# Smart Rings vs. Smartwatches: Utilizing Motion Sensors for Gesture Recognition
## 3 Approach and Methodology
### Algorithmic Methodology
#### 3.3.2 Feature Derivation and Selection  
The goal of the feature derivation stage is to extract multiple characteristics from the data in order to differentiate gesture types. The best feature is one that uniquely identifies a gesture type and is identical on every gesture instance. However, this is not possible for  
Figure 10: Preprocessed magnitude data for the _Circle Clockwise_ gesture. The two columns contrapose accelerometer and gyroscope data and each row shows data originating from a different session. Every signal is scaled equally, and the outliers are removed. Additionally, the time shift is corrected, and the high frequency noise is filtered. the gesture catalog, since different gestures share similar characteristics. Thus, multiple features are extracted for each gesture instance and then combined with the assumption that a collection of features describes a gesture better than a single feature. Each gesture instance provides eight different signals, and each signal can be used to calculate multiple features. Therefore, the total number of features depends on the dimensionality of the preprocessed data. Figure 10 shows that different instances of the same gesture contain a different number of measurements, even after being preprocessed. Since most machine learning models can only handle feature vectors with a fixed size, the feature derivation stage must transform signals with different lengths into feature vectors with fixed lengths. Therefore, each feature derivation algorithm must be able to handle signals with variable input sizes. Each signal can be described by the change of its values over time, but every used feature derivation algorithm reduces the signal to a single value. Thus, a technique is required to extract time information. To solve this challenge, a generic windowing approach with dynamic sized windows is facilitated. This approach divides the signal into a fixed number of windows and then applies a feature derivation algorithm to every window, essentially producing the same feature multiple times for successive parts of the signal. A low number of windows produces a coarse description of the signal, while a high number of windows describes the signal rather precisely. Since the goal is to create features that are very similar inside a gesture class, the number of windows must be low enough to capture the descriptive signal information in the same window. However, too few windows might oversimplify the signal and result in weak features. Figure 11 demonstrates this problem by comparing two similar signals with different window sizes. Furthermore, using windowed feature derivation algorithms with a low number of windows eliminates the need for signal centering in the preprocessing step, since the time shift is implicitly corrected by the windowing approach. The optimal number of windows per signal can be empirically determined by repeatedly training a model with different window sizes and was estimated to be five. In total, the following features are considered: (i) crossing (i.e., counting how often the amplitude crosses a certain threshold inside the signal), (ii) min-max (i.e., applied to each window; calculation of the min and max value inside each window), (iii) sum (i.e., sum of all values in a signal is proportional to its area), (iv) average (i.e., mean and median of measurements in each window--possibly contributes 80 features to the feature vector when five windows and eight signals are considered), (v) frequency (i.e., window approach not applied since whole signal is required; discrete Fourier transformation) and (vi) length. In total--when all features are concatenated--the feature vector consists of 793 features. The feature vector eventually contains weak features or features that contain redundant information about the signals. Therefore, feature selection is performed to identify strong  
Figure 11: Comparison of window sizes with two similar signals. The peak values of the signals on the left reside in different windows.