# Scale-BOSS-MR: Scalable Time Series Classification Using Multiple Symbolic Representations +
## 3 Framework Description: From SCALE-BOSS to SCALE-BOSS-MR  
As already pointed out, two main ideas behind the SCALE-BOSS framework are as follows: (a) Exploit symbolic representations of time-series, and (b) leverage efficient machine learning algorithms for clustering and classification. Especially, we focus on models that exploit representatives of time series, so as to balance between computational efficiency and prediction accuracy. As shown in Figure 1, the first step of this framework is to compute the symbolic representation of the training set. Any symbolic representation such as SFA or SAX can be used here. Figure 1: SCALE-BOSS workflow. Then, the second step computes the Term-Frequency Vectors for the training set, thus creating a Bag-Of-SFA Symbols (BOSS) for the training set. The third step computes the models of time series, which will be used subsequently for making time series label predictions: To construct such a model, we can use either a clustering or a classification mechanism exploiting the term-frequency vectors. In any case, our interest is on these models that learn representatives of classes/clusters to whom test cases will be compared with, without excluding others. Having these models, the fourth step computes the symbolic representation for the test set, while the fifth step computes the term-frequency vectors for the test set. The sixth and final step predicts the label for the test case exploiting the model used. Specifically, in this work, and in case we use a time-series clustering mechanism, a 1-NN classifier classifies the test time series by comparing it to the representatives of each cluster. On the other hand, if a classifier is used, then the test time series is classified using the trained classifier model. For the different instantiations of the framework, here we succinctly mention all the choices made and alternatives in the TSC pipeline:  
1. We have chosen SFA as the symbolic representation. The framework can be tuned to other symbolic representations, but we have chosen SFA because it has been proven superior to others (e.g., SAX) [15; 24]. 2. Regarding clustering algorithms, we evaluated the use of K-Means, Mini-Batch K-Means, BIRCH, DBSCAN, and K-Medoids. 3. Regarding classifiers, we tested the framework with SGD, LinearSVC, AdaBoost, Multi-Layer Perceptron, Naive Bayes, QDA, RBF-VSM, Decision Trees (DT), and Random Forest (RF). 4. Regarding the distance measure for comparing time series in the clustering approach, we use the cosine similarity of their term-frequency vectors. It is not our purpose to describe here all alternative clustering and classification methods that have been used, but subsequently,we provide details on the most effective ones, focusing on those that provide a condensed representation of time series in a form of time series class representatives. Considering the clustering algorithms, all algorithms exploit representatives, except DBSCAN [25; 26], which was used as a classic algorithm of density-based time series clustering methods. From the classifiers, we consider that DT and RF provide an elaborated representation of time series along model (decision tree) paths, which can be considered to model training set variations, much like class time series class representatives do. Close to tree representations, BIRCH [27] is an incremental clustering algorithm using Clustering Feature Trees. BIRCH uses the concept of a _Clustering Feature_ (CF): this is a triple that contains the number of data points in the cluster, the linear sum of the points, and the square sum of the points. A _CF tree_ is a height-balanced tree with two parameters: the branching factor \(B\) and the threshold \(T\). Each non-leaf node contains at most \(B\) entries of the form \((CF,child_{i})\), and each leaf node consists of \(L\) CFs. In addition, each leaf node has two pointers, \"prev\" and \"next\", which are used to chain all leaf nodes together for efficient scans.