With the rapid development of data collection and processing technologies, more and more complex data with different views or modalities are emerging. Generally, we call them multi-view data. Some toy examples of multi-view data are illustrated in Fig. 2. For example, in natural language processing, the same semantic meaning can be described by different languages, and each language corresponds to a view. When depicting objects, the morphology of the whole object can be depicted by images from different angles, each angle corresponds to a view. In clinical diagnosis, X-ray images, electrocardiograms, and clinical examination results can be taken as different views/modalities. In EEG signals analysis, time-domain, frequency-domain and time-frequency-domain can be extracted by wavelet packet decomposition (WPD), short-time Fourier transform (STFT), kernel principal component analysis (KPCA) etc. Each type of features can be taken as a view. These views have different feature spaces, but they all describe the same object, reveal different characteristics of the object.

In earlier studies, most traditional algorithms for epileptic EEG signals analysis were single-view based, which not only fail to tap the consensus and complementary information of each view, but also may lead to dimensional disasters. In subsequent studies, some scholars demonstrated that multi-view learning has better classification performance than single-view learning [16,17]. Jiang et al. proposed a multi-view Takagi-Sugeno-Kang fuzzy system. This system uses multi-view data to enable the model to produce more comprehensive and reasonable results than traditional single-view learning models [18]. Zhu et al. proposed a novel double-index-constrained, multi-view, fuzzy clustering algorithm (DIC-MV-FCM), which has better clustering performance than traditional clustering algorithms when dealing with multi-view EEG signals [19]. Although all of the above studies demonstrated the advantages of multi-view learning over single-view learning, none of them focused on the possible overfitting effects of multi-view learning in the model training process.

Transfer learning is a machine learning technique whose main idea is to exploit the similarities between data, models and tasks. Transfer learning attempts to learn a model by applying the pre-learned knowledge in a domain with sufficient training data to a new domain and increase the generalization performance of the model. Transfer learning can usually be classified as instance transfer, feature transfer, relationship transfer, and model transfer [20]. In transfer learning, the domain where the learning is performed in advance is called the source domain and domain that accepts the knowledge learned in advance is called the target domain. Instance-based transfer is done by changing the existence form of samples to reduce the difference between source and target domain; feature-based transfer is done by mapping the source and target domain in some feature space and minimizing the distance between them through feature transformation; relationship-based transfer is done by creating a mapping of the correlation knowledge between two domains; model-based transfer is done by sharing certain parameters between the source domain model and the target domain model and adjusting them to accomplish knowledge transfer.

Transfer learning has also received extensive attention from researchers in the research field related to EEG signals processing. Jeng et al. proposed a transfer learning framework based on low-dimensional topic representation to address the problem of human variability in brain-computer interface [21]. Sameri et al. used a multi-stage fine-tuning approach during transfer learning to train end-to-end CNN models to learn discriminative features from EEG signals [22]. Zhang et al. proposed a Kullback–Leibler divergence-based transfer learning algorithm to deal with the effects of the non-stationarity of the motor imagery EEG signals [23].

In epilepsy diagnosis studies, Wang et al. found that in some scenarios, the classification of epileptic EEG signals was not finely delineated. Therefore, they utilized sub-band mean amplitude spectrum map (MAS) of multichannel EEG for signal representation and used three commonly used deep convolutional neural networks for feature transfer learning separately, achieving classification performance of prefrontal epilepsy signals on a fine time scale [24]. Song et al. proposed a new EEG-based epilepsy detection strategy, the main idea of which is to use an improved transfer learning model to decode EEG models in the nonlinear dynamic domain, and this framework does not lose important nonlinear features to a certain extent, a property that makes the model outperform seven well-known neural network transfer learning models and provides new insights into EEG decoding [25]. Although transfer learning algorithms have been extensively used in the study of EEG signals, there are still relatively few transfer learning-based algorithms for seizure detection, necessitating additional study and performance validation.

Multi-view learning, which involves learning from several views, can enhance a model’s performance by enabling it to comprehend information from various views more thoroughly. Transfer learning enables us to use information from similar issues to aid the model in problem-solving, which can enhance the model’s generalization capabilities and stability. Therefore, by including a multi-view learning algorithm into transfer learning, it is possible to avoid both the one-sided description of single-view data as well as the lack of experimental data.

Currently, there are not many studies using multi-view learning algorithms in the field of transfer learning. At first, Xu et al. chose the adaboost algorithm to implement multi-view transfer learning, and although the experimental results proved the feasibility of the algorithm, this algorithm was developed based on two-view data and did not make good use of multi-view learning [26]. With the change of research direction, this type of algorithm is mostly used in the research of object classification. For instance, Liu et al. was studied on categorizing moving objects in traffic scenes used the adaboost-based multi-view transfer learning technique. A modest number of labeled target scene instances in this system can greatly enhance performance and reduce labeling time and labor requirements [27]. Bian et al. considered that using deep neural networks for automatic dermatological classification would largely limit the scalability of the model, and proposed a multi-view filtered transfer learning network to represent the discriminative information from different image views with a reasonable weighting strategy [28]. In the research area related to EEG sensing signals processing, Jiang et al. proposed an online multi-view transfer learning model with high interpretability for identifying fatigue driving based on EEG sensing signals, considering that the existing classification models are based on single-view data and are not interpretable transfer learning models. In this model, features in both the source and target domains are multi-view data, allowing more pattern information to be utilized during model training [29]. Abbas et al. proposed a real-time driver inattention and fatigue detection system by extracting hybrid features from multi-view cameras and biosignal sensors [30]. Although multi-view transfer learning algorithms have been used in the study of EEG sensing signals, further research and performance validation are still required for the algorithms that have been explored for seizure identification.

