**3.2 Entropy-oriented scoring of human motion**

The proposed research employs entropy [76] to grade a user's movement behavior, which is defined as a times series of joint kinetic features such as positions and rotations. The distance/dissimilarity between two time series can be measured in time-domain or frequency-domain [58, 59]. In time-domain, Approximate Entropy (AppEn) and Sample Entropy (SampEn) [76, 77] can be employed to formulate the regularity and predictability about the normalized Euclidean distance between the time-series of users' and reference data.

As our preliminary work, **Figure 7** compares the entropy values of an advanced Tai-Chi user and a beginner. The whole Tai-Chi set is divided into multiple subsequence (or clip), which consists of 25 to 100 frames, and the comparison is made clip-by-clip. In **Figure 7**, each subsequence consists of 25 frames. It is observed that an advanced Tai-Chi user has smaller entropy than a beginner. Besides the overall entropy of a user, VIGOR also provides the entropy of each joint so that the virtual Tai-Chi coach can provide accurate instruction to users.

Entropy or cross-entropy analysis can be performed for the time-series in the frequency domain which is derived from discrete Fourier transformation (DFT) or discrete wavelet transformation (DWT) [58, 59]. A hybrid metric that combines both time-domain and frequency-domain information may be considered as well.
