# The Geometry and Topology of Data and Information for Analytics of Processes and Behaviours: Building on Bourdieu and Addressing New Societal Challenges

## TL;DR

This paper emphasizes the importance of geometric and topological methods in data analytics, critiques traditional sampling, and advocates for a Bourdieu and Benzécri-inspired approach to connect data with societal decision-making, illustrated through case studies.

## Contribution

It introduces a novel perspective combining geometry, topology, and Bourdieu's social theory to enhance data analytics for societal challenges.

## Key findings

- Geometric and topological methods improve data understanding.
- Questioning traditional sampling methods.
- Case studies demonstrate practical applications.

## Abstract

We begin by summarizing the relevance and importance of inductive analytics based on the geometry and topology of data and information. Contemporary issues are then discussed. These include how sampling data for representativity is increasingly to be questioned. While we can always avail of analytics from a "bag of tools and techniques", in the application of machine learning and predictive analytics, nonetheless we present the case for Bourdieu and Benz\'ecri-based science of data, as follows. This is to construct bridges between data sources and position-taking, and decision-making. There is summary presentation of a few case studies, illustrating and exemplifying application domains.