# Real-Time Physical Activity Recognition on Smart Mobile Devices Using Convolutional Neural Networks
## 4 Results
### Statistical Feature Analysis
#### 4.6.1 Ablation Study  
The statistical features that describe the global characteristics of the input window can be grouped into the following feature types:  
* Average, which consists of the features, one for each axis
* Standard deviation, which consists of three features, one for each axis
* Average absolute difference, which consists of three features, one for each axis
* Average resultant acceleration, which consists of just one feature, since it combines the input from all the axes
* Binned distribution, which consists of 30 features, 10 for each axis  
All of the above is explained in detail in Section 3.2. In order to study the effect of each feature, we ran experiments using no features (DCNN-0), and then, we started adding every feature one-by-one. This resulted in five different experiments, where the number of features was respectively 3, 6, 9, 10, and 40. The respective experiment names are DCNN-X, where X is the number of features. The mean and standard deviation of the accuracy after running 10 trainings with different initializations for each feature selection can be seen in Table 13. The results were acquired with a window size of 200. We can see that there is a significant drop of performance, when using only the raw input. By just adding the average of the time series in the three axes, there is an adequate increase of accuracy, which can be explained by the fact that the accelerometer data are centered. This means that there is no way for the network to infer this information from the raw data, even ignoring the fact that being a convolutional neural network, it produces local features. Adding the standard deviation results in a slight increase, if any, while also adding the average absolute difference results in a more considerable increase. Both of them describe the variability of the data, so it would be expected to have a similar effect. The difference is that the standard deviation, being the sum of squares, will give more weight to high variations of individual points. Adding the average resultant acceleration gives another slight boost, which is understandable, since it is a measure of magnitude and is partly described by means of each axis. Finally, the addition of the binned distribution, which further improves the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**50**} \\ \hline  & **Walking** & **Jogging** & **Stairs** & **Sitting** & **Standing** & **Lying Down** \\ \hline Walking & 10,916.7/87.3\% & 499.3/4.0\% & 333.8/2.7\% & 385.3/3.1\% & 264.2/2.1\% & 99.3/0.8\% \\ Jogging & 291.2/6.7\% & 3496.6/80.3\% & 19/0.4\% & 530.7/12.2\% & 15.2/0.3\% & 1.7/\textless{}0.1\% \\ Stairs & 381.6/67.4\% & 47.1/8.3\% & 93.6/16.5\% & 24.7/4.4\% & 17.6/3.1\% & 1.8/0.3\% \\ Sitting & 223.3/3.4\% & 367.4/5.6\% & 14.4/0.2\% & 4619.4/70.1\% & 866.6/13.1\% & 502.7/7.6\% \\ Standing & 208.4/7.3\% & 63.6/2.2\% & 5.4/0.2\% & 899/31.4\% & 1586.1/55.6\% & 92.3/3.2\% \\ Lying Down & 46.5/1.7\% & 1.7/\textless{}0.1\% & 0.9/\textless{}0.1\% & 2211.7/80.6\% & 213.5/7.8\% & 268.7/9.8\% \\ \hline  & \multicolumn{6}{c}{**200**} \\ \hline  & **Walking** & **Jogging** & **Stairs** & **Sitting** & **Standing** & **Lying Down** \\ \hline Walking & 10,941.9/89.1\% & 601.6/4.9\% & 188.1/1.5\% & 316.8/2.6\% & 190.7/1.6\% & 38.9/0.3\% \\ Jogging & 244.1/5.8\% & 3614.3/85.5\%/ & 6.3/0.1\% & 353.9/8.4\% & 7.2/0.2\% & 0.8/\textless{}0.1\% \\ Stairs & 355.6/66.5\% & 54.2/10.1\% & 114/21.3\% & 4.5/0.8\% & 6.2/1.2\% & 0.1/\textless{}0.1\% \\ Sitting & 227.6/3.5\% & 485.5/7.6\% & 4.1/\textless{}0.1\% & 4629.7/72.1\% & 678.6/10.6\% & 402.9/6.3\% \\ Standing & 208.6/7.7\% & 147.5/5.4\% & 1.6/\textless{}0.1\% & 678.9/24.9\% & 1608.6/59.1\% & 77.4/2.8\% \\ Lying Down & 83.8/3.1\% & 4.6/0.2\% & 0.2/\textless{}0.1\% & 2121.8/79.2\% & 187.2/7.0\% & 280.6/10.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Confusion matrix of the 10-fold cross-validation of the Actitracker dataset.