###### Abstract  
In-air signatures are promising applications that have been investigated extensively in the past decades; an in-air signature involves gathering datasets through portable devices, such as smartwatches. During the signing process, individuals wear smartwatches on their wrists and sign their names in the air. The dataset we used in this study collected in-air signatures from 22 participants, resulting in a total of 440 smartwatch in-air signature signals. The dynamic time warping (DTW) algorithm was applied to verify the usability of the dataset. This paper analyzes and compares the performances of multiple convolutional neural networks (CNN) and the transformer using median-sized smartwatch in-air signatures. For the four CNN models, the in-air digital signature data were first transformed into visible three-dimensional static signatures. For the transformer, the nine-dimensional in-air signature signals were concatenated and downsampled to the desired length and then fed into the transformer for time sequence signal multi-classification. The performance of each model on the smartwatch in-air signature dataset was thoroughly tested with respect to 10 optimizers and different learning rates. The best testing performance score in our experiment was 99.8514% with ResNet by using the Adagrad optimizer under a \(1\times 10^{-4}\) learning rate. artificial intelligence; sensors; in-air signature recognition; time sequence; convolutional neural networks (CNN); transformer; pattern recognition; optimizers +
Footnote †: journal: _Applied_  
on median-sized in-air signature datasets while the transformer [11] is not suitable for median-sized in-air signature time sequence multi-classification tasks and shows overfitting in different degrees over 50 repetitions. In our research, we used the smartwatch in-air signature dataset [4] consisting of 22 participants and 440 in-air signatures (with 220 being genuine and 220 being forgeries). The convolutional neural network models and the representative time sequence model, the transformer, were tested on the median-sized in-air signature dataset based on a smartwatch. We implemented the DTW algorithm [14] to verify the usability of the smartwatch dataset first, and from there, the experiment took two different branches. For convolutional neural network models, in-air signature signals were first converted to static 3D restorations as images; four CNN models, i.e., LeNet [15], AlexNet [16], VGG [17], and ResNet [18], were implemented and tested for the smartwatch in-air signature dataset. For the time sequence model, the smartwatch nine-dimensional in-air signature dataset goes through normalization, concatenation, and downsampling, and then the dataset is fed into the transformer for classification, which works as the baseline case for comparison. This paper is organized in the following manner. In the introduction section, the research procedure, experiment setup, and recent representative research on in-air signature recognition are discussed. In the materials and methods section, the dynamic time warping (DTW) algorithm is used to analyze the smartwatch in-air signatures. The proposal for the restoration of in-air signature section includes coverage of the system architecture, methodology for restoring in-air signatures, and a comparative study of CNN models. In the results section, we demonstrate the performance of ResNet together with the performance comparison of convolutional neural networks and the transformer with respect to different optimizers. In this section, the fine-tuned ResNet model is nominated and a comparison of different models is presented. Finally, we summarize our research and discuss the research limitations and future directions.