## 7 Results and Discussion
### Adaptation Results  
For the test persons, carrying the phones and answering yes or no to the recognition results does not require a big effort, but the results show that the information obtained is very valuable in both adaptation and evaluation of the classifier performance. As an example, a scatter plot of the two most important transformed features of the data from the class _street/road_ is shown in Figure 6. In the upper panel, the original 95 percent confidence ellipse (The ellipse containing 95% of the mass of the Gaussian probability density function when using the estimated covariance calculated from the training data) of the _street/road_ training data is depicted using a dashed line, and the ellipse after the adaptation in solid line. The data with _yes_-tag is plotted with small circles, and the data with _no_-tag with small crosses.  
\begin{table}
\begin{tabular}{l c c c c c c} \hline  & **run**. & **bicycle**. & **walk**. & **stand**. & **table** & **vehic**. \\ \hline \(\mathbf{Mean}(\mathbf{km}/\mathbf{h})\) & \(7\) & \(15\) & \(4\) & \(0.5\) & \(0.5\) & \(60\) \\ \(\mathbf{Std}(\mathbf{km}/\mathbf{h})\) & \(2\) & \(5\) & \(2\) & \(0.5\) & \(0.5\) & \(30\) \\ \hline \end{tabular}
\end{table}
Table 10: The means and standard deviations of the GPS speeds that were used in the activity classifier.  
The bottom panel of Figure 6 is the same for the features three and four. Figure 7 shows the estimated probability density functions (\(p(y)\)) obtained using Matlab's _ksdensity_ function. The figure shows the _yes_-tag likelihoods (dash-dotted) and _no_-tag likelihoods (solid line) before and after the adaptation. The dashed curve is the Chi squared probability density function which would be the optimal distribution for the _yes_-tag likelihoods. This means that if our model would be correct and our assumption of the Gaussian distributed features would be true, the dash-dotted curve (\"yes\" distribution) should follow the dashed curve (chi2 pdf). One can clearly see that there is not much difference between the _yes_- and _no_-likelihoods before adaptation (upper plot in Figure 7). This means that we cannot assign a confidence measure based on these likelihoods alone. The reason is that the original training data was not sufficient to obtain accurate class parameters or the adaptation data is collected in an environment having different features compared to the training data. After the adaptation is completed, the bottom plot in Figure 7 shows a clear improvement: the _no_-likelihoods are visibly separated from the _yes_-likelihoods.  
Figure 6: Class _street/road_ features.  
Figure 7: Class _street/road_ probability distribution functions.  
After the adaptation round is complete, a convenient way to estimate the accuracy of the classifiers is to use the prior probabilities, \(P(user\ answers\ yes)\), using Equation (20). To evaluate accuracy of the proposed adaptation method the data from the very first data collection campaign was used (Section 2.1). Ten users with the most data were selected and the classifier was trained leaving one user out of the training data set at the time. Data from this user was then divided to half, other half containing test set for classifier and other half was used to create virtual _yes_ and _no_ answers using. This enabled us to know also the ground truth of the _no_ answers (which was not available in the second data collection campaign presented in Section 2.2). Table 11 presents the classification data of these ten users before the adaptation was applied. Classifier precision and recall are 50% and 67%,respectively. The results after the adaption are presented in Table 12. In this case precision is 68% and recall 70%. Naturally, the _no_ answers were more valuable information for the adaptation process. It was noticed that already couple of _no_ answers could improve the class parameters.