# ECE-TTS: A Zero-Shot Emotion Text-to-Speech Model with Simplified and Precise Control
## 2 Ece-Tts
### Emotion Control Strategy  
#### 2.3.1 Emotion Style Adjustment Through Adaptive Coordinate Transformation  
To achieve accurate modeling of emotional features, we adopt the Emotion-Adaptive Coordinate Transformation method [35], which transforms the extracted VAD values into EASV. The transformation process consists of the following steps:  
1. Emotion Dimension Extraction. First, we use an emotion recognition model \(\psi\) to predict VAD values for each reference speech sample \(x_{i}\) in the speech dataset \(X\), obtaining  
\[e_{i}^{k}=\psi(x_{i}), \tag{11}\]  
where \(e_{i}^{k}\) is a three-dimensional vector \((d_{v},d_{a},d_{d})\), representing \(V\), \(A\), and \(D\), respectively. 2. Calculation of the Neutral Emotion Centroid. For neutral emotion data, we compute the neutral emotion centroid as a reference baseline for the coordinate transformation:  
\[M=\frac{1}{N_{n}}\sum_{i=1}^{N_{n}}e_{i}^{n}, \tag{12}\]  
where \(N_{n}\) is the total number of neutral samples, and \(e_{i}^{n}\) denotes the VAD values of the \(i\)-th neutral emotion sample. 3. Emotion Coordinate Shift. To model a spherical coordinate system for each emotion, we shift the emotion coordinates from different emotion sets \(E_{k}\), obtaining the transformed Cartesian coordinates:  
\[\hat{e}_{i}^{k}=e_{i}^{k}-M_{k}, \tag{13}\]  
where \(M_{k}\) is the centroid coordinate obtained by maximizing the distance ratio between a specific emotion and the neutral emotion:  
\[M_{k}=\underset{M}{\text{argmax}}\frac{E_{\hat{e}_{i}^{k}\in E_{k}}\left[ \left\|M-e_{i}^{k}\right\|_{2}\right]}{E_{\hat{e}_{i}^{k}\in E_{k}}\left[ \left\|M-e_{i}^{n}\right\|_{2}\right]}, \tag{14}\]  
here \(e_{i}^{k}\) and \(e_{i}^{n}\) denote the coordinates of the \(i\)-th sample in emotion set \(E_{k}\) and neutral set \(E_{n}\), respectively. 4. Conversion to Spherical Coordinates. Using the shifted Cartesian coordinates \(\hat{e}_{i}^{k}=\left(\hat{d}_{v},\hat{d}_{a},\hat{d}_{d}\right)\), we convert them into spherical coordinates \(s_{i}^{k}=(r,\theta,\varphi)\) as follows:  
\[r=\sqrt{d_{v}^{2}+d_{a}^{2}+d_{d}^{2}},\quad\theta=arccos\left(\frac{\hat{d} _{d}}{r}\right),\quad\varphi=arctan\left(\frac{\hat{d}_{v}}{\hat{d}_{a}} \right), \tag{15}\]  
5. Outlier Processing. To reduce the impact of outliers during model training, we apply the Interquartile Range (IQR) method [57] after coordinate transformation:  
\[r_{clamp}=min\left(max(r,r_{min}),r_{max}\right),\quad r_{IQR}=\frac{r_{ clamp}-r_{min}}{r_{max}-r_{min}}, \tag{16}\]  
where \(r_{\min}\) and \(r_{\max}\) are calculated based on the IQR method. Specifically, \(r_{\min}\) is set to the first quartile (Q1) minus 1.5 times the IQR, and \(r_{\max}\) is set to the third quartile (Q3) plus 1.5 times the IQR. Through the above steps, we successfully transform emotion dimension values into Emotion-Adaptive Spherical Vectors, represented as \(s_{i}^{k}=\left(r_{\text{clamp}},\theta,\varphi\right)\), which serves as the emotion feature representation for our model. It is worth noting that, compared to existing methods, the proposed EASV-based modeling approach eliminates the need for additional emotion encoders or style adaptation modules. Specifically, the Emo-VITS model [9] designs dedicated emotion encoders to extract both global and local emotional features from reference audio and fuses them through an attention mechanism. Similarly, GenerSpeech [13] introduces a multi-level style adaptor to simultaneously model global emotion characteristics and local prosodic features. These approaches add new sub-modules to the original TTS framework, thereby significantly increasing model complexity and training cost. In contrast, our method simply leverages a pretrained emotion recognition model during the data processing stage to extract continuous VAD emotion dimensions, and then applies an adaptive coordinate transformation to obtain structurally clear EASV representations, which are directly used as emotion feature inputs.