# Sequence-Information Recognition Method Based on Integrated mDTW
## 1 Introduction  
Measuring the similarities of different samples is fundamental to many fields of computational intelligence. Many algorithms take distances to value similarities of samples for classification, detection, and other pattern-recognition tasks. In most of the research, samples are represented by a set of vectors through encoding processes. Then, the Minkowski distances of those vectors could be computed as similarities. Minkowski distances are defined as \(\text{dist}(x,y)=\sum_{k=1}^{d}{(x_{k}-y_{k})^{p}}\), which is one of the most popular metrics to value samples distances. When \(p=1\), Minkowski distance is named Manhattan distance; when \(p=2\) it is called Euclidean distance. Another popular measure is Mahalanobis distance, which could be viewed as distorted Euclidean distance. Overall, these studies highlight the need for most of the current research. In the past decade, significant progress has been made in sequence-information processing. Sequence-information processing refers to the analysis and manipulation of data sequences, such as text, speech, or biological sequences. This field involves techniques like natural language processing (NLP) and sequence alignment, which enable machines to understand, generate, and transform sequential data efficiently. However, there is still room for improvement in related methods, especially in terms of interpretability, model integration, and other aspects. Existing methods do not perform well in explaining thecomplex temporal structure inherent in the data [1; 2]. As a remedy, Dynamic Time Warping (DTW) [3] has emerged as a compelling alternative [4; 5; 6]. DTW's most notable advantage lies in its resilience against signal warping, encompassing shifts and scaling along the time axis or even the Doppler effect. Consequently, DTW has evolved into one of the most favored metrics for tasks involving pattern matching. For example, when dealing with signals from different sampling frequencies, the conventional point-wise Euclidean distance may yield different results, especially when one signal is merely a compressed version of another. Without using mDTW for sequence point registration, it is not possible to determine which two points are directly used to calculate the Euclidean distance. Therefore, for two time series, the use of DTW is necessary. In this case, DTW performs well by expertly capturing the scale variation and the minimum distance between the generated signals. What sets DTW apart is not only its ability to produce distance values but also its ability to reveal the exact alignment of two sequences. DTW is unique in that it not only computes distance values but also aligns two sequences precisely, which is particularly critical in intelligent computing applications. Moreover, DTW is not just a similarity measure. As a robust feature-extraction tool, it enhances its versatility and value in the context of intelligent computing. The processing of online character data is a typical and formidable challenge in the field of time-series processing. Accurate and efficient recognition of handwritten characters is of great significance, especially in an environment where smart devices are constantly evolving. Over recent decades, the domain of sequence-information processing, including non-rigid sparse point matching, Handwritten Chinese Character Recognition (HCCR), and Human Action Recognition (HAR), has become a research hotspot and has made remarkable achievements and progress. Furthermore, the intricacies embedded in the Chinese written language, characterized by a vast number of character classes, introduce an additional layer of complexity to the recognition task. The sheer volume of characters, each with its unique features, poses a formidable challenge for researchers and practitioners alike. The intricate structure inherent in most Chinese characters further amplifies the difficulty of the HCCR task, contributing to its status as a persistent and demanding challenge within the research community.