# Sequence-Information Recognition Method Based on Integrated mDTW
## 2 Related Works  
### Related Works of DTW  
DTW (Dynamic Time Warping) [3] distance is a method employed to calculate the similarity between two time series. It was initially proposed and utilized in the field of speech recognition and has subsequently found wide application in various domains, including time-series classification, pattern recognition, anomaly detection, clustering analysis, and more. DTW excels at finding the best match between two sequences by elastically stretching or compressing the time series, enabling effective comparison and matching even when the sequences exhibit offsets or rate changes on the time axis. This is achieved by identifying the best alignment (i.e., the optimal path) between the two sequences, which minimizes the sum of the pairwise distances along this path, therefore accurately reflecting the similarity between the two sequences. This alignment allows for nonlinear stretching of the sequences on the time axis, making DTW particularly suitable for handling time series of different lengths or with varying rates. In time-series classification tasks, DTW serves as a valuable similarity measure, aiding in the determination of what category a sequence belongs to. By calculating the DTW distance between the sequence to be classified and sequences of known categories, the category with the smallest distance can be confidently selected as the classification result. Furthermore, DTW can be utilized to identify specific patterns in time series or detect anomalies. By comparing a time series with a known pattern or a sequence within the normal range and calculating the DTW distance between them, it becomes possible to determine whether the time-series matches the expected pattern or deviates from the normal range. In time-series clustering tasks, DTW distance proves to be an effective distance measure in clustering algorithms. By calculating the DTW distance between different sequences, similar time series can be clustered together, enabling the discovery of sequence groups with similar morphologies but possible offsets on the time axis. DTW stands out as a potent and versatile tool within the realm of temporal data mining, finding applications across various domains due to its unique capabilities. One illustrative domain where DTW demonstrates its process is in acoustic data analysis, where it exhibits invariance to Doppler effects. This particular attribute makes DTW invaluable for tasks involving the precise alignment and comparison of acoustic signals, regardless of potential frequency shifts induced by motion or other factors. Expanding the scope of DTW's applications, it plays a crucial role in the analysis of biological signals such as Electrocardiogram (ECG) [7] or Electroencephalogram (EEG) [8; 9]. Researchers leverage DTW to effectively characterize and discern patterns within these signals, aiding in the identification and understanding of potential diseases. The flexibility of DTW in handling diverse types of temporal data makes it an indispensable tool for extracting meaningful insights from complex biological signals. Moreover, in the context of time-series classification problems, DTW serves as a feature extractor when combined with predefined patterns or features, as highlighted in the work by [PERSON] et al. [10]. This approach allows DTW to contribute significantly to the classification of time-series data, where the alignment of sequences is essential for accurate pattern recognition. The use of Hamming distance [1; 11] in conjunction with DTW alignment in this setting is referred to as Edit distance, a well-studied variant that enhances our understanding of the relationships between different temporal sequences [12]. In essence, the versatility of DTW spans diverse applications, from mitigating Doppler effects in acoustic data to aiding in the diagnosis of diseases through the analysis of biological signals.