Interactively visualizing pattern-based summaries of fuzzy tensors

Abstract

Many datasets are $n$ -way fuzzy tensors, that is, $n$ -dimensional tables where every cell grades in $[0,1]$ the truth of a statement instantiated by the $n$ elements indexing the cell. In the special case where $n=2$ , fuzzy matrices encode to what extent objects (the rows) have attributes (the columns). Boolean tensors are another special case, in which the statement is always either false ( $0$ ) or true ( $1$ ). Theoretically simple pattern-based models exist for $n$ -way Boolean or fuzzy tensors, and so do algorithms to discover sets of patterns well summarizing the tensors, according to these models. However, intuitively understanding such summaries has remained difficult. Tools specifically assisting data scientists in that endeavor are lacking. This article addresses that issue. It proposes the first interactive visualization for pattern-based summaries of fuzzy tensors. Pieces of information that are relevant to the interpretation of a summary are extracted from the study of the disjunctive box cluster model. They are turned into visual objects, attributes or interaction techniques. Special attention is given to allowing the exploration of summaries with many large patterns, as shown with the analysis of 55 patterns involving thousands of elements and summarizing a $12\times 170670\times 29$ real-world tensor.