Optimizing CbO-based algorithms via heuristic attribute reordering in L-fuzzy contexts

This paper investigates how reordering attributes in L-fuzzy contexts affects CbO algorithm performance. We propose and test heuristics, like ordering by non-zero entries or lower cone size, and show they can reduce runtime by up to 40%, providing a guide for selecting the best pre-processing strategy.

Keywords

Attribute reordering, Close-by-One, CbO, InClose, FastCbO, Performance optimization, L-fuzzy contexts

The performance of Close-by-One (CbO) family algorithms for constructing concept lattices is known to be sensitive to the order in which attributes are processed. While this is often overlooked, a strategic ordering can significantly prune the search tree, leading to substantial performance gains. This paper investigates the impact of attribute ordering on the efficiency of L-fuzzy lattice construction algorithms. We propose and analyze several heuristic ordering strategies, including ordering by the number of non-zero entries (nnz) and by the average size of the lower cone of attribute grades. Through extensive empirical evaluation on fuzzy CbO variants (FastCbO, InClose), we demonstrate that a simple, data-driven reordering of the formal context prior to computation can reduce runtime by up to 40% in certain scenarios. We analyze the theoretical underpinnings of why certain orderings are more effective and provide a practical guide for selecting an optimal strategy based on context characteristics.

Introduction

Algorithms from the Close-by-One (CbO) family, such as FastCbO and InClose, build the concept lattice by traversing a search tree. The branching factor of this tree at any given node is determined by the set of attributes yet to be processed. Consequently, the order in which attributes are introduced influences the tree’s shape and the effectiveness of pruning strategies. An attribute that leads to a large closure early on can significantly reduce the number of subsequent branches, accelerating the computation.

Despite its potential impact, attribute ordering is rarely treated as a tunable parameter. This paper addresses this gap, specifically within the L-FCA framework. We hypothesize that by processing “more informative” attributes first, we can induce earlier and more aggressive pruning of the search space. Our contributions are:

1. A formal analysis of how attribute ordering interacts with the canonicity tests and pruning mechanisms of fuzzy CbO-style algorithms.
2. The proposal of several heuristic ordering strategies, notably one based on the average lower cone size, which aims to prioritize attributes with higher grades.
3. A comprehensive empirical study (partially presented in ) that quantifies the performance impact of these heuristics on state-of-the-art fuzzy algorithms.

Methodology and expected results

Heuristic ordering strategies

We will formally define and implement the following ordering heuristics for an L-fuzzy context: * Default order: The original order of attributes in the dataset. * NNZ (Number of non-zeros): Order attributes in increasing order of the number of objects for which they have a non-zero grade. The intuition is to deal with sparse attributes first. * Lower cone (LC): For each attribute $m$, calculate its average lower cone size: $\mu(m) = \frac{1}{|G|} \sum_{g \in G} |\{l' \in L \mid l' \le I(g,m)\}|$. Attributes are processed in decreasing order of $\mu(m)$. The intuition is to prioritize attributes that are “stronger” or have higher grades across objects, as they are more likely to lead to larger closures and thus more effective pruning.

Experimental protocol

We will use the optimized fuzzy InClose5* and fuzzy FastCbO implementations. For a wide range of synthetic contexts (varying $|G|, |M|, |L|$, and density), we will:

1. Apply each of the reordering heuristics to the context.
2. Run each algorithm on the reordered context.
3. Measure runtime, number of closure computations, and number of canonicity tests performed.

The goal is to produce plots that clearly show the performance difference between ordering strategies under different context conditions.

Expected results

Based on preliminary findings, we expect the LC ordering to provide the most significant performance boost for InClose algorithms, by reducing the number of nodes in the search tree. For NextClosure, it is expected to reduce the number of intents computed. We also expect to find that the effectiveness of a given heuristic depends on the algorithm used; for example, an ordering that benefits InClose (which uses incremental closures) might not be optimal for FastCbO (which computes full closures).

Work plan

• Weeks 1-2: Formalize the heuristic definitions and finalize their implementation.
• Weeks 3-7: Run the full experimental battery. This involves a large number of algorithm-ordering-dataset combinations.
• Weeks 8-10: Deeply analyze the results. Go beyond “which is faster” to explain why a certain ordering works best for a specific algorithm by instrumenting the code to track key internal metrics (e.g., average tree depth, pruning effectiveness).
• Weeks 11-12: Write the manuscript, focusing on providing actionable advice for practitioners.

Potential target journals

1. Information Sciences (Q1): Excellent choice for a paper with strong, practical algorithmic and empirical contributions.
2. Expert Systems with Applications (Q1): Suitable if the paper is framed as a guide to “best practices” for efficiently applying FCA.
3. FUZZ-IEEE Conference: A great venue for the initial publication, as demonstrated by your prior work.

Minimum viable article (MVA) strategy

This is a self-contained empirical study, perfect for a single, strong publication. * Paper 1 (The MVA - conference and journal): * Scope: The complete study as described above. The novelty lies in the systematic investigation and the proposal of the LC heuristic. A first version can beG to a conference. * Goal: To establish attribute reordering as a critical and simple pre-processing step for efficient FCA computation. * Target venue (conference): FUZZ-IEEE or IPMU. You have already published abstracts on this topic , so a full paper is the next logical step. * Target venue (journal): Following the conference, an extended version with more experiments and deeper analysis should be submitted to Information Sciences.