## 4 Automatic Evaluation of Dance Performance
### Encoding Model with Autoencoder  
When an autoencoder [59] (see Appendix A) is applied to dance feature extraction, it should be possible to generate more essential expressions by capturing features of dance movement such as speed, rhythm, and continuity of movement. These features are important elements in analyzing and evaluating the quality of dance.  
The motion data that serve as the input and output of the autoencoder are the poses (joint positions and rotations) at each point in time, arranged in chronological order. The  
Figure 11: Distribution of evaluation scores.  
Figure 10: Dance annotation system.  
time series length was set to four counts (approximately 1.5 s). The encoder was designed to first compress the pose information at each time point and convert it into spatial features, and then capture temporal motion features such as motion and continuity over the entire frame.  
GCN [60] (see Appendix B) can be applied to data with a skeleton structure, such as the human skeleton, to analyze the relationship (edges) between body parts (nodes) and joints. For example, it is possible to analyze the relationship between multiple parts of the body, such as the interaction between the movements of the hands and feet, or the relationship between the central part of the body and the movements of the extremities.  
In this study, graph convolution was introduced as part of the encoder model to capture spatial relationships between joint points. Bidirectional LSTM (BiLSTM) was used to capture time series features; BiLSTM is expected to capture time-series data in the context of forward and backward motion and effectively extract temporal features, especially continuity and rhythm of motion. The output of the encoder is the last cell of the LSTM and the state of the hidden layer. The decoder takes the output (compressed feature representation) from the encoder and reconstructs the original time-series data. To apply the encoder process in reverse, the decoder consists of a TimeDistributed layer that transforms the input data into a time series, an LSTM layer that restores temporal features, and an MLP layer that restores the location information of joint points at each point in time. The TimeDistributed layer uses the LSTM state output by the encoder as the initial state to recover the spatial features of the pose at each point in time. Finally, through the MLP layer, the goal is to produce an output that is as close as possible to the original input data. The model architecture of the autoencoder is shown in Figure 12.  
Mean squared error (MSE) was used as the loss function to train the autoencoder model and mean absolute error (MAE) was used as the evaluation metric. The MSE and MAE measure the error between the reconstructed output and the original input data and evaluate how accurately the model can reconstruct the data. Other methods exist to calculate losses that account for errors in a time series. Among them, Dynamic Time Warping (DTW) is useful in certain contexts not related to rhythm (e.g., pose and balance). However, it can lose information in contexts that include time elements such as strength and timing. DTW was not used in this study because we wanted to use a common encoder.