Facial Emotion Recognition (FER) represents a critical domain within the realms of machine vision and artificial intelligence, finding widespread applications in both academic research and various industries. While there exist multiple sensors for conducting FER, recent studies emphasize the effectiveness of utilizing facial images/videos to discern emotions due to the rich information embedded in visual expressions. This study specifically addresses the task of detecting compound emotions using the iCV Multi-Emotion Facial Expression Dataset (iCV-MEFED) and explores different learning frameworks. In our initial approach, a deep learning Convolutional Neural Network (CNN) model was employed to extract features from each image. Subsequently, a Multi-Class Support Vector Machine (mSVM) classifier was utilized to identify the corresponding emotions. Our research presents two novel approaches for compound facial emotion recognition. The first methodology, a machine learning-based framework, achieved a 26% accuracy rate, which represents an improvement over previous state-of-the-art results. This approach demonstrated superior performance in misclassification analysis, with a 74.00% accuracy rate. The second methodology employs a deep learning CNN-based model enhanced by WCHGSO-DNFN optimization. This approach yielded a 28% accuracy rate on the iCV-MEFED dataset, again surpassing existing benchmarks. In misclassification comparisons, this method achieved a 72.00% accuracy rate, consistently outperforming competing approaches.