Detecção de ponto de mudança em séries temporais utilizando o espectro do grafo

Abstract

Time series are a sequence of values distributed over time. Analyzing time series is important in many areas, including medical, financial, aerospace, commercial, and entertainment. Change point detection is the problem of identifying change in the meaning or distribution of data in a time series. The academic and commercial interest in the subject has been increased in the last decade due to the increase of power and complexity of sensors, as well as the advance of technological processes, which allowed the capture and recognition of a large volume of data. Many widely used algorithms find it difficult to achieve optimal results when the number of dimensions increases or the data volume grows exponentially, there are also time series where most algorithms do not have satisfactory results (over 0.80 precision) even considering twodimensional data as in context-based distributions. Most known algorithms are more efficient in specific scenarios and less efficient in others, so a greater number of solution options increases the likelihood that the user will get an algorithm that best meets their needs. Solutions to these issues are of great ecological and economic interest. The objective of this work is the development of an unsupervised change point detection algorithm that is applicable in series with multiple change points and large data volume with high precision. To achieve this goal, the new SpecDetec method was developed, an algorithm that uses graph spectrum clustering to detect shift points. The algorithm was published in a package in CRAN as SpecDetec and is available for unrestricted use. The SpecDetec was evaluated using the UCR Archive which is a large database of different time series. The performance of SpecDetec has been compared with other state-of-the-art algorithms for detecting shift points. The results showed that graph spectrum clustering is an efficient technique for detecting shift points, as Spec has achieved better accuracy compared to the state of the art in some specific scenarios and is as efficient as in most cases evaluated. In contexts where it is possible to support a tolerance of up to 0.05, SpecDetec is recommended as it was superior to other algorithms in most databases.