# MFCC Selection by LASSO for Honey Bee Classification
## 3 Results
### Classification Quality  
For application purposes, it would be enough to detect and count only drone bees. But for full analysis of the classification quality, we present the results for the honey bee classification problem with two defined classes: worker bees and drone bees. And the three common parameters used to evaluate the performance of a statistical classification model are accuracy, precision, and recall, which are shortly described below. Accuracy measures the overall correctness of the predictions for the particular model, i.e., in our case, the set of selected by LASSO Mel-frequency cepstral coefficients. The accuracy is computed using the following expression:  
\[Accuracy=\frac{TP+TN}{TP+TN+FP+FN}, \tag{11}\]  
where \(TP\) is the count of true positive cases; \(TN\)--true negative; \(FP\)--false positive; and \(FN\)--false negative. It is the ratio of correctly classified instances (true positives and true negatives) to the total number of instances in the test data set. Recall, also known as sensitivity, or the true positive rate, measures the proportion of correctly predicted positive instances out of the total actual positive instances. Recall focuses on the model's ability to detect drone bees, which is a primary goal of the paper. The recall is defined as  
\[Recall=\frac{TP}{TP+FN}. \tag{12}\]  
Precision measures the proportion of correctly predicted positive instances out of the total instances predicted as positive. It is the ratio of true positives to the sum of true positives and false positives. Precision focuses on the model's ability to avoid false positives and is particularly useful when the cost of false positives is high. The precision is calculated by the formula  
\[Precision=\frac{TP}{TP+FP}. \tag{13}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Regularization** & \multicolumn{3}{c}{**No. of Features**} & \multicolumn{2}{c}{**No. of Features**} \\
**Parameter \(\alpha\)** & **AIC** & **for AIC** & **BIC** & **for BIC** \\ \hline
0.0500 & 988.7 & 22 & 990.4 & 22 \\
0.0300 & 824.2 & 29 & 826.4 & 29 \\
0.0200 & 718.6 & 41 & 721.8 & 41 \\
0.0150 & 650.2 & 49 & 654.0 & 49 \\
0.0100 & 571.4 & 60 & 578.1 & 60 \\
0.0065 & 536.2 & 69 & 542.4 & 69 \\
0.0050 & 529.2 & 80 & 534.9 & 80 \\
0.0030 & 527.2 & 93 & 533.6 & 93 \\
0.0020 & 526.7 & 101 & 533.5 & 101 \\
0.0006 & 526.6 & 111 & 534.3 & 111 \\
0.0001 & 526.5 & 120 & 535.0 & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numbers of selected MFCC features by the LASSO algorithm and associated values of information criteria AIC and BIC for different values of regularization parameter \(\alpha\). Another measure of classification performance, independent of the true negative count is the F1-score. Its value varies from 0 to 100%, and the common interpretation is that values over 90% indicate very good performance of a classifier. The F1-score is defined as follows:  
\[F1\text{-}score=\frac{2 TP}{2 TP+FP+FN}. \tag{14}\]  
The results of the honey bee audio recording classification are presented in Figures 8 and 9. Both figures show the values of the evaluation parameters: accuracy, precision, and recall. The first graph, Figure 8, applies to the classification results for different number of features selected by LASSO: 29, 41, 49, 60, 69, 80, 93, 101, 111 from the set **MFCC+Delta+ DeltaDelta**, and additionally for the full set of 120 coefficients. On the other hand, the second graph, Figure 9, presents the evaluation parameters for the three cases with no use of LASSO selection:  
* Full set of 40 **MFCC** features, i.e., Mel-frequency cepstral coefficients;
* Full set of 80 features in **MFCC+Delta**, consisting of 40 MFCC features + 40 first derivatives;
* Full set of 120 features in **MFCC+Delta+DeltaDelta**, which is created by 40 MFCC features + 40 first derivatives + 40 second derivatives. The exact classification results, for the feature sets selected by LASSO and for the full sets of MFCC features, are placed in Tables 2 and 3.