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Epilepsy is one of the most common brain disorders. For epilepsy diagnosis or treatment, the neurologist needs to observe epileptic spikes from electroencephalography (EEG) data. Since multi-channel EEG records can be naturally represented by multi-way tensors, it is of interest to see whether tensor decomposition is able to analyze EEG epileptic spikes. In this paper, we first proposed the problem of simultaneous multilinear low-rank approximation of tensors (SMLRAT) and proved that SMLRAT can obtain local optimum solutions by using two well-known tensor decomposition algorithms (HOSVD and Tucker-ALS). Second, we presented a new system for automatic epileptic spike detection based on SMLRAT. We propose to formulate the problem of feature extraction from a set of EEG segments, represented by tensors, as the SMLRAT problem. Efficient EEG features were …