## 3 Processing and Analysis of Measurements
### Segmentalized Principal Component Analysis (sPCA) for Acceleration Signal
Figures 6 and 7 illustrate the COP measurements of the five visual conditions (Conditions 1 to 5, as shown in Table 1) in the SOT of this research. It is found in the figures that the examinee generally has more sway variance in the AP direction than in the ML direction. A similar phenomenon can also be observed in most of the other COP measurements. The inference is reasonable because the structure of legs and ankles has more capability against the perturbation in the ML direction than in the AP direction while the examinee stands in the normal posture. Therefore, it is assumed in this study that the acceleration measurement in AP direction dominates the balancing characteristics as the examinee sways for most tests. Figure 5: Schematic plot of acceleration variance in Y- and Z-directions. Figure 6: COP measurements in medial-lateral (ML) and anterior-posterior (AP) direction under Conditions 1–3. Based on the concept of PCA, the first principal component corresponds to the COP signal component in the AP direction. The second principal component corresponds to the COP signal component in the ML direction. The third principal component is attributed to the gravitation of the vertical component. This inference was drawn from the fact that the acceleration measurement had less variance in the direction parallel to the gravitation than the directions perpendicular to the gravitation. Although the PCA is capable of transforming the acceleration signals into the three principal components corresponding to the AP, ML and vertical directions conceptually, it is, however, apparently unable to reflect the instantaneous variation in the projection of gravitation onto the three measured components in case of the time-varying tilting accelerometer if the PCA is employed to process the signal throughout the whole data length (20 s). In order to address this concern and to deal with the time-varying problem of directivity variation on the oblique accelerometer, the segmentalized PCA (sPCA) was proposed in this research to accurately extract the time-varying components corresponding to the acceleration components that are perpendicular to the gravity at the different instants during the human body's sway. As illustrated in Figure 8a, the acceleration measurements in X-, Y- and Z-directions were divided into four segments and then the PCA was applied for each segment to determine the three principal components (PC-1, PC-2 and PC-3), as shown in Figure 8b. With the connected principal components of each segment, Figure 9a shows the comparison between the COP measurement in the Y-axis (AP) and the first principal component (PC-1) of acceleration signals. It is noted that the PC-1 of the acceleration measurements has similar variation trend with the COP measurement in the AP direction and the correlation coefficient between the two sets of series was calculated as 0.841. As compared with the PC-2 and PC-3 of the acceleration signals, their variation trends are very different from the COP measurement in the AP direction (as shown in Figure 9b), and thus, they have correlation coefficients of \(-0.512\) and \(-0.089\), respectively. The high correlation coefficient between the COP measurement in the AP direction and the PC-1 of the acceleration measurements demonstrates that it is sufficient to accurately predict the COP measurement in the AP direction. Therefore, it is feasible to utilize the processed acceleration measurement to represent the COP signal for evaluating the human body's balancing ability. Figure 7: COP measurements in ML and AP direction under Conditions 4–5. Figure 8: (**a**) Segments of acceleration measurements, (**b**) Principal components in each segmentalized part. Figure 9: _Cont._