Neighbor Profile: Bagging Nearest Neighbors for Unsupervised Time Series Mining

Unsupervised time series mining has been attracting great interest from both academic and industrial communities. As the two most basic data mining tasks, the discoveries of frequent/rare subsequences have been extensively studied in the literature. Specifically, frequent/rare subsequences are defined as the ones with the smallest/largest 1-nearest neighbor distance, which are also known as motif/discord. However, discord fails to identify rare subsequences when it occurs more than once in the time series, which is widely known as the twin freak problem. This problem is just the "tip of the iceberg" due to the 1-nearest neighbor distance based definitions. In this work, we for the first time provide a clear theoretical analysis of motif/discord as the 1-nearest neighbor based nonparametric density estimation of subsequence. Particularly, we focus on matrix profile, a recently proposed mining framework, which unifies the discovery of motif and discord under the same computing model. Thereafter, we point out the inherent three issues: low-quality density estimation, gravity defiant behavior, and lack of reusable model, which deteriorate the performance of matrix profile in both efficiency and subsequence quality. To overcome these issues, we propose Neighbor Profile to robustly model the subsequence density by bagging nearest neighbors for the discovery of frequent/rare subsequences. Specifically, we leverage multiple subsamples and average the density estimations from subsamples using adjusted nearest neighbor distances, which not only enhances the estimation robustness but also realizes a reusable model for efficient learning. We check the sanity of neighbor profile on synthetic data and further evaluate it on real-world datasets. The experimental results demonstrate that neighbor profile can correctly model the subsequences of different densities and shows superior performance significantly over matrix profile on the real-world arrhythmia dataset. Also, it is shown that neighbor profile is efficient for massive datasets.