This paper presents a procedure for the patient-specific prediction of epileptic seizures. To this end, a combination of nonnegative matrix factorization (NMF) and smooth basis functions with robust regression is applied to power spectra of intracranial electroencephalographic (iEEG) signals. The resulting time and frequency components capture the dominant information from power spectra, while removing outliers and noise. This makes it possible to detect structure in preictal states, which is used for classification. Linear support vector machines (SVM) with L1 regularization are used to select and weigh the contributions from different number of not equally informative channels among patients. Due to class imbalance in data, synthetic minority over-sampling technique (SMOTE) is applied. The resulting method yields a computationally and conceptually simple, interpretable model of EEG signals of preictal and interictal states, which shows a good performance for the task of seizure prediction on two datasets (the EPILEPSIAE and on the public Epilepsyecosystem dataset).