Efficient Pooling of Time Series Data using Sketching Techniques

In this article, we explore the concept of sketching in time series analysis. Sketching is a technique that allows us to efficiently pool data into a compressed representation while preserving critical information. The idea has been around since the 1940s but has only recently been applied to time series analysis.
The article begins by explaining that efficient data pooling is crucial in time series analysis, as it helps reduce the amount of data that needs to be processed without sacrificing important information. The authors then introduce the concept of sketching and how it can be used for efficient data pooling. Sketching involves representing a large dataset with a smaller one while preserving essential details.
The article highlights several key applications of sketching in time series analysis, including network monitoring, linear algebra, machine learning, and spatial statistics. The authors note that sketching has been valuable in these domains, providing significant improvements in efficiency without compromising accuracy.
One of the most significant benefits of sketching is its ability to handle dynamic additions or deletions of dimensions with minimal overhead. This allows data analysts to consider "what-if" scenarios in real time while exploring the data. The authors also mention that z-normalization, a technique used in conjunction with sketching, can convert the data into unitless shapes, making it easier to compare and analyze.
The article then delves into the challenges of incorporating sketching into time series analysis, particularly when dealing with multidimensional time series. The authors explain that simply applying MP (mean pairwise) on the summed time series can lead to missed discord if irrelevant dimensions are included. To address this issue, they designed a sketching method that enables MP to be built on the sketch of the multidimensional time series.
In summary, the article provides an overview of sketching in time series analysis, highlighting its efficiency, flexibility, and ability to handle dynamic data. By leveraging these properties, data analysts can significantly improve their workflows while maintaining accurate results.