# A Semi-Supervised Lie Detection Algorithm Based on Integrating Multiple Speech Emotional Features
## 2 Method
### Feature Processing  
As described in [4; 5; 13; 14], acoustic statistical features can effectively represent false information in speech, while deep learning algorithms can extract time-frequency domain features from log-Mel spectrogram [20]. So 312-dimensional acoustic statistical features \(X_{a}\) based on artificial a priori knowledge and log-Mel spectrogram features \(X_{s}\) commonly used in the field of speech lie detection are used, aiming at mining the correlation information within similar features and among different features, and exploring the effect of fusion of static statistical features and dynamic time-frequency features in the time domain. In this paper, acoustic statistical features contains Pitches, spectral_centroid, spectral_flatness, Mel Frequency Cepstral Coefficients (MFCC), chroma_stft, melspectrogram, spectral_contrast, zero_crossing_rate, Magnitudes, Root-mean-square energy (Rmse).  
Let \(X_{a}=\left\{x_{a}^{1},x_{a}^{2},...,x_{a}^{O}\right\}\in R^{d_{a}\times O}\) and \(X_{s}=\left\{x_{s}^{1},x_{s}^{2},...,x_{s}^{O}\right\}\in R^{d_{a}\times O}\),where \(d_{a}\) and \(d_{s}\) denote the dimensions of acoustic statistical features and Mel spectrogram features, respectively, \(x_{a}^{i}\) and \(x_{s}^{i}\) is the single feature representation of all samples, and \(i=1,2,...,O\), \(o\) is the feature order number, \(O\) denoting the total number of feature samples.  
Semi-supervised speech lie detection research requires a database containing a small number of labeled samples \(D_{l}=\left\{X_{l},Y_{l}\right\}\) and a database containing a large number of unlabeled samples \(D_{u}=\left\{X_{u}\right\}\), where \(X_{l}=\left(X_{al},X_{sl}\right)\), \(X_{al}=\left\{x_{all}^{1},x_{all}^{2},\cdots,x_{all}^{M}\right\}\in R^{d_{a} \times M}\), \(X_{sl}=\left\{x_{sl}^{1},x_{sl}^{2},\cdots,x_{sl}^{M}\right\}\in R^{d_{a} \times M}\), \(x_{al}^{m}\) and \(x_{sl}^{m}\) are representations of labeled samples. \(Y_{l}=\left\{y_{1}^{1},y_{1}^{2},...,y_{l}^{m}\right\}\) denote labels, \(m=1,2,...,M\), \(M\) are the total number of labeled samples; \(X_{u}=\left(X_{au},X_{su}\right)\), \(X_{au}=\left\{x_{au}^{1},x_{au}^{2},\cdots,x_{au}^{M}\right\}\in R^{d_{a} \times N}\), \(X_{su}=\left\{x_{su}^{1},x_{su}^{2},\cdots,x_{su}^{M}\right\}\in R^{d_{a} \times N}\), \(x_{au}^{n}\) and \(x_{su}^{n}\) are representations of unlabeled samples, \(n=1,2,...,N\), \(N\) denote the total number of samples of unlabeled data, there \(O=M+N\). In order to improve the classification accuracy and robustness of the semi-supervised model, in this paper, random noise enhancement technique is used to strongly enhance and weakly enhance the unlabeled data with the following formula:  
\[x_{autweak}^{n} =x_{au}^{n}+\lambda_{autweak}\cdot noise(x_{au}^{n}) \tag{1}\] \[x_{autstrong}^{n} =x_{au}^{n}+\lambda_{autstrong}\cdot noise(x_{au}^{n})\] (2) \[x_{suweak}^{n} =x_{su}^{n}+\lambda_{autweak}\cdot noise(x_{su}^{n}) \tag{3}\]  
Figure 1: A semi-supervised lie detection algorithm based on integrating multiple speech emotional features.  
\[x_{sustrong}^{n}=x_{su}^{n}+\lambda_{sustrong}\cdot noise(x_{su}^{n}) \tag{4}\]  
where \(x_{sustrong}^{n}\) and \(x_{sustrong}^{n}\) denote the 312-dimensional acoustic statistical features that have been weakly enhanced by noise addition and strongly enhanced by noise addition, respectively, while \(\lambda_{sustweak}\) and \(\lambda_{sustrong}\) denote their weak enhancement coefficients and strong enhancement coefficients, respectively; \(x_{sustweak}^{n}\) and \(x_{sustrong}^{n}\) denote the log Mel spectrogram features that have been weakly enhanced by noise addition and strongly enhanced by noise addition, respectively, while \(\lambda_{sustweak}\) and \(\lambda_{sustrong}\) denote their weak enhancement coefficients and strong enhancement coefficients, respectively; and \(noise()\) is the Gaussian noise generating function, which generates the corresponding noise according to the shape of the original data noise data according to the shape of the original data.