# Interpretability Study of Gradient Information in Individual Travel Prediction
## 3 Methods
### Saliency Methods Based on Gradient Information  
In the field of computer vision, saliency methods based on gradient information, initially proposed by [PERSON] [40], serve as an interpretability tool. This method generates contribution maps to visually reveal the key features on which the model relies during the recognition or classification process. These features may include color, shape, texture, etc., which together form the basis of the model's decision-making. The core of this method is that it only relies on a pre-trained classification model to complete the generation of the saliency map.  
[PERSON]'s research introduced two main techniques to explain the working principles of convolutional neural networks. One of them is the calculation of class contribution maps for specific images and categories. Specifically, the task takes an image \(I\), a category \(c\), and the model's score for that category \(S_{c}\) as input, and outputs a contribution map \(M\) that ranks the influence of each pixel in \(I\) on the score \(S_{c}(I)\). To illustrate, suppose there is a linear model for calculating the score of category \(c\), which can be represented as follows:  
\[S_{c}(I)=w_{c}^{T}I+b_{c} \tag{13}\]In this context, \(I\) represents the vectorized representation of the image, and \(w_{c}\) and \(b_{c}\) are the model's weight vector and bias, respectively. In this linear case, the magnitude of each element in the weight vector \(w\) directly reflects the importance of the corresponding pixel to category \(c\). However, since the model's predictions involve multiple layers of nonlinear transformations, the class score \(S_{c}(I)\) is a highly nonlinear function of the image \(I\), and thus the reasoning of the linear model cannot be directly applied. To approximate this relationship in deep networks, a first-order Taylor expansion is used within the neighborhood of the given image \(I_{0}\) to approximate \(S_{c}(I)\), resulting in a linearized local representation as follows:  
\[S_{c}(I)\ \approx\ w^{\mathrm{T}}I+b \tag{14}\]  
This process involves the computation of the gradient, since \(w\) is the derivative of \(S_{c}\) at point \(I_{0}\) with respect to image \(I\). The greater the absolute value of the gradient, the more significant the impact of the corresponding pixel on the classification results. Based on the principles outlined above, we can conclude that gradient information can, to some extent, reflect the model's prediction process.  
Based on the above principles, we can conclude that gradient information can reflect the prediction process of the model to a certain extent. Introducing this principle into the field of individual travel prediction, the input of the model is transformed into time series data containing multiple sequences and features, and the interpretability method outputs a gradient information matrix with the same dimension as the input. In this context, the gradient information represents the contribution of each sequence feature to the final travel prediction result. If the gradient information at a certain position is significantly higher than that at other positions, it means that the travel event at that moment has a decisive influence on the prediction.