# Scale-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations +
###### Abstract  
Time-Series-Classification (TSC) is an important machine learning task for many branches of science. Symbolic representations of time series, especially Symbolic Fourier Approximation (SFA), have been proven very effective for this task, given their abilities to reduce noise. In this paper, we improve upon SCALE-BOSS using multiple symbolic representations of time series. More specifically, the proposed SCALE-BOSS-MR incorporates into the process a variety of window sizes combined with multiple dilation parameters applied to the original and to first-order differences' time series, with the latter modeling trend information. SCALE-BOSS-MR has been evaluated using the eight datasets with the largest training size of the UCR time series repository. The results indicate that SCALE-BOSS-MR can be instantiated to classifiers that are able to achieve state-of-the-art accuracy and can be tuned for scalability. time series; time series classification; symbolic representations; multiple representations; accuracy; execution time +
Footnote †: This is the extended version of the paper “SCALE-BOSS: A framework for scalable time-series classification using symbolic representations” published in the year 2022 as a proceedings of the 12 th Hellenic Conference on Artificial Intelligence. Footnote †: This is the extended version of the paper “SCALE-BOSS-MR: A framework for scalable time-series classification using symbolic representations” published in the year 202 In a previous work, we have proposed the SCALE-BOSS framework [9] to balance between efficiency and accuracy for TSC. The SCALE-BOSS framework has two main variations: One using clustering and the other using classification algorithms for TSC along a pipeline. These variations exploit symbolic time series representations, resulting in concrete TSC algorithms. Specifically, we can build different TSC classifiers with the only requirement that the clustering algorithm uses some form of cluster representatives. Then, simply using a 1-NN classifier, we can classify time series by comparing them only to the (few, compared to the series in the training set) representatives. On the other hand, we can use classification methods that work on the term-frequency vector of the symbolic representation. One of the main conclusions of that study is that we can build very efficient TSC methods using clustering and classification methods that exploit time series' class representatives, such as k-means, mini-batch k-means, or random forests. We have shown that SCALE-BOSS [9] manages to achieve significant improvement on the efficiency of training and testing TSC models, but with room to improve the accuracy of predictions. Here, we leverage ideas from state-of-the-art algorithms,extending the SCALE-BOSS framework [9] using multiple time series representations to achieve state-of-the-art accuracy, while maintaining high computational efficiency. Specifically, the contributions of this work are as follows:  
1. We incorporate into SCALE-BOSS-MR and explore the use of * multiple window sizes; * multiple dilation parameters; * trend information by means of time series' first-order differences. to balance accuracy with the scalability of TSC algorithms exploiting symbolic time series representation. 2. We present extensive results from a multitude of classifiers built using the SCALE-BOSS-MR framework. The proposed classifiers can provide either state-of-the-art accuracy or state-of-the-art scalability. Some of the proposed classifiers provide a balance between accuracy and scalability, meaning that they retain state-of-the-art accuracy while also being significantly faster than other state-of-the-art classifiers that use symbolic representations. The paper is organized as follows: Section 2 provides an overview of the literature and describes how it relates to SCALE-BOSS-MR. Section 3 describes the pipeline of the framework and its instantiations. Section 4 evaluates different TSC algorithms created using the proposed framework, and finally, Section 5 concludes the paper.