Divisibility and Compactness Analysis of Physiological Signals for Sentiment Classification in Body Sensor Network

Affective computing draws more and more attention to the human-computer interaction. Based on physiological signals acquired by body sensor network, within the affection recognition process, the problem that training samples have larger class distance and smaller intraclass distance must be considered. For the class divisibility and intraclass compactness problem, researching method of samples validity was proposed based on metric multidimensional scaling. With dissimilarity matrix, scalar product matrix was calculated. Subsequently, individual attribute reconstructing matrix could be got using principal components factor analysis to display samples difference in low dimension. By means of experiment results, training and testing samples for sentiment classifier will be selected instructionally.


Introduction
To realize natural human-computer interaction, more personalized services are required during the interactive process. Therefore, it is an effective way to bring in a user's affection with body sensor network to the service. The artificial psychological and affective computing are becoming new research directions in the field of artificial intelligence [1]. Generally, researches focus on simulating affective recognition, modeling, and expression mainly. The affective recognition consists of two types. One is recognizing user's affection which is user centered, and the other is recognizing affection in content, such as light effect, context, and characters in film, music, and art painting, which is content centered [2].
For the first type, researches can use multitypes of sensors to measure user's affection. Kim et al. surveyed the amount of sweat, pulse, body temperature, and blood pressure. Based on this physiological information, they determined the user's affective state after data fusion and fuzzy inference [3]. Nguyen used fewer sensors, only with pulse and body temperature, to acquire affection [4]. Arapakis proposed a method with facial expression [5]. In addition, the measuring method also includes the questionnaire or its extended form. It is an indirect way. González et al. used emotion quotient (EQ) test table [6]. Ai Thanh Ho provided a group of different colors to select for user and determined the user's affection based on his selection. The features of these affection acquiring methods are compared in Table 1.
The method based on the user's physiological information to judge the affective state is better than others in portability, signal continuity, sensibility, and comfort as shown in Table 1. Therefore, researches on physiological divisibility of affection attract the interest of researchers in the field of human-computer interactionMany psychologists got different conclusions on autonomic nervous system (ANS). On the one hand, paper [7], regarded that the "detest" affection has specific ANS proposed. But on the other hand, the opposite researching view was also studied in [8]. However, the existence of specific affection ANS has got more and more support from recent studies [7][8][9][10][11][12][13][14][15][16]. In the research of affection recognition based on physiological signals, some affective physiological data sample libraries were established as shown in Table 2. However, these libraries provide a foundation for comparison and analysis of affective physiological feature selection and sentiment classification, whether they are valid, that is, whether or not having a larger class distance · · · · · · · · · · · · · · · · · · · · · · · · · · ·  and a smaller intraclass distance, as training data is worthy of study. For the affective physiological database proposed in [17], this paper analyzes the divisibility and compactness of 20 groups of samples with 8 kinds of affections.

Affective Physiological Samples
Affective database DataSet I, which is established by Picard,

