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RVFL-X: A Novel Randomized Network Based on Complex Transformed Real-Valued Tabular Datasets

M. Sajid, Mushir Akhtar, A. Quadir, M. Tanveer

TL;DR

This work addresses the challenge of leveraging complex-valued representations for real-valued tabular data by introducing two data-to-complex conversion methods (natural and autoencoder-based) and a complex-valued RVFL variant, RVFL-X. The authors show that complex inputs, weights, and activations can be integrated into a RVFL framework while maintaining its simplicity and efficiency, producing real-valued outputs. Extensive experiments on 80 UCI datasets across four category groups demonstrate that RVFL-X, especially the Auto variant, achieves higher accuracy, lower variance, and superior rankings compared to 10 SOTA baselines, with statistical tests supporting significance. The results suggest RVFL-X offers robust generalization and practical potential for a wide range of real-world tabular-data tasks, with opportunities for deeper or ensemble extensions.

Abstract

Recent advancements in neural networks, supported by foundational theoretical insights, emphasize the superior representational power of complex numbers. However, their adoption in randomized neural networks (RNNs) has been limited due to the lack of effective methods for transforming real-valued tabular datasets into complex-valued representations. To address this limitation, we propose two methods for generating complex-valued representations from real-valued datasets: a natural transformation and an autoencoder-driven method. Building on these mechanisms, we propose RVFL-X, a complex-valued extension of the random vector functional link (RVFL) network. RVFL-X integrates complex transformations into real-valued datasets while maintaining the simplicity and efficiency of the original RVFL architecture. By leveraging complex components such as input, weights, and activation functions, RVFL-X processes complex representations and produces real-valued outputs. Comprehensive evaluations on 80 real-valued UCI datasets demonstrate that RVFL-X consistently outperforms both the original RVFL and state-of-the-art (SOTA) RNN variants, showcasing its robustness and effectiveness across diverse application domains.

RVFL-X: A Novel Randomized Network Based on Complex Transformed Real-Valued Tabular Datasets

TL;DR

This work addresses the challenge of leveraging complex-valued representations for real-valued tabular data by introducing two data-to-complex conversion methods (natural and autoencoder-based) and a complex-valued RVFL variant, RVFL-X. The authors show that complex inputs, weights, and activations can be integrated into a RVFL framework while maintaining its simplicity and efficiency, producing real-valued outputs. Extensive experiments on 80 UCI datasets across four category groups demonstrate that RVFL-X, especially the Auto variant, achieves higher accuracy, lower variance, and superior rankings compared to 10 SOTA baselines, with statistical tests supporting significance. The results suggest RVFL-X offers robust generalization and practical potential for a wide range of real-world tabular-data tasks, with opportunities for deeper or ensemble extensions.

Abstract

Recent advancements in neural networks, supported by foundational theoretical insights, emphasize the superior representational power of complex numbers. However, their adoption in randomized neural networks (RNNs) has been limited due to the lack of effective methods for transforming real-valued tabular datasets into complex-valued representations. To address this limitation, we propose two methods for generating complex-valued representations from real-valued datasets: a natural transformation and an autoencoder-driven method. Building on these mechanisms, we propose RVFL-X, a complex-valued extension of the random vector functional link (RVFL) network. RVFL-X integrates complex transformations into real-valued datasets while maintaining the simplicity and efficiency of the original RVFL architecture. By leveraging complex components such as input, weights, and activation functions, RVFL-X processes complex representations and produces real-valued outputs. Comprehensive evaluations on 80 real-valued UCI datasets demonstrate that RVFL-X consistently outperforms both the original RVFL and state-of-the-art (SOTA) RNN variants, showcasing its robustness and effectiveness across diverse application domains.

Paper Structure

This paper contains 20 sections, 18 equations, 2 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Motivation and Contribution
  3. Related Work
  4. Notations
  5. RVFL Neural Network
  6. Proposed Work
  7. Conversion of Real-valued Data to Complex-valued Data
  8. Natural Method
  9. Autoencoder-Based Method
  10. RVFL-X
  11. Experiments, Results and Discussion
  12. Compared Models, Datasets and Experimental Setup
  13. Evaluation on C-1 Category Datasets
  14. Evaluation on C-2 Category Datasets
  15. Evaluation on C-3 Category Datasets
  16. ...and 5 more sections

Figures (2)

  • Figure 1: Architecture of the proposed RVFL-X network.
  • Figure 2: Sensitivity analyses of the proposed RVFL-X-N and RVFL-X-Auto models w.r.t. $\alpha$.