How Complex is your classification problem? A survey on measuring classification complexity (1808.03591v3)

Abstract: Characteristics extracted from the training datasets of classification problems have proven to be effective predictors in a number of meta-analyses. Among them, measures of classification complexity can be used to estimate the difficulty in separating the data points into their expected classes. Descriptors of the spatial distribution of the data and estimates of the shape and size of the decision boundary are among the known measures for this characterization. This information can support the formulation of new data-driven pre-processing and pattern recognition techniques, which can in turn be focused on challenges highlighted by such characteristics of the problems. This paper surveys and analyzes measures which can be extracted from the training datasets in order to characterize the complexity of the respective classification problems. Their use in recent literature is also reviewed and discussed, allowing to prospect opportunities for future work in the area. Finally, descriptions are given on an R package named Extended Complexity Library (ECoL) that implements a set of complexity measures and is made publicly available.

• The paper introduces a comprehensive survey of classification complexity measures and presents the ECoL R package for practical evaluation.
• It categorizes measures into six groups—feature-based, linearity, neighborhood, network, dimensionality, and imbalance—to clarify challenges in algorithm performance.
• It provides theoretical insights and practical guidelines to optimize feature selection, data preprocessing, and algorithm configuration.

Analysis of Classification Complexity: Insights from a Comprehensive Survey

The paper provides a comprehensive review of techniques developed for assessing the complexity of classification problems. The characterization of classification complexity is essential for understanding when and why certain machine learning algorithms succeed or fail. This understanding drives improvements in algorithm development as well as strategic preprocessing of datasets.

Key Contributions and Measures

The paper revisits the foundational work of Ho and Basu, which categorized classification complexity based on class ambiguity, data sparsity, dimensionality, and boundary complexity. It extends the analysis by examining a broader array of complexity measures and introduces an R package, Extended Complexity Library (ECoL), which provides tools for computing these measures.

The measures are systematically divided into six categories:

1. Feature-based Measures: These assess individual features' discriminative power, like the Maximum Fisher's Discriminant Ratio (F1) and its directional variant (F1v).
2. Linearity Measures: These evaluate whether data can be linearly separated, leveraging techniques like the linear SVM.
3. Neighborhood Measures: This set evaluates local data neighborhoods, including the complexity of decision boundaries, with measures like Fraction of Borderline Points (N1).
4. Network Measures: These treat data points as vertices in a graph, exploring connectivity and clustering in data.
5. Dimensionality Measures: These focus on data sparsity, indicating how sparsely data points populate feature space.
6. Class Imbalance Measures: They quantify the degree of class imbalance, which can notably affect predictive performance.

Each of these measures offers a unique perspective on classification complexity, and when synthesized, they provide a multifaceted view that is indispensable for comprehensive problem analysis.

Practical and Theoretical Implications

Practical Applications: The complexity measures are instrumental in practical machine learning tasks such as guiding feature selection, noise detection, data preprocessing, and understanding algorithm domains of competence. By better characterizing datasets, practitioners can refine the choice and configuration of algorithms to improve predictive performance.

Meta-Learning and Algorithm Selection: In a meta-learning context, these measures serve as meta-features in predicting the performance of learning algorithms. By examining the interplay between complexity measures and algorithm performance, the study aids in constructing frameworks for recommending algorithms or preprocessing methods for newly encountered datasets.

Theoretical Insights: The investigation of complexity measures provides insights into the structural nuances of data that influence learning. This information is pivotal for theoretical advancements in understanding the limitations and capabilities of different machine learning approaches.

Future Directions

The insights presented in this survey invite several avenues for future development. There's a potential for refining complexity measures to address specific types of data, such as those encountered in high-dimensional, small-sample scenarios. Furthermore, extending these concepts beyond classification to domains like regression and clustering could pave the way for more generalized complexity analyses.

Developing integrated frameworks that automatically assess data complexity and recommend algorithmic strategies is another prospective direction. Additionally, these endeavors could connect more closely with developments in explainable AI, providing transparency into why certain data characteristics affect model outcomes.

In conclusion, the paper underscores the necessity of complexity analysis in supervised learning. As machine learning applications continue to expand into varied and demanding domains, the importance of such foundational work becomes ever more apparent, serving as a bridge between core scientific understanding and application in real-world data scenarios.