## 3 Methodologies
### User Preference Prediction Based on Psychographic Segmentation and Neural Network
#### 3.2.2 User Preference Prediction Based on Psychographic Segmentation and Deep Neural Network  
Let \(U\) and \(I\) be the number of consumers and products, \(R\) the training interaction matrix, and \(\hat{R}\) the predicted interaction matrix. Let \(Y\) be a set of \(y_{u,i}\), \(\hat{Y}\) be a set of \(\hat{y}_{ui}\), \(y_{ui}\) be the preference of user \(u\) to product \(i\), and \(\hat{y}_{ui}\) denote the corresponding predicted score. We use a partially observed vector (rows of the features set \(X\) and \(\hat{X}\)) as a combination of consumer representation \(\mathbf{x}^{(u)}\) and product representation \(\mathbf{x}^{(i)}\), where \(\mathbf{x}^{(u)}=\left\{u_{P_{1}}^{psy},u_{P_{2}}^{psy},\ldots,u_{P_{D}}^{psy},u_{N_{1}}^{psy},u_{N_{2}}^{psy},\ldots,u_{N_{D^{\prime}}}^{psy}\right\}\), \(\mathbf{x}^{(i)}=\left\{\begin{subarray}{c}\mathbf{y}_{P_{1}}^{psy},\ldots,\mathbf{y}_{P_{ D}}^{psy},\h  
prediction for a molecule by the \(b\)th tree. Outputs of all trees are aggregated to produce one final prediction. \(\hat{Y}\) in regression is the average of the individual tree predictions.  
Support Vector Machine (SVM): The ability of the support vector machine has been recognized in automated user/product modeling to predict retailer outcomes [67; 68]. An SVM discriminates between data by constructing a hyperplane \(w^{T}\varphi(X)+b=0\) by minimizing \(\frac{\|w\|^{2}}{2}+C\sum e_{i}\), subject to \(y_{i}\big{(}w^{T}\varphi(x_{i})+b\big{)}\geq 1-e_{i}\), \(e_{i}\geq 0\)\(\forall i\), where \(\varphi(x_{i})\) is either \(x_{i}\) or a higher dimensional representation of \(x_{i}\), \(C\) is the cost parameter, \(w\) is the weight vector, \(e_{i}\) is margin of tolerance where no penalty is given to errors [69].  
Deep Neural Network (DNN): Thanks to deep learning's (DL) capability in solving many complex tasks while providing state-of-the-art results, academia and industry alike have been in a race to apply deep learning to a wider range of applications [70]. Although neural networks are widely used in market segmentation [71; 72], few researchers have introduced deep neural networks (DNNs) into market segmentation to predict user preferences. DNN enables effective capture of non-linear and non-trivial user-product relationships. A typical DNN consists of an input layer, a few hidden layers, and an output layer with number of nodes equal to the cardinality of categories. We use the typical mean square error (MSE), i.e., \(\sum_{i=1}^{B}\big{(}y_{i}-\hat{y}_{i}\big{)}^{2}\) as a loss function of our DNN method, where \(\hat{y}_{i}=h(g(x_{i}))\), \(g\) is some linear combination of node values in the hidden layers of the network, and \(h\) is an activation function (typically sigmoid or hyperbolic tangent function). Training a neural network involves minimizing the loss function defined above using gradient descent and backpropagation of the gradient across multiple hidden layers to update the weights between nodes. Here, we initialize the weight using Gaussian distribution with expectation 0 and variance 1, then form a neural network with two hidden layers for consumer preference regression tasks.