Time series streams are ubiquitous in many application domains, e.g., transportation, network monitoring, autonomous vehicles, or the Internet of Things (IoT). Transmitting and storing large amounts of such fine-grained data is however expensive, which makes compression schemes necessary in practice. Time series streams that are transmitted together often share properties or evolve together, making them significantly correlated. Despite the rich literature on compression methods, the state-of-the-art approaches do not typically avail correlation information when compressing times series. In this work, we demonstrate how one can leverage the correlation across several related time series streams to both drastically improve the compression efficiency and reduce the accuracy loss.We present a novel compression algorithm for time series streams called CORAD (CORelation-Aware compression of time series streams based on sparse Dictionary coding). Based on sparse dictionary learning, CORAD has the unique ability to exploit the correlation across multiple related time series to eliminate redundancy and perform a more efficient compression. To ensure the accuracy of the compressed time series, we further introduce a method to threshold the information loss of the compression. Extensive validation on real-world datasets shows that CORAD drastically outperforms state-of-the-art approaches achieving up to 40:1 compression ratios while minimizing the information loss.
In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both the stationary and non-stationary settings. To treat the non-stationary setting, we introduce a novel, exponentially weighted estimator for the Spearman rank correlation, which allows the local nonparametric correlation of a bivariate data stream to be tracked. To the best of our knowledge this is the first algorithm to be proposed for estimating a time varying Spearman rank correlation that does not rely on a moving window approach. We explore the practical effectiveness of the Hermite series based estimators through real data and simulation studies demonstrating good practical performance. The simulation studies in particular reveal competitive performance compared to an existing algorithm. The potential applications of this work are manifold. The Hermite series based Spearman rank correlation estimator can be applied to fast and robust online calculation of correlation which may vary over time. Possible machine learning applications include, amongst others, fast feature selection and hierarchical clustering on massive data sets.
Nonparametric correlations such as Spearman's rank correlation and Kendall's tau correlation are widely applied in scientific and engineering fields. This paper investigates the problem of computing nonparametric correlations on the fly for streaming data. Standard batch algorithms are generally too slow to handle real-world big data applications. They also require too much memory because all the data need to be stored in the memory before processing. This paper proposes a novel online algorithm for computing nonparametric correlations. The algorithm has O(1) time complexity and O(1) memory cost and is quite suitable for edge devices, where only limited memory and processing power are available. You can seek a balance between speed and accuracy by changing the number of cutpoints specified in the algorithm. The online algorithm can compute the nonparametric correlations 10 to 1,000 times faster than the corresponding batch algorithm, and it can compute them based either on all past observations or on fixed-size sliding windows.