# Scale-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations +
## 3 Framework Description: From SCALE-BOSS to SCALE-BOSS-MR
All entries in a leaf node must satisfy a threshold requirement, with respect to a threshold value, and thus, a leaf node represents a cluster made up of all the subclusters represented by its entries. While the K-BOSS-VS method [15] applies K-means to each class label of the training set to obtain the K representatives per class, we have evaluated the use of clustering variants that increase the computational efficiency of the overall method, such as Mini-Batch K-Means [28], thus resulting in the MB-K-BOSS-VS configuration. Mini-Batch K-Means is an online variant of the K-Means clustering algorithm that converges using only a subset of the dataset and has results very close to the full K-Means clustering algorithm. In addition to these clustering algorithms, we also evaluated the use of the K-Medoids algorithm [29]. This is a fast and simple algorithm that calculates the distance matrix once and then finds the cluster medoids in each iteration step. Using decision trees to classify symbolic representations of time series, instead of using similarities between the representatives and the test set, we feed the normalized term-frequency vectors of the training set into a decision tree (DT) classifier or a random forest (RF) classifier. Then, the trained model is used to infer the class label for each time series in the test set. RF is essentially an ensemble variant of DT, allowing us to vary the number of trees, much like varying the number of class representatives in K-BOSS-VS. In the evaluation reported in [9], we show that amongst the classifiers, Random Forest and MLP provided the best results. For clustering algorithms, Mini-Batch K-Means and K-Means provided the best accuracy. In any case, although computationally efficient, the accuracy achieved by these methods is lower than that of state-of-the-art methods. SCALE-BOSS-MR refines the SCALE-BOSS framework by fusing multiple representations into a single term-frequency vector that is in turn fed into the regular SCALE-BOSS pipeline. This procedure was mostly inspired by WEASEL [18]. Multiple representations of time series result from the use of first differences of time series in combination with multiple temporal time series' windows and multiple dilation filters. Given any specific dilated window, this is processed to obtain a term-frequency vector using unigrams or bigrams, and all the term vectors from all dilated windows are stacked column-wise to provide the representation of the time series. More specifically, as we can see in Figure 2, the SCALE-BOSS-MR framework works, stage by stage, as follows:  
1. Computes the dilated windows for the training set given a configuration of \(W\) window sizes in a set of \(window\_configs\) and \(D\) dilation filters in a set of \(dilation\_filter\_configs\). This results in \(DW=W\times D\) dilated windows configurations;
2. Computes the \(DW\) first-order differences' dilated windows, i.e., dilated windows for the time series created by the first-order differences of the original time series;
3. Computes the term-frequency vectors of dilated windows for the original time series and of the dilated windows for the first-order differences' time series, then stacks the term-frequency vectors column-wise;
4. Fits the model using the time series representations of the training set;
5. In the next three stages, computes the symbolic representation for the dilated windows of a time series from the test set, as well as the corresponding first-order differences' time series, then computes and stacks the term-frequency vectors. Algorithm 1 provides a succinct and comprehensive description of SCALE-BOSS-MR.  
More specifically, lines 1-9 describe the main SBMR function: in lines 2 and 3, the algorithm loops over window configurations and dilation sizes configurations. For each window configuration, it computes the dilated time series according to the dilation parameter and produces the term-frequency vector.