Case based time series prediction using biased time warp distance for electrical evoked potential forecasting in visual prostheses

Abstract

Case based time series prediction (CTSP) is a machine learning technique to predict the future behavior of the current time series by referring similar old cases. To reduce the cost of the visual prostheses research, we devote to the investigation of predictive performance of CTSP in electrical evoked potential (EEP) prediction instead of doing numerous biological experiments. The heart of CTSP for EEP prediction is a similarity measure of training case for target electrical stimulus by using distance metric. As EEP experimental case consists of the stationary electrical stimulation values and time-varying EEP elicited values, this paper proposes a new distance metric which takes the advantage of point-to-point distance's efficient operation in stationary data and time series distance's high capability in temporal data, called as biased time warp distance (BTWD). In BTWD metric, stimulation set difference (Diff_I) and EEP sequence difference (Diff_II) are calculated respectively, and a time-dependent bias configuration is added to reflect the different influences of Diff_I and Diff_II to the numerical computation of BTWD. Similarity-related adaptation coefficient summation is employed to yield the predictive EEP values at given time point in principle of k nearest neighbors. The proposed predictor using BTWD was empirically tested with data collected from the electrophysiological EEP eliciting experiments. We statistically validated our results by comparing them with other predictor using classical point-to-point distances and time series distances. The empirical results indicated that our proposed method produces superior performance in EEP prediction in terms of predictive accuracy and computational complexity.

Introduction

As the interests in time series have been explored by the number of domains in which time series occur: medicine, industry, entertainment, finance, computer science, meteorology and in almost every other field of human activity [1], the problem of time series prediction (TSP) has attracted great attention [2], [3], [4], [5], in which the historical observation values are collected and analyzed to predict the possible values of future time point. Different from traditional TSP approaches based on neural network (NN) model or regression model, case based TSP (CTSP) allows us to use previous data in predicting current data without completely understanding the underlying mechanism of time series behavior [6], actually, it would be very useful for experts to make their decision and predict the future behavior of the current time series by referring similar old case from past.

The purpose of optic nerve visual prosthesis is to deliver the electrical impulses to optic nerve with the penetrating electrode, and the visual perception is then emerged from the visual cortex, therefore, the analysis of responses of the visual cortex after the electrical stimulation to the optic nerve is a key part in optic nerve visual prosthesis [7], [8], [9], [10]. To explore the temporal property of responses, electrical evoked potentials (EEPs) are elicited over the rabbit skull when the optic nerve was stimulated with specific electrical stimulation current, as shown in Fig. 1. However, subjected to experiment cost and material restriction, the EEP response data triggered by various stimulations are too sparse and inadequate to be analyzed, and the characteristics of EEP data are time series, non-linear, inherently noisy, non-stationary, and deterministically chaotic [11]. To reduce the cost of the visual prostheses research, it is useful to exploit existing EEP electrophysiological data to predict new EEP response at given time point under new electrical stimulations, e.g., the current intensity, the pulse duration, the frequency of the stimuli, etc. In our previous works [11], [12], we presented an adapted support vector machine (SVM) based TSP model to predict EEP movement but with higher computational complexity. Enlighten by the advantages of CTSP, we devote to the investigation of predictive performance of CTSP to solve the EEP forecasting problem.

In this research, we attempt to employ CTSP to undertake EEP prediction task, and each experimental sample is expressed as an EEP experimental case, which involves stationary electrical stimulation values and time-varying EEP elicited values. The contribution of this paper is twofold. On the one hand, we try to construct a new distance function of similarity measure for EEP prediction. For the sake of implementing CTSP, training case should capture the evolution of the observed phenomenon over time [13], but time-varying information in cases will be neglected or the retrieval procedure will require massive calculated quantity when classical point-to-point distance or time series distance is used to measure the similarity of each case. The motivation of this research lies in employing a novel distance metric to calculate the similarity of EEP biological case by referring classic distance metrics, and intending to introduce the bias parameter to reflect the different influences from stationary electrical stimulation values and time series EEP elicited values for new predictive result, so the proposed distance is called biased time warp distance (BTWD). This paper is the first attempt to develop a new similarity measurement in CTSP which takes the advantages of classical point-to-point distance function's efficient operation in stationary data and time series distance function's high capability in temporal data.

On the other hand, we try to investigate the superiority of BTWD in actual EEP prediction, and the predictive performances of CTSP with BTWD and other TSP approaches are planned to be compared. Initial EEP experimental data are collected from the studies of rabbit's visual cortex by optic nerve stimulation carried out inside the pia mater, on the pia mater and on the dura mater. In the assessment of predictive performance, we employ 30-time cross-validation strategy by combining hold-out method and leave-one-out cross-validation. Predictive performance is evaluated by predictive results produced on hold-out data. Statistical analysis is employed to find whether or not there are significant differences among comparative predictors in the light of the predictive results.

The breakdown of this paper is organized as follows. The next section summarizes the research trends in TSP, and the motivation and originality of this research. Section 3 presents the specification on the BTWD. Section 4 describes the empirical design. Section 5 presents the empirical results and relevant discussions. The last section provides the conclusions and suggestions for further research.