## 1 Introduction  
Epilepsy is a functional disorder caused by paroxysmal abnormal discharge of brain cells. According to the World Health Organization, about 50 million patients worldwide of all ages are suffering from epilepsy [1]. Conventional manual seizure inspection of long-term EEG monitors is time-consuming. With the rapid development of pervasive sensing in daily healthcare system and machine learning technologies, computer-aided diagnosis mechanisms, such as automated seizure detection based on electroencephalogram (EEG), provides tremendous support for a patient's health and quality of life [2]. Such automated seizure detectors can trigger alarm when users are or will possibly be in a state of seizure. So far, algorithms for automated epileptic seizure detection proposed in most studies consist of three parts: (1) signal domain transformation, such as frequency domain via Fourier transform [3], wavelet time-frequency domain via discrete wavelet transform (DWT) [4; 5], weighted and specific shapes via Hermite transformation [6] or original domain without transformation [7]; (2) feature extraction in the target domain, such as energy features [8] and complexity features [9]; and (3) machine learning based classification using a support vector machine (SVM) [10], k-nearest neighbor (KNN) [11] or artificial neural network (ANN) [12]. However, all the aforementioned three parts have shown limitations in some application scenarios, which are discussed in the following paragraphs separately. For signal domain transformation, in spite of the many transformed domains explored for automated epileptic seizure detection, the most discriminative information resides in the time-frequency domain due to the evident transient characteristics and rich frequency components of epilepsy EEG. Accordingly, discrete wavelet transform (DWT) [4; 5] has been widely applied in EEG based epileptic seizure detection applications because it can represent both the time and frequency characteristics of EEG signals. However, some drawbacks of DWT, such as shift variance, lack of directionality and the oscillation attribute of DWT coefficients [13], limit its effectiveness in some applications. Moreover, the iterated downsampling operations during wavelet decomposition may introduce severe aliasing [13]. Such aliasing can lead to information loss of original signals. Dual tree DWT (DTDWT) [13] can overcome the aforementioned drawbacks of DWT at the cost of increasing information redundancy (a \(2^{d}\) redundancy factor for \(d\)-dimensional signals). But large redundancy may greatly reduce learning efficiency, which in turn weakens the performance of the trained models. For feature extraction in the target domain, complexity features [9] have received a great deal of attention in the biomedical signal processing field in recent years. To measure the complexity property of EEG signals during epileptic seizures, entropy-based features have been widely used, such as sample entropy [9], fuzzy entropy [10], approximate entropy [14], permutation entropy [15] and distribution entropy [9]. All these entropy indicators listed above measure EEG complexity on a single scale. The single scale complexity measure may fail to quantify the underlying dynamics of the extremely complex physiological signals. Therefore, multi-scale entropy (MSE) was proposed [16]. However, the coarse-graining procedure during MSE computation can shorten the length of time sequence but a precise entropy relies heavily on a longer sequence length. For machine learning based classification between normal (or interictal) and ictal seizure EEG, as mentioned earlier, large redundancy may greatly reduce the learning efficiency and increase model complexity. Epileptic seizure detection is a pattern recognition task with a small dataset size due to the scarcity of ictal seizure EEG. With only a small database available for model training, the large amount of redundancy in the seizure detection scenario will especially weaken the model performance.