مدل پیش بینی پتانسیل های برانگیخته شده برق در پروتز های تصویری بر اساس رگرسیون بردار پشتیبانی با وزن های متعدد

Electrical evoked potentials (EEPs) elicited by electrical stimuli to the optical nerve are an important study object in optical nerve visual prostheses to investigate the temporal property of responses of the visual cortex. Concentrating on reducing the cost of the visual prostheses research, this paper proposes an intelligent EEPs prediction model based on the support vector regression with multiple weights (SVR–MW) method in substitution of numerous biological experiments. In SVR–MW, to improve the predictive performance of traditional SVR, more temporal weights and similarity-based weights are given to the recent training data extracted from similar experimental cases for new electrical stimulus parameters than the distant data from less similar cases during regression estimation. For temporal weight (TW), we propose two TW functions i.e., linear temporal weight (LTW) function and exponential temporal weight (ETW) function to calculate the temporal weight of training sample at different time nodes. For similarity-based weight (SW), the similarity measurement (SM) is the key issue, and we adopt the multi-algorithm-oriented hybrid SM methods i.e., textual SM, numerical SM, interval SM and fuzzy SM to solve the SW computation for training data derived from different experimental cases. The proposed method was empirically tested with data collected from actual EEPs eliciting experiments. Empirical comparison shows that SVR–MW is feasible and validated for EEPs prediction in visual prostheses research.

Visual prostheses research to restore vision offers a promising approach for the blind and has become a rapidly growing scientific field in neuro-rehabilitation engineering [1]. In recent years, the optic nerve visual prostheses based on optic nerve stimulation with a penetrating electrode array have been focused upon by many researchers [2], [3] and [4]. One of the key issues in optic nerve visual prosthesis is the research of responses of the visual cortex after the electrical stimulation to the optic nerve. To investigate the temporal property of responses, the electrical evoked cortical potentials (EEPs) are elicited over the rabbit skull when the optic nerve was stimulated using different electrical stimulation parameters, e.g., intensity, frequency, and charge density, et al. However, subjected to experiment cost and material restriction, the experimental EEPs recorded data with different stimulation parameters are too sparse and inadequate to be analyzed in optic nerve visual prosthesis research. Concentrating on reducing the cost of the visual prostheses research, this paper tries to explore an innovative intelligent model with machine learning technique to predict the new EEPs results in view of new electrical stimulation based on existing EEPs experimental cases rather than doing numerous biological experiments, in which target stimulation parameters are considered as the inputs, and the corresponding output result is the special EEP value at the given time node. But, the characteristics of EEPs training data in experimental cases are time series, non-linear, inherently noisy, non-stationary, and deterministically chaotic [5]. This means that not only is a single data series non-stationary in the sense of the mean and variance of the series, but the relationship of the data series to other related data series may also be changing [6]. Thus, modeling such non-stationary data is expected to be a challenging task. Time series prediction (TSP) is an important issue that has served as the impetus for many academic studies, range from stock indexes forecasting [7], [8], [9], [10] and [11], price analysis [12] and [13], due-date assignment [14] and [15] to sales forecasting [16] and [17]. Recently, support vector machines (SVMs), proposed by Vapnik [18] and [19], have been successfully employed in solving classification and regression problems [6], [20], [21], [22], [23] and [24]. TSP can attribute to regression problems, so SVMs such as support vector regression (SVR), least-squares SVM (LS–SVM) and robust support vector regression networks (RSVRN) are applied to deal with TSP issue [10], [25], [26], [27], [28] and [29]. Classic SVM approaches for regression problems use some arbitrarily chosen loss functions which equally penalize errors on all training samples, therefore all training examples are considered equally significant. However, in TSP, the relationship between input variables and output variable gradually changes over time, and recent past data could usually provide more important information than the distant past data [30] and [31]. On the other hand, the regression functions achieved by SVMs are less robust, namely, sensitive to noises [32]. Therefore, it is advantageous to give high weights on the information provided by “useful” sample. For EEPs prediction, the EEPs experimental case with higher similarity for new stimulation input could be more significant than dissimilar cases, in terms of the case-based prediction principle. Enlightened by these facts, we intend to research a EEPs time series forecasting model based on SVR with multiple weights (SVR–MW) to predict the EEP values responses to new stimulation inputs, in which more temporal weights and similarity-based weights are given to the recent training data from similar experimental cases than the distant data from less similar cases. The breakdown of this paper is organized as follows: Section 2 provides a brief description of the literature surveys for the related areas. Section 3 discusses the SVM–MW for regression estimation in detail. Section 4 gives an example to illustrate the implementation of the proposed method. Section 5 focuses on the performance comparisons with other predictive methods. In the final section, the conclusions and future work are presented.

EEPs analysis is a key issue in optic nerve stimulation research. However, subjected to experiment cost and resource restriction, the EEPs experimental data are too sparse and inadequate to be analyzed. In this paper, we propose a new intelligent EEPs prediction model for investigating the EEPs responses of the visual cortex after the electrical stimulation to the optic nerve. This paper firstly attempts to put forward an adapted SVR method capable of taking the advantages of similarity measurement algorithms and temporal weight function to generate the more accurate TSP model. Motivated by the characteristic of EEPs data, that is, recent data from similar cases could provide more information than distant data from dissimilar ones, thus, we give the more TWs and SWs to the recent data from similar experimental cases than the distant data from dissimilar cases. Accordingly, the new method is called SVR–MW. Furthermore, we give predictive performance comparison to investigate the superiority of SVR–MW predictor. From the views of predictive performance and significance tests, we can draw the conclusion that SVR–MW is suitable and applicable for EEPs prediction. Note that all conclusions drawn should be considered together with the specific experimental design. This research has some limitations. Firstly, the size of the testing data set in this experiment is quite small to validate the usefulness of our proposed method. Therefore, additional techniques such as resubstitution method, McNemar test and t-statistics test should be done in the future to mitigate the few samples problem. Secondly, several parameters should be optimized in SVR–MW and the optimization process requires too much time and computer resource. Hence, future research should focus on the global optimization method to optimize these parameters simultaneously to make optimization more efficient. Finally, besides in biomedical field, we believe that the proposed method is suitable for TSP in other practical applications areas, so the applicability of SVR–MW in other applications areas could be investigated in future.