# BIMO: Bootstrap Inter-Intra Modality at Once Unsupervised Learning for Multivariate Time Series
## 3 Results and Discussion
### Robustness to Noisy Data  
Most real-world time-series data contain some noise. Typically, the photoplethysmogram (PPG) signal, which is also referred to as the blood volume pulse, contains many noises. A PPG signal is simple and highly useful in daily life since it can be easily measured from the wrist. However, it is difficult to apply in an end-to-end deep learning model because it is susceptible to many internal and external noises of the measurement environment [40; 41]. Therefore, most existing PPG-based studies have focused on signal processing and feature engineering [4; 42; 43; 44; 31].  
In this study, we validated the noise robustness of BIMO, which is an end-to-end deep learning model, using noisy PPG signals. We used a PPG signal from the WESAD dataset [31]. The WESAD dataset is labeled with four emotional states: baseline, stress, amusement, and meditation. We performed a classification task with leave-one-subject-out cross-validation, stress versus nonstress, where nonstress is defined by combining the state baseline and amusement states [31].  
We compared the performance with BIMO and existing SOTA supervised learning models for PPG, which is a weak feature engineering method [31] and a strong feature engineering method named OMDP [4]. The weak feature engineering-based method uses a peak detection algorithm, which is computed by simple statistical features. OMDP  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **BIMO** & **USRL** & **DTW** \\ \hline ArticularyWordRecognition & 0.830 & **0.987** & **0.987** \\ Atrial Fibrillation & **0.417** & 0.133 & 0.200 \\ BasicMotions & **1.000** & **1.000** & 0.975 \\ Cricket & 0.861 & 0.986 & **1.000** \\ DuckDucKGeese & **0.688** & 0.675 & 0.600 \\ EigenWorms & 0.852 & **0.878** & 0.618 \\ Epilepsy & 0.926 & 0.957 & **0.964** \\ Ering & **0.922** & 0.133 & 0.133 \\ EthanolConcentration & **0.354** & 0.236 & 0.323 \\ FaceDetection & **0.550** & 0.528 & 0.529 \\ FingerMovements & **0.550** & 0.540 & 0.530 \\ HandMovementDirection & **0.444** & 0.270 & 0.231 \\ Handwriting & 0.346 & **0.533** & 0.286 \\ Heartbeat & **0.740** & 0.737 & 0.717 \\ Libras & 0.650 & 0.867 & **0.870** \\ LSST & 0.404 & **0.558** & 0.551 \\ MotorImagery & **0.600** & 0.540 & 0.500 \\ NATOPS & 0.872 & **0.944** & 0.883 \\ PEMS-SF & **0.733** & 0.688 & 0.711 \\ PenDigits & 0.975 & **0.983** & 0.977 \\ Phoneme & **0.280** & 0.246 & 0.151 \\ RacketSports & 0.737 & **0.862** & 0.803 \\ SelfRegulationSCP1 & **0.853** & 0.846 & 0.775 \\ SelfRegulationSCP2 & 0.550 & **0.556** & 0.539 \\ StandWalkJump & **0.500** & 0.400 & 0.200 \\ UWaveGestureLibrary & 0.819 & 0.884 & **0.903** \\ \hline \hline \end{tabular}
\end{table}
Table 5: Accuracy of BIMO and SOTA unsupervised methods (USRL, DTW) on UEA datasets. Bold text indicates the best accuracy.  
employs a two-step signal processing method in terms of both time and frequency and an ensemble-based peak detection method; it extracts diverse features from detected peaks.  
As a result, we found that BIMO outperformed the supervised learning methods (Table 6), indicating that BIMO is comparable to previous SOTA models. This is a very meaningful result, since BIMO opens up the possibility that unsupervised end-to-end data-driven feature learning is also possible for noisy time-series data.