## 2 Datasets, Feature Extraction, and Classification Methods
### Feature Extraction  
The most straightforward way to apply a classification strategy on this dataset would be to use the complete 512-dimensional vector (raw data) as the feature vector. However, raw data often contain noise, redundancies, or irrelevant information; thus, there are different feature selection/extraction techniques that could be applied on such a feature space and subsequently be used instead or added to this feature vector. The following additional feature extraction techniques are considered in our case:  
* **Basic aggregation features**: A series of basic features are extracted. They are defined as aggregations at different levels:
* Along the signals of the eight channels: Average (AVG) and the average of the absolute values (ABS). There are 64 values in each case and 128 (=64 \(\times\) 2) values in total.
* For each channel (\(\times\)8): Absolute mean square (AMS) and root mean square (RMS). There are 8 for each channel and 16 values in total.
* At a global level: Maximum, minimum, mean, AVG, average of absolute values (ABS), and root means square (RMS). There are five values in total.
* **ROCKET** (Random Convolutional KErnel Transform [23]): It is a method that achieves state-of-the-art classification accuracy in several benchmarks, but it only requires a fraction of the training time used by other existing standard methods. Other methods for time series classification focus only on a single type of representation such as shape, frequency, or signal variance. Convolutional kernels are able to represent multiple characteristics of different types simultaneously.
* **TSFRESH** (Time Series FeatuRe Extraction based on Scalable Hypothesis tests): This methodology aims to avoid the time-consuming process of meaningful feature identification and extraction, from time series data. It consists of an algorithm and a Python package. The Python package implements the extraction of 794 features using multiple characterization methods, each of them executed with various sets of parameters. This framework also includes feature selection to identify those features that are statistically significant. The algorithm is described in [32]. The software package is presented in [24]. The total number of features is therefore 6352 (=8 \(\times\) 794).  
In this framework, each feature vector is individually analyzed in relation to its significance for predicting the target class label. As a result, a vector of \(p\)-values is obtained. This vector is assessed against the Benjamini-Yekutieli procedure [33], which allows the method to decide which features to keep. This selection strategy considers the application of a threshold, whose default value is 0.05. However, this selection is so restrictive in some  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Dataset** & **Problem** & **\# of Samples** & **\# of Classes** \\ \hline
19 & Identify 7 dominoes & I & 80 & 8 \\
20 & Identify 9 touch on half-sphere & I & 600 & 10 \\
21 & Order 3 costersy NO case & O & 480 & 16 \\
22 & Order 3 medictacks NO case sorted & O & 164 & 16 \\
23 & Order 4 medictacks NO case sorted & O & 672 & 65 \\
24 & Order 4 credictacks WITH case sorted & O & 390 & 65 \\
25 & Rotation interval half numeric & R & 120 & 12 \\
26 & Rotation interval one numeric & R & 120 & 12 \\
27 & Slide inside-out on desk surface & P & 110 & 11 \\
28 & Slide outside-in ruler & P & 110 & 11 \\
29 & session1 \(\times\) 10 & C & 530 & 53 \\
30 & session2 \(\times\) 10 & C & 530 & 53 \\
31 & session3 \(\times\) 10 & C & 530 & 53 \\
32 & session4 \(\times\) 10 & C & 530 & 53 \\
33 & session5 \(\times\) 10 & C & 530 & 53 \\
34 & session6 \(\times\) 10 & C & 530 & 53 \\ \hline \hline \end{tabular}
\end{table}
Table 1: \(Cont.\)cases that most of the features are discarded. An iterative method is applied that considers the threshold values \(\{0.05,0.1,0.2,0.5\}\) and selects the first one that keeps at least a 10% of the total number of attributes.