# The Use of Correlation Features in the Problem of Speech Recognition
## 4 Results  
Before proceeding the comparing different algorithms results, it should be noted that the main task is the recognition of a speech message, i.e., the task is classify the message type from 20 studied messages, so classification metrics are used for algorithm evaluation. Another important parameter is the recognition speed, so this parameter is also measured. To be precise, the time taken to recognize one message on average is measured. Moreover, since there were also machine learning methods among the studied algorithms, the test data consisted of two examples of messages spoken by each speaker, i.e., the data split approach used the classical proportion of 80% by 20% when separating data into training and testing. Thus, the size of the test sample was 400 speech messages, among which there were 20 examples of each class. Given the balance of training and test data, the accuracy metric was chosen as the main metric. Table 2 shows the results of efficiency evaluation using the proposed feature extraction methods and known algorithms. As for ANN algorithms, the 1D and 2D Convolutional networks were studied as well as simple recurrent networks and long short term memory (LSTM) networks. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Accuracy** \\ \hline Decision tree (depth 10) & 92.50\% \\ Support vector machine & 93.50\% \\ Fully connected neural network (3 layers, 20-20-20 neurons) & 94.25\% \\ Recurrent neural network (recurrent layer 24 neurons) & 95.50\% \\ Long Short Term Memory Network (LSTM layer 24 neurons) & 96.00\% \\
1D Convolutional Neural Network (16 filters) & 94.00\% \\ Fully Connected Network based on correlation function & 96.50\% \\ Recurrent network based on correlation function & 97.25\% \\ LSTM network based on correlation function & 97.50\% \\ Convolutional network based on correlation function & 95.75\% \\ Convolutional network based on correlation portrait & 97.50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Recognition accuracy. Figure 9: Comparison of autocorrelation portraits. The highest accuracy is provided by the convolutional network after processing the correlation portraits and LSTM networks. It can be explained that long memory is important characteristic for voice messages. However, it is also noticeable that preprocessing in the form of a correlation function also increases the recognition quality. Table 3 presents the performance results. The analysis shows that simple algorithms work faster, but they lead to the greatest errors. The best model is the two-dimensional convolutional network. It is almost eight times slower than a recurrent model. However, for pure data, LSTM looks to be best in terms of speed and asset quality. The implementation of quantization of the weights of the convolutional neural network made it possible to reduce the processing time of one message to 831.3 ms. Finally, we will study the efficiency of the proposed algorithms under the influence of white Gaussian noise. Let q be the ratio of signal variance to noise variance. Table 4 presents the recognition results under noise conditions. From the results of Table 3 it is clear that the two-dimensional model is the most resistant to intense noise, however, at a noise level 10 times greater than the signal level, the recognition results drop significantly. It is interesting that traditional machine learning work very badly if the data are noisy. However recurrent structure is more resistance to noise impact. LSTM shows low resistance to noise data. It is possible to use long short term memory networks for processing pure data.