Objective. Seizure prediction devices for drug-resistant epileptic patients could lead to improved quality of life and new treatment options, but current approaches to classification of electroencephalography (EEG) segments for early identification of the pre-seizure state typically require many features and complex classifiers. We therefore propose a novel spatio-temporal EEG feature set that significantly aids in separation and easy classification of the interictal and preictal states. Approach. We derive key spectral features from the embedded dynamic mode decomposition (EmDMD) of the brain state system. This method linearizes the complex spatio-temporal dynamics of the system, describing the dynamics in terms of a spectral basis of modes and eigenvalues. The relative subband spectral power and mean phase locking values of these modes prove to be good indicators of the preictal state that precedes seizure onset. Main results. We analyze the linear separability and classification of preictal and interictal states based on our proposed features using seizure data extracted from the CHB-MIT scalp EEG and Kaggle American Epilepsy Society Seizure Prediction Challenge intracranial EEG databases. With a light-weight support vector machine or random forest classifier trained on these features, we classify the preictal state with a sensitivity of up to 92% and specificity of up to 89%. Significance. The EmDMD-derived features separate the preictal and interictal states, improving classification accuracy and motivating further work to incorporate them into seizure prediction algorithms.