| 活動內容 | How to construct a dynamic system has been appealing to researchers in physics, applied mathematics, computer science, and engineering since it can facilitate system identification, trajectory tracking, and time series forecast. In recent years, advanced smart systems capable of identifying dynamics inherent in the observed data are in high demand as they can enable the machine intelligence for predicting and detecting human behaviors and environmental evolution. According to our recent studies, the time series can be transformed into critical homological structures and/or features such that robust machine learning can be established using the homological analysis, especially for classifying, detecting, and predicting object motions, human behaviors, and fundamental characteristics in time varying (dynamic) signals. The conventional statistical signal processing and machine learning approaches are often under the unrealistic assumption of i.i.d. (statistically independently and identically distributed) data and thus the dynamics across data samples are not allowed. Based on the aforementioned new machine learning paradigm, it is possible to convert any non i.i.d. time series resulting from a Markov process to a neat geometric structure so the detection. prediction, and classification can be accurately fulfilled. In this talk, the mathematical framework and algorithms of the advanced homological analysis to learn dynamics by smart systems will be introduced and then the corresponding effectiveness on several practical applications will be demonstrated. |