Enterprise AI Analysis: Scientific Reports (2025) 15:41888

Deep Maxout Networks for Non-Linear Decision Making

The Deep Maxout Network (DMN) is an advanced deep learning framework characterized by its unique maxout activation function, which generalizes the ReLU activation. This function performs a maximum operation over multiple linear functions, enabling the network to learn intricate piecewise linear decision boundaries.

The DMN architecture consists of an input layer (39-dimensional MFCC features), three hidden maxout layers with 256, 512, and 256 units respectively, and a softmax output layer for classifying 4 emotion categories (anger, happiness, neutral, sadness).

Training incorporates batch normalization and a dropout rate of 0.5 after each layer to prevent overfitting. The Adam optimizer is used with an initial learning rate of 0.001 and a batch size of 64, minimizing cross-entropy loss.

Modified Water Cycle Algorithm for Adaptive Tuning

The Modified Water Cycle Algorithm (M-WCA) is a nature-inspired metaheuristic algorithm specifically enhanced to optimize the Deep Maxout Network (DMN) hyperparameters. This includes tuning parameters such as DMN layer depth, number of maxout units, dropout rates, learning rates, and batch size.

Key improvements include the integration of Lévy flight dynamics, which enables long-distance jumps in the search space. This prevents the algorithm from getting trapped in local optima and improves global exploration efficiency in high-dimensional spaces.

A self-adaptive population enhancement mechanism dynamically adjusts the number of candidate solutions based on their cost values. It incorporates mutation, crossover, and elitist strategies to maintain diversity, ensure optimal solutions are preserved, and prevent premature convergence, leading to a more robust optimization process.

Synergistic Integration for Enhanced Performance

The proposed framework achieves significant synergy through the tight integration of MFCCs, Deep Maxout Networks (DMN), and the Modified Water Cycle Algorithm (MWCA).

MFCCs provide a compact, perceptually meaningful representation of emotional speech. These features are directly fed into DMN's Maxout units, allowing the network to effectively learn piecewise linear decision boundaries that model complex, non-linear emotional transitions.

The MWCA critically tunes the DMN's architectural parameters (e.g., number of Maxout units, dropout rates, learning rate) within a closed-loop optimization framework. This ensures that the DMN is optimally configured to capture the stability and discriminability of MFCC features across emotional classes.

This holistic approach ensures that signal conditioning, feature representation, and network optimization contribute synergistically to the overall effectiveness and adaptability of the emotion recognition system, leading to superior performance.

Robust Performance Across Diverse Datasets

The DMN-MWCA model's performance was rigorously evaluated on two widely recognized and diverse datasets: the Emo-DB (German emotional speech) and the CASIA-Chinese Emotional Speech Corpus.

On Emo-DB, the model achieved an impressive 93.1% average accuracy and a 92.4% F1-score. On the CASIA dataset, it demonstrated strong performance with an 89.7% accuracy.

These results indicate the model's capacity for strong cross-corpus generalization, performing effectively even when switching to different languages and cultural contexts. The DMN-MWCA significantly outperformed baseline models including WCA-DMN, LSTM, CNN, SVM, and DMN without optimization, with statistically significant improvements (p < 0.01).

Further analysis showed superior performance compared to other state-of-the-art deep learning architectures like Transformer, CNN-LSTM, BiLSTM-Attention, and ResNet-18. Narrow 95% confidence intervals (±0.4% for Emo-DB, ±0.5% for CASIA) confirm the high consistency and reproducibility of the model's performance across repeated trials.