r-th Root Ranking Loss is a specific loss function used in a proposed model for the task of multivariate time series retrieval. It is a specialized loss function tailored for a Deep r-RSJBE model, designed to enhance the precision at the top of the ranking list when retrieving relevant multivariate time series segments from historical data or a database. The use of the r-th root operation introduces a specific mathematical aspect to the ranking loss optimization.


Deep r-th Root Rank Supervised Joint Binary Embedding for Multivariate Time Series Retrieval

Multivariate time series data are becoming increasingly common in numerous real-world applications, e.g., power plant monitoring, health care, wearable devices, automobiles, etc. As a result, multivariate time series retrieval, i.e., given the current multivariate time series segment, how to obtain its relevant time series segments in the historical data (or in the database), attracts a significant amount of interest in many fields. Building such a system, however, is challenging since it requires a compact representation of the raw time series, which can explicitly encode the temporal dynamics as well as the correlations (interactions) between different pairs of time series (sensors). Furthermore, it requires query efficiency and expects a returned ranking list with high precision on the top. Despite the fact that various approaches have been developed, few of them can jointly resolve these two challenges. To cope with this issue, in this paper, we propose a Deep r-th root of Rank Supervised Joint Binary Embedding (Deep r-RSJBE) to perform multivariate time series retrieval. Given a raw multivariate time series segment, we employ Long Short-Term Memory (LSTM) units to encode the temporal dynamics and utilize Convolutional Neural Networks (CNNs) to encode the correlations (interactions) between different pairs of time series (sensors). Subsequently, a joint binary embedding is pursued to incorporate both the temporal dynamics and the correlations. Finally, we develop a novel r-th root ranking loss to optimize the precision at the top of a Hamming distance ranking list. Thoroughly empirical studies based upon three publicly available time series datasets demonstrate the effectiveness and the efficiency of Deep r-RSJBE.