**2.1. ROC analysis**

meanwhile, 16–31 Hz signals (beta-wave) appears in the mental tasks such as active thinking, high alert, anxious, etc. Gamma-wave, EEG with higher than 32 Hz, displays during cross-modal sensory processing such as combining the stimuli of visual and auditory. On the other hand, the location of electrodes on scalp records different EEG signals spatially, and they are called EEG signals in different "channels". The allocation of electrodes is usually with the international 10–20 system. The name of 10–20 system comes from those adjacent electrodes that are allocated in distances of 10 or 20% of the total front-back or right-left of skull. More channels, more spatial features, may result in higher recognition rate of mental tasks. On the other hand, few channels

In last decades, EEG has been utilized in the field of the brain-computer interface (BCI) for its ability of the mental task recognition [2–6]. Mental tasks indicate the state of activity of the brain with some specific tasks. For example, imagining writing a letter, counting, calculating, or raising a hand, a leg, etc. There are many classifiers for EEG recognition that have been proposed such as linear discriminant analysis (LDA), support vector machine (SVM), artificial neural networks (ANN), fuzzy inference systems, Bayesian graphical network (BGN), and so on. However, for the reasons of the complex nature of EEG signals, for example, noise and outliers, nonstationarity, high dimensionality, individual difference, etc., the pattern recogni-

To normalize the raw EEG signals, Nakayama and Inagaki proposed to reduce the number of the time series data of power spectrum of frequency given by fast Fourier transformation (FFT) with average values and normalize the FFT by a nonlinear normalization function [4]. To extract discriminant features of EEG signals for mental task recognition, Li and Zhang proposed a regularized tensor discriminative feature space, which includes multichannels, power spectrum of frequency, and those data in time series: channel × frequency × time [5]. Obayashi et al. applied Nakayama and Inagaki's pre-processing method to their practical EEG recognition system with single channel information in [6]. In [7], Jrad and Congedo used spatially weighted SVM (*sw*SVM) to build a spatial filter for each temple feature. In the previous works of authors [8], discriminant temporal frequency data were utilized to reduce the flattening of different EEG patterns adopting the pre-processing method of [4], temporal spatial frequency concept, and average moving processing of [7] were adopted to obtain higher rate of mental

Recently, we proposed to find the discriminant feature of temporal frequency by receiver operating characteristic (ROC) analysis in [9]. The discriminant feature of temporal frequency indicates the power spectra of FFT in an interval of time series of EEG data, which are higher relative to a mental task comparing with other intervals (windows). ROC analysis has been widely utilized in medical & diagnostic science [10, 11], microarray classification [12], and recently in EEG classification [13]. It is a stochastic criterion to classify two kinds of probabil-

In this chapter, discriminative feature extraction methods of EEG signals, which play an important role for classifiers, are discussed. Specially, an advanced temporal–spatial spectrum

ity distributions and the details will be described in the next section.

feature extraction method is introduced [9].

tion (classification) problem of EEG signals is still a high hurdle for BCI realization.

give lower computational cost in the EEG classification systems.

66 Human-Robot Interaction - Theory and Application

task recognition.

Receiver operating characteristic (ROC) analysis was first used in radar signal detection in 1940s. The classification results of data in two kinds of distributions can be divided into four categories: true positive (TP), false positive (FP), true negative (TN), and false negative (FN). A curve is plotted by the rate of TP against the rate of FP and it can be a measure of classification accuracy.

Now, let the TP of class A be in the shadow area *α*, and FP in area 1−*β*, where *β* is the TP of class B (See **Figure 1**). When the dividing line between A and B is slid along *x* axis, a ROC curve is plotted indexing the divisibility of the two probability density functions (See **Figure 2**). If two distributions completely overlapped, *α* = 1−*β*.

In **Figure 2**, the area below the ROC curve is called "area under the curve" (AUC). This value takes from 0.0 to 1.0, and it is an indicator of the divisibility of the two distributions. If the value of AUC becomes 0.5, two distributions are completely overlapped. Conversely, when the value of AUC reaches 1.0 (or 0.0), it means that the two distributions are completely separated.

In the practice procedure of ROC analysis, the area of *α*, that is, the rate of TP, and 1−*β*, the rate of TN, can be calculated by the number of training samples, which are labeled data belonging to different classes.
