In 1869, the first draft of the periodic table was published by Russian chemist Dmitri Mendeleev. In terms of data science, his achievement can be viewed as a successful example of feature embedding based on human cognition: chemical properties of all known elements at that time were compressed onto the two-dimensional grid system for tabular display. In this study, we seek to answer the question of whether machine learning can reproduce or recreate the periodic table by using observed physicochemical properties of the elements. To achieve this goal, we developed a periodic table generator (PTG). The PTG is an unsupervised machine learning algorithm based on the generative topographic mapping (GTM), which can automate the translation of high-dimensional data into a tabular form with varying layouts on-demand. The PTG autonomously produced various arrangements of chemical symbols, which organized a two-dimensional array such as Mendeleev's periodic table or three-dimensional spiral table according to the underlying periodicity in the given data. We further showed what the PTG learned from the element data and how the element features, such as melting point and electronegativity, are compressed to the lower-dimensional latent spaces.

This article started out as an addendum to a chapter in our book, Data Visualization: A History of Visual Thinking and Graphic Communication (Friendly & Wainer, 2020). In this we claimed that much of the history of data visualization could be seen as combination of three forces: (1) important scientific problems of the day, (2) a developing abundance of data, and (3) the cognitive ability of some heroes in this history to conceive solutions to problems by visual imagination. In the book and what follows we make frequent reference to cognitive aspects of the visual understanding of phenomena and their expression in graphic displays: "inner vision", "graphic communication", "visual insight" are some of the terms we use. An early metaphor for this and an early title for our book was "A gleam in the mind's eye." We give some additional explanations and examples here. We also want to place this topic in a wider framework.