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Flexible categorization using formal concept analysis and Dempster-Shafer theory

Marcel Boersma, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Apostolos Tzimoulis, Nachoem Wijnberg

TL;DR

This paper develops a formal framework combining Formal Concept Analysis and Dempster-Shafer theory to study explainable categorizations driven by agents' epistemic attitudes. It introduces crisp and non-crisp interrogative agendas to generate parametric categorization systems and presents a stability-based method to map non-crisp agendas to a single, interpretable concept lattice. A meta-learning algorithm learns agenda weights across lattices to produce both global and local explanations for classification and outlier detection tasks, demonstrated in a financial statements network. The approach offers a principled, interpretable pathway for human-machine collaboration in auditing and other data-rich domains, with potential extensions to data mining and knowledge management.

Abstract

The framework developed in the present paper provides a formal ground to generate and study explainable categorizations of sets of entities, based on the epistemic attitudes of individual agents or groups thereof. Based on this framework, we discuss a machine-leaning meta-algorithm for outlier detection and classification which provides local and global explanations of its results.

Flexible categorization using formal concept analysis and Dempster-Shafer theory

TL;DR

This paper develops a formal framework combining Formal Concept Analysis and Dempster-Shafer theory to study explainable categorizations driven by agents' epistemic attitudes. It introduces crisp and non-crisp interrogative agendas to generate parametric categorization systems and presents a stability-based method to map non-crisp agendas to a single, interpretable concept lattice. A meta-learning algorithm learns agenda weights across lattices to produce both global and local explanations for classification and outlier detection tasks, demonstrated in a financial statements network. The approach offers a principled, interpretable pathway for human-machine collaboration in auditing and other data-rich domains, with potential extensions to data mining and knowledge management.

Abstract

The framework developed in the present paper provides a formal ground to generate and study explainable categorizations of sets of entities, based on the epistemic attitudes of individual agents or groups thereof. Based on this framework, we discuss a machine-leaning meta-algorithm for outlier detection and classification which provides local and global explanations of its results.
Paper Structure (25 sections, 7 theorems, 30 equations, 8 figures, 4 tables, 1 algorithm)

This paper contains 25 sections, 7 theorems, 30 equations, 8 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation and main contribution.
  3. Interrogative agendas.
  4. Background theory.
  5. Meta-algorithm.
  6. Related work.
  7. Structure of the paper.
  8. Preliminaries
  9. Formal contexts and their concept lattices
  10. Discretization of continuous attributes and conceptual scaling.
  11. Belief, plausibility and mass functions
  12. Categorizations induced by interrogative agendas
  13. Crisp framework.
  14. Non-crisp framework.
  15. Example: financial statements network
  16. ...and 10 more sections

Key Result

Proposition 4

For any non-crisp agenda $m$ and all $\beta_1, \beta_2 \in [0,1]$, if $\beta_1 \leq \beta_2$, then $\mathcal{C}(m,\beta_2)\subseteq \mathcal{C}(m,\beta_1)$ and $\mathbb{L}(m,\beta_2)\subseteq \mathbb{L}(m,\beta_1)$.

Figures (8)

  • Figure 1: Concept lattice associated with the crisp agenda $\{x_1, x_2, x_5\}$ of agent $j_1$
  • Figure 2: Concept lattice associated with the crisp agenda $\{x_1, x_2, x_3\}$ of agent $j_2$
  • Figure 3: Concept lattice associated with the crisp agenda $\{x_1, x_3\}$ of agent $j_3$
  • Figure 4: Concept lattice associated with the crisp agenda $\rhd c =\{x_1,x_2,x_3,x_5\}$
  • Figure 5: This concept lattice is all of the following: (1) the concept lattice associated with the crisp agenda $\Diamond c=\{x_1\}$ in case, (2) most preferred categorization associated with the non-crisp agendas $m_1$ of $j_1$, $m_2$ of $j_2$, and $\oplus c$ (3) categorization obtained from non-crisp agendas $m_1$ and $\oplus c$ using stability-based method for $\beta=0.5$.
  • ...and 3 more figures

Theorems & Definitions (19)

  • Definition 1
  • Remark 2
  • Definition 3
  • Proposition 4
  • proof
  • Remark 5
  • Definition 6
  • Lemma 7
  • proof
  • Proposition 8
  • ...and 9 more