# Scale-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations +
## 2 Literature Review
It uses SFA, but it does a few novel things: First, WEASEL performs feature discretization to reveal differences between classes; second, it uses windows of variable lengths, also considering the order of windows; and finally, it uses statistical feature selection, leading to significantly reduced runtime. Finally, WEASEL uses unigram and bigrams' symbolic representation of the time series. WEASEL is more scalable and accurate than BOSS, but it is not as scalable as BOSS-VS, as shown in [9]. ROCKET [7] is a non-symbolic time series classification algorithm that uses numerous (10,000) convolution kernels together with a linear classifier (ridge regression or logistic regression). A significantly faster version of ROCKET, called MiniRocket, is presented in [8], which uses fewer parameters than ROCKET to extract features, without sacrificing accuracy. Multi-Rocket [10] uses first differences to further improve accuracy compared to Mini-Rocket: Given a time series \(x\) with subsequent points with arithmetic values \(x_{i}\), \(i=0,1,\ldots\), first-order differences are computed following \(out_{i}=x_{i+1}-x_{i}\), revealing time series trend information. Dilation allows for certain elements in the input time series to be downsampled by a factor \(d\), by including every \(d\)-th time series value. The ROCKET family of algorithms does not employ a symbolic representation of time series, and it proves to be very scalable while maintaining state-of-the-art accuracy. However, first-order differences and dilation parameters can also be applied on top of algorithms that use symbolic representations to increase their accuracy. Leveraging these ideas, WEASEL 2.0 [11] builds an ensemble of classifiers, choosing at random window sizes, dilation and the use of first-order differences. Combining windowing and dilation, each window at offset \(i\) and of length \(l\) includes \(l\) time series elements which are downsampled starting from \(i\) by a factor \(d\): This combination increases the receptive field of the algorithms with respect to the windowing process. Using these techniques, WEASEL 2.0 manages to provide state-of-the-art accuracy while maintaining computational efficiency. Similarly, MR-SQM [19; 20] uses different kinds of symbolic representations to improve accuracy. TDE [21] is a classification algorithm that combines design features of four classifiers (BOSS, WEASEL, S-BOSS, and cBOSS). Like BOSS, TDE is a homogeneous ensemble of nearest neighbor classifiers that uses distance between histograms of word counts and injects diversity via parameter variation. TDE takes the ensemble structure from cBOSS, which is more robust and scalable. The use of spatial pyramids is adapted from S-BOSS and it uses bi-grams like WEASEL. TDE is significantly more accurate than WEASEL and S-BOSS while retaining the scalability of cBOSS. In [22], the authors present Contracted Shapelets, a method to speedup shapelet-based time series classification by performing early abandon. The authors present binary shapelets in order to address three problems of shapelet transform: loss of class information, managing easy vs. hard to classify classes, and addressing multi-class problems. In [23], the authors propose Proximity Forest, an algorithm that learns accurate models from datasets with millions of time series and classifies a time series in milliseconds. The models are ensembles of highly randomized Proximity Trees. Whereas conventional decision trees branch on attribute values (and usually perform poorly on time series), Proximity Trees branch on the proximity of time series to exemplar time series, leveraging the decades of work into developing relevant measures for time series. The authors show that their multi-resolution multi-domain linear classifier achieves a similar accuracy to the state-of-the-art COTE ensemble, as well as to recent deep learning methods (FCN, ResNet). TS-CHIEF (Time Series Combination of Heterogeneous and Integrated Embedding Forest) [6] rivals HIVE-COTE in accuracy, but it is significantly faster.