Time series motif discovery
Nuno Constantino Castro · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2012
Time series data are daily produced in massive proportions in virtually every field. Most of the data are stored in time series databases. To find patterns in the databases is an important problem. These patterns, also known as motifs, provide useful insight to the domain expert and summarize the database. They have been widely used in areas as diverse as finance and medicine. Despite there are many algorithms for the task, they typically do not scale and need to set several parameters. We propose a novel algorithm that runs in linear time, is also space efficient and only needs to set one parameter. It fully exploits the state of the art time series representation (SAX _ Symbolic Aggregate Approximation) technique to extract motifs at several resolutions. This property allows the algorithm to skip expensive distance calculations that are typically employed by other algorithms. We also propose an approach to calculate time series motifs statistical significance. Despite there are many approaches in the literature to find time series motifs e_ciently, surprisingly there is no approach that calculates a motifs statistical significance. Our proposal leverages work from the bioinformatics community by using a symbolic definition of time series motifs to derive each motif's p-value. We estimate the expected frequency of a motif by using Markov Chain models. The p-value is then assessed by comparing the actual frequency to the estimated one using statistical hypothesis tests. Our contribution gives means to the application of a powerful technique - statistical tests - to a time series setting. This provides researchers and practitioners with an important tool to evaluate automatically the degree of relevance of each extracted motif. Finally, we propose an approach to automatically derive the Symbolic Aggregate Approximation (iSAX) time series representation's parameters. This technique is widely used in time series data mining. Its popularity arises from the fact that it is symbolic, reduces the dimensionality of the series, allows lower bounding and is space efficient. However, the need to set the symbolic length and alphabet size parameters limits the applicability of the representation since the best parameter setting is highly application dependent. Typically, these are either set to a fixed value (e.g. 8) or experimentally probed for the best configuration. The technique, referred as AutoiSAX, not only discovers the best parameter setting for each time series in the database but also finds the alphabet size for each iSAX symbol within the same word. It is based on the simple and intuitive ideas of time series complexity and standard deviation. The technique can be smoothly embedded in existing data mining tasks as an efficient sub-routine. We analyse the impact of using AutoiSAX in visualization interpretability, classification accuracy and motif mining results. Our contribution aims to make iSAX a more general approach as it evolves towards a parameter-free method.