Analysis of Divisibility and Compactness
In the affective state discriminating process with physiological signals, for feature-based classification methods, the training samples and selected feature impact on the classifier directly. Due to the different deployment of sensors in body sensor network and the participant's daily life, training samples have more noise. So samples, which have a larger class distance and a smaller intraclass distance, should be selected to train the classifier. In addition, for different feature sets, dispersion between classes or within one class should be discussed. Therefore, after selecting a certain feature set, validity analysis for affective physiological sample is one of the key factors in training the affective state classifier. Based on the multidimensional scaling theory, this paper illustrates a general validity analysis method by using the dataset proposed in [17]. From the view of similarity or dissimilarity of affective physiological signals, we represent the samples in the low-dimensional space to reveal the underlying structure of the sample.
The literature in psychophysiology and related disciplines described features about affective state recognition based on facial muscle movement, heart rate changes, and so on [10]. Picard et al. proposed 6 static characteristics. They are mean value , standard deviation , mean value of the first-order differential absolute value , its normalized valuẽ, mean value of the second-order differential absolute value , and its normalized valuẽ [17]. Suppose that the th ∈ {1, 2, 3, 4} type of physiological signal acquiring devices gets the th ∈ {1, 2, . . . , } measured value . And its normalized value is . So the 6 static features can be obtained by formulas (1) and (2) as follows: wherẽ= ( − )/ , International Journal of Distributed Sensor Networks 3 According to multidimensional scaling theory [21], build a dissimilarity matrix Δ × with affective state feature matrix and especially ∈ {8, 24} in this paper. in Δ can be calculated as Then, calculate the inner product matrix Γ. Its element is Designate reconstructed matrix in low-dimensional space asΩ × ( < 24), which could be got through affective state feature matrix. And correspondingly, its affective state dissimilarity matrix is recorded as . Based on the theory of metric multidimensional scaling, Δ is similar to in a sense. Then, Γ=ΩΩ . Solving (6), affective state feature reconstructed matrix in low-dimensional spaceΩ could be got. That is to say affective state feature could be presented in low-dimensional space. At the same time, it is easy to obtain eigenvalues which the th dimension ofΩ is corresponding to: wherêare elements ofΩ. . And based on the theory of metric multidimensional scaling above, after reconstructing affective state feature matrix in low-dimensional space, analyze the class distance of samples measured by the body sensor network. According to Kruskal's stress requirements, in this paper, each affection feature vector is reconstructed in two-dimensional space as shown in Figure 2.

Experiment
In Figure 2, N, A, H, G, P, L, J, and R represent 8 classes of affective states, respectively. The axes of the left figures mean relative distance between reconstructive points. Take Figure 2(a) as an example; points L and J are closer, which demonstrates that the two types of affection, romantic love L and happiness J, only have few differences for the first day samples while affective physiological data are described with 6 static features above. Their class divisibility is too poor to train an effective classifier. Points R, P, H, and G have few differences in dimension II but some differences in dimension I. However, there are large differences for points A and N no matter in dimension I or II.
The right part of Figure 2(a) shows the linear fit scatter plot of reconstruction process. The -axis means the samples disparity, and the -axis reflects the fitting distance. Fitting coefficient 2 = 0.999 is good enough. Young's S-stress and Kruskal's stress reach 0.407% and 1.264%, respectively. And the determination coefficient RSQ is 0.99922, which means that the proportion of explaining by relative spatial distance is larger. The affection eigenvector reconstruction process data of the th day are summarized in Table 3.

Intraclass Compactness. Affective state feature matrix
consists of the same type of affective state feature vector for 20 days. Based on metric multidimensional scaling theory stated above, reconstruct affective state feature in low-dimensional space to analyze the intraclass distance of samples. The reconstruction in twodimensional space is as shown in Figure 3.
In Figure 3, points Day 1-Day 20 denote the eigenvectors of 20 days for the same kind of affective state. From the left part of Figure 3, the axes also mean relative distance between reconstructive points. Points Day 1, Day 3, Day 4, and Day 5 are far away from the rest of the reconstructive points. That is to say intraclass distances of the same type of affective physiological data for the first day and the 3th-5th days are larger. Their intraclass compactness is poor. In addition, the 7th day samples also have a larger intraclass distance for anger affective state.
The right part of Figure 3 shows the linear fit scatter plot of reconstruction process. The -axis means the samples disparity, and the -axis reflects the fitting distance. Fitting coefficient 2 is close to 1. Young's S-stress, Kruskal's stress, and determination coefficient RSQ for the reconstructive process of 8 types of affective state feature vector are summarized in Table 4.

Conclusions
As training samples of a classifier, the validness of affective physiological feature vectors is worthy of study. Larger classes distance and smaller intraclass distance are needed. An analysis method is proposed for body sensor network, which collects affective physiological data. Particularly, in this paper, we take the affective physiological database DataSet I as an example, and analyze divisibility and compactness of 20 groups of samples belonging to 8 types of affections.
Based on the 6 static features described by formulas (1)       same affective type, intraclass compactness is poor for the 1st, 3rd, 4th, and 5th days.