Neonatal seizures are the most common neurological emergency in the neonatal period and are associated with a poor long-term outcome. Early detection and treatment may improve prognosis. This paper aims to develop an optimal set of parameters and a comprehensive scheme for patient-independent multi-channel EEG-based neonatal seizure detection. We employed a dataset containing 411 neonatal seizures. The dataset consists of multi-channel EEG recordings with a mean duration of 14.8 h from 17 neonatal patients. Early-integration and late-integration classifier architectures were considered for the combination of information across EEG channels. Three classifier models based on linear discriminants, quadratic discriminants and regularized discriminants were employed. Furthermore, the effect of electrode montage was considered. The best performing seizure detection system was found to be an early integration configuration employing a regularized discriminant classifier model. A referential EEG montage was found to outperform the more standard bipolar electrode montage for automated neonatal seizure detection. A cross-fold validation estimate of the classifier performance for the best performing system yielded 81.03% of seizures correctly detected with a false detection rate of 3.82%. With post-processing, the false detection rate was reduced to 1.30% with 59.49% of seizures correctly detected. These results represent a comprehensive illustration that robust reliable patient-independent neonatal seizure detection is possible using multi-channel EEG.