Computational and Mathematical Methods in Medicine

Volume 2015 (2015), Article ID 680769, 7 pages

http://dx.doi.org/10.1155/2015/680769

## Enhanced Z-LDA for Small Sample Size Training in Brain-Computer Interface Systems

^{1}Key Laboratory for Neuro-Information of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu 611731, China^{2}Center for Information in Bio-Medicine, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 10 July 2015; Revised 28 September 2015; Accepted 28 September 2015

Academic Editor: Irena Cosic

Copyright © 2015 Dongrui Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Background*. Usually the training set of online brain-computer interface (BCI) experiment is small. For the small training set, it lacks enough information to deeply train the classifier, resulting in the poor classification performance during online testing. *Methods*. In this paper, on the basis of Z-LDA, we further calculate the classification probability of Z-LDA and then use it to select the reliable samples from the testing set to enlarge the training set, aiming to mine the additional information from testing set to adjust the biased classification boundary obtained from the small training set. The proposed approach is an extension of previous Z-LDA and is named enhanced Z-LDA (EZ-LDA). *Results*. We evaluated the classification performance of LDA, Z-LDA, and EZ-LDA on simulation and real BCI datasets with different sizes of training samples, and classification results showed EZ-LDA achieved the best classification performance. *Conclusions*. EZ-LDA is promising to deal with the small sample size training problem usually existing in online BCI system.

#### 1. Introduction

Brain-computer interface (BCI) could translate brain intention into computer commands, and it has been widely used for cursor control [1], word spelling [2], neurological rehabilitation [3], and so forth. Generally, BCI system consists of stimulus presentation, signal acquisition, feature extraction, and translation modules [4]; among them feature extraction and translation algorithms play important roles for the final BCI performance. Three factors, including heteroscedastic class distribution, small sample size training, and nonstationary physiological signals, should be taken into consideration when selecting the translation algorithms for BCI system. Regarding the translation module, linear discriminant analysis (LDA) is one of the most popular classification algorithms for BCI application due to its simplicity, and it has been widely used in motor imagery-based BCI [5], P300 speller [6], and motion-onset visual evoked potential-based BCI (mVEP-BCI) [7]. Besides, the use of linear discriminant analysis (LDA) for functional near-infrared spectroscopy- (fNIRS-) based BCIs is worth mentioning. LDA has been shown to work effectively for the binary [8] and multiclass [9] classifications of motor imagery signals for the development of fNIRS-based BCIs.

However, LDA is established on the homoscedastic class distribution assumption, which is usually not held for practical BCI application. In order to handle this problem, we proposed an improved method named -score LDA (Z-LDA) [10]. Z-LDA defines the decision boundary through -score utilizing both mean and standard deviation information of the projected data, and evaluation results showed better classification performance could be obtained under the heteroscedastic distribution situation. But Z-LDA does not take into account the small sample size training problem that usually existed in actual online BCI system [11]. When the number of the training samples is small, the estimated classifier tends to be overfitted, resulting in the poor generalization during online testing. Various approaches have been proposed to address this issue [12]. Li et al. designed a self-training semisupervised SVM algorithm to train the classifier with small training data [11]. Xu et al. proposed a strategy which enlarges training set by adding test samples with high probability to improve the classification performance of Bayesian LDA under small sample training situation [13, 14]. The strategy hypothesizes that unlabeled samples with high probability provide valuable information for refining the classification boundary.

In essence, Z-LDA defines the confidence of samples in terms of its position in the estimated distribution, which could be used to update the classifier for the online BCI system. In the current study, we will extend Z-LDA to deal with the small size training problem.

#### 2. Materials and Methods

##### 2.1. Probability Output of Z-LDA

In LDA [15], the weight sum of the unlabeled sample is calculated based on the project vector which is estimated from the training set, and the corresponding prediction label is then determined by the shortest distance between and the labels of each class. For Z-LDA [10], we assume that of samples in each class follow normal distribution and normalize it through -score aswhere , are the corresponding mean and standard deviation of the weight sum for training set . Thus, follows standard normal distribution; Z-LDA make the prediction based on the distance between and mean of the standard normal distribution (i.e., 0). Suppose is the closest one near to 0; then the unlabeled sample will be classified to training set . In the binary classification, the decision boundary of Z-LDA is defined as [10]

Generally, the cumulative distribution function of the standard normal distribution is denoted asFor the transformed -score of Z-LDA, the area represents the cumulative probability that is shown in Figure 1. Based on this, we define the prediction probability of Z-LDA asThe area which represents is also marked on Figure 1. It is easy to know that decreases with the increased distance between and the mean of the standard normal distribution, and the range of is . Obviously, the larger denotes the higher confidence that the sample belongs to class ; thus the above definition is reasonable.