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Considering the lack of experimental data, traditional transfer learning algorithms can transfer data or model knowledge from different source domains to exploit patterns related to the target. However, the transfer learning process requires knowledge sharing and exchange among participants, which poses a greater risk to the data privacy of participants.

Based on the above motivations, we propose a multi-view transfer learning algorithm. In order to solve the above problems, this paper introduces a knowledge transfer mechanism, which aims to avoid the mutual contact of multiple participants in the transfer learning process, and chooses to protect the privacy of participants by directly using the multi-view knowledge of the source domain. And the multi-view weighting mechanism is used to measure the advantages and disadvantages of multiple views to describe the object more comprehensively and scientifically as possible.

In this study, some of important notations are listed in Table 1. Usually, bold numbers represent vectors, and un-bold italics represent scalars.

The epilepsy EEG signals licensed and provided by the University of Bonn, Germany, are used in this study. The dataset consists of 5 sub-datasets (Set A, Set B, Set C, Set D, and Set E). Each sub-dataset contains 100 single-channel EEG segments with a duration of 23.6 s and a sampling frequency of 173.61 Hz. A brief description of the five sub-datasets is presented in Table 2.

In the stage of EEG signals acquisition, the obtained signals often contain different kinds of noises [32–34], which may affect the physician’s analysis and diagnosis. Therefore, it is important to pre-process the EEG signals before the beginning of the next stage. Fig. 3 shows a toy example of the collected EEG signals.

In recent years, with the continuous research for EEG signals, more and more feature extraction methods have been proposed to process the raw data. To better study the information contained in EEG signals, we select three classical feature extraction methods, i.e., WPD [35], STFT [36] and KPCA [37], to extract the time-domain features, frequency-domain features and time-frequency features, respectively, as shown in Fig. 4.

Unlike previous studies using the Bonn dataset, this study treats each feature space as a view. Therefore, we have three views in this study. In addition, since the data distributions of A, B, C, D and E are different, we generate 6 different transfer scenarios by grouping different sub-datasets. For example, we randomly select 70% samples from A and E to generate a source domain, and select the rest 30% samples from A and randomly select 30% samples from D to generate the corresponding target domain. Therefore, in this study, we generate 12 transfer scenarios including 6 2-view scenarios and 6 three-view scenarios, as shown in Tables 3 and 4.

To highlight the performance of the suggested algorithm, four state-of-the-art algorithms are introduced for comparison.

Baseline 1 (MV-NTL-LSR as BL1), which is a multi-view machine learning algorithm. MV-NTL-LSR is trained on the source domain and directly tested on the target domain. MV-NTL-LSR is a non-transfer regression algorithm.

Baseline 2 (MV-NR-LSR, as BL2), which is a multi-view transfer learning algorithm. MV-NR-LSR is trained on the source domain and tested on the target domain by leveraging knowledge learned from the source domain.

Baseline 3 (BL3), which are three single-view transfer learning algorithms, i.e., geodesic flow kernel (GFK), transfer component analysis (TCA), and joint distribution adaptation (JDA), having the following two forms of input data: (i) transfer learning with single-view data; and (ii) transfer learning with multiple-view data stitched and merged into single-view data.

Baseline 4 (BL4), which is the coupled local-global adaptation (CLGA) algorithm proposed by Liu et al. [38]. It transfers the source domain knowledge into the target domain for training in each scenario and updates the view weights in real-time.

All algorithms are implemented in MATLABR2020a and run on a PC with Intel (R) Core (TM) i7-7500U, 8.00 GB with the Windows operating system. Parameter settings are shown in Table 5. 5-cross validation combined with the grid search strategy is used to search for the optimal parameters. All experiments are repeated 10 times and the average accuracy and the standard deviation are recorded.

In this section, the average classification performance of the four baselines and the proposed MVTL-LSR are reported, as shown in Tables 6–9. As can be seen that, in scenarios 1, 2, 7, and 8, the classification performance of BL1 and the single-view transfer learning algorithm performs well because the data distributions in the source and target domain are the same. In other scenarios, the proposed MVTL-LSR algorithm achieves the best classification performance on both 2-view and 3-view data sets. Additionally, the comparison results exhibit the following characteristics. 1)

Since BL1 is a straightforward multi-view learning algorithm without knowledge transfer, it is unable to adapt to situations in which the distribution of data in the source and target domains is different. In scenarios 1, 2, 7 and 8, BL1 has similar performance to the proposed MVTL-LSR. However, in other scenarios, MVTL-LSR performs significantly better than BL1. Therefore, the present algorithm is not picky about transfer scenarios.

In this section, we perform a sensitivity analysis of the parameters for MVTL-LSR. There are a penalty coefficient λ and two trade-off coefficients η and γ in the proposed objective. In addition, a parameter is used to describe the number of instances ratio in the specific process of conducting the experiment, i.e., R.