Smartwatches are equipped with sensors that allow continuous monitoring of physiological and physical activities, making them ideal sources of data for data analysis. However, accurately identifying individuals based on smartwatch data can be challenging due to the presence of outliers. Hence, outlier detection techniques play a crucial part in this context by identifying and handling these data points. Auto-encoders are one of the prominent ways to address outlier detection. Auto-encoders minimize a loss function to identify outlier samples. To explore the most optimal loss function for smartwatch data, this paper conducts a comparative analysis between three unsupervised loss functions, fused directional loss, mean square error, and regularized loss extracted from the current literature. The performance of three functions in personal identification is employed as the performance criteria due to the lack of outlier labels. The results indicate that the auto-encoder's performance in personal identification is slightly better than random guessing. The model struggled to effectively capture individual characteristics of the training data. This led to the outlier samples and non-outlier samples not being separable in the evaluation set. Consequently, the variation in the performance across and within a loss function was primarily influenced by the characteristics of the data rather than the model itself. Thus, the auto-encoder has limitations in personal identification, which led to an inconclusive comparison of the loss functions.