to the STEM versus social sciences and humanities dimension. Visualization of Latent Components Assessed in O*Net Occupations (VOLCANO) is provided to the research community as a freely accessible tool, along with a Shiny app for users to extract quantitative scores along the relevant dimensions. VOLCANO brings much-needed standardization to unwieldy occupational data. Moreover, it can be used to create new occupational spaces customized to specific research domains.