## 3 Results  
Five healthy subjects, three females and two males, were recruited in this studied case to simulate the expected human motional patterns. The average age of these subjects is 22.8 years old with a standard deviation of 1.92 years old, and the average height is 161.8 cm with a standard deviation of 7.43 cm. Since the collected signals from the subjects were highly similar, one dataset of signals from a subject was randomly employed in the following study. Figure 3 depicts the original time-dependent signals collected by the tri-axial G-sensor in each corresponding sensing axis. Each numbered principal axis (PA) is correspondent to each sensing axis. In the proposed experimental scheme, two different periodic times, 20 and 40 s, were adopted and the motions were repeated eight times within three minutes. The different periodic times between these studying cases were deliberately arranged in the experiments in order to check the immunity of DDFM from the different experimental circumstances. The signals shown from Figure 3a-c sequentially describe the repeated motional patterns from lying face-up to turning left (TL) in each PA and that from (d)-(f) shows the patterns from lying to turning right (TR), respectively. By considering the hardware architecture shown in Figure 1, the direction of PA 1 was the same as the rotating axis of the subject body so that the signal variation in PA 1 was much weaker than that in both PA 2 and PA 3 in each studied case. The waveforms of PA 3 shown in Figure 3c,f are similar and they also have similar signal levels in the lying states. On the contrary, the directions of waveforms of PA 2 shown in Figure 3b,e are opposite, even though they also have similar signal levels in the lying states. These sequential variations of motional patterns in PA 2 and PA 3 caused by the architecture of the G-sensor constitute the feasible features of the motional pattern recognition in the study and may be used to compensate for the lack of sensor number. Thus, these features were used as the prior information in the DDFM algorithm. Figure 3: The original time signals collected from each corresponding sensing axis of the G-sensor. The analog signals delineated from (**a–c**) describes the motional patterns of a human from lying face-up to turning left (TL), whereas those from (**d–f**) show the patterns from face-up to turning right (TR). The experiments were repeated eight times within three minutes with two different time periods, 20 and 40 s. The results classified using the DDFM are also exhibited in each plot in advance. PA = principal axis. To introduce the DDFM to the time-dependent signal analysis, the datasets were first mapped into 2D pseudo-physical spaces as shown in Figures 4 and 5. Figures 4 and 5 respectively exhibit the classified results of motional patterns of Lying-to-TL and Lying-to-TR states. By comparing these classified results, it is obvious that the difference in the periodic times employed in the experiments would not substantially affect the accuracy of the DDFM algorithm. Meanwhile, the overshooting signals depicted in Figure 3 also only offered insignificant noise levels. As expected, the scattered plots of Figure 4a,b exhibit the ignorable motional patterns in PA 1, whereas that of Figure 4c reveals significant physical couplings between body motions and the rotating directions of the G-sensor. Additionally, according to Steps (6)-(9) in the proposed algorithmic flow, the most probable cluster number and the corresponding cluster boundaries could be well defined by estimating the systematic global Hamiltonian functional and the energy characteristics of LDF morphologies, respectively. The data PDFs in the 2D pseudo-physical spaces were statistically estimated using the GMM method associated with the expectation-maximization (EM) algorithm, and the corresponding trend curves of the global Hamiltonian functional were also delineated in Figures 4d and 5d.