# An Intelligent Time-Series Model for Forecasting Bus Passengers Based on Smartcard Data
## 2 Literature Review
### Intelligent Forecast Methods  
This section introduces four intelligent forecast methods, and they are applied to forecast the collected data in this study: multilayer perceptron, support vector regression, radial basis function neural network, and long short-term memory network. (1) Support vector regression (SVR)  
The support vector machine (SVM) is a supervised learning algorithm for data classification and regression analysis that was developed by [PERSON] and colleagues [31]. The SVM is used for classification problems, known as support vector classification (SVC) problems, and regression problems, known as support vector regression (SVR) problems. The main purpose of SVR is to find the best separation hyperplane to separate clustered data to solve nonlinear problems. SVR is quite good when dealing with small samples and can handle high-dimensional attributes without relying on all available data for classification, but its disadvantage is that its efficiency is very low for a large number of forecast samples. In addition, the SVM needs to find a suitable kernel function, such as linear, polynomial, sigmoid, or radial basis functions, and it is sensitive to missing data. The SVM can be used to solve problems in many fields, such as text classification, image classification, and time-series prediction. In forecasting traffic passenger flow, SVR is suitable for nonlinear and complex models. [PERSON] et al. [32] considered that SVR cannot be fully trained with real-time data. To address this, they developed online SVR models. To reduce the computational complexity of the SVM, [PERSON] et al. [22] proposed the combined seasonal decomposition and least squares support vector to get the best hybrid method for short-term forecasting of airline passengers. (2) Multilayer perceptron neural network (MLP)  
Perceptron is a type of artificial neural network invented by [PERSON] [33]. It can be regarded as the simplest form of feedforward neural network, and it is a binary linear classifier. An MLP consists of at least three layers of nodes (input layer, hidden layer, and output layer). Except for the input nodes, each node is a neuron that uses a nonlinear activation function. The MLP uses supervised backpropagation learning, and its multilayer structure and nonlinear activation function distinguish it from linear perception. The MLP is a nonlinear learning model that can be processed in parallel and has good fault tolerance. It can be used as a real-time online learning model with associative memory, adaptivity, and self-learning ability. To make the output of the MLP as close to the actual target value as possible, a set of optimal weight values must be found in the training model, and one would need to determine the number of neurons used in each hidden layer. Past studies have used MLP models to forecast multifactor problems. [PERSON] et al. [34] used the MLP to forecast the network-wide co-movement patterns of all traffic flows, and they used ARIMA to postprocess the residual of the MLP. [PERSON] et al. [35] proposed a multiple temporal unit MLP to forecast short-term passenger demand. The radial basis function (RBF) network proposed by [PERSON] and [PERSON] has an input layer, a hidden layer, and an output layer [36]. In an RBF network, the nonlinear transformation is from the input layer to the hidden layer, and then the linear transformation is from the hidden layer to the output layer. This can achieve mapping from the input layer space to the output layer space, approximate any nonlinear function, and deal with difficult problems. The RBF network is conceptually similar to the k-nearest neighbor (k-NN) algorithm. In the self-organizing learning stage, basis function centers can be obtained; in the supervised learning stage, the weight between the hidden layer and the output layer is obtained, and each parameter can be learned quickly, thus overcoming the local minima problem. To solve the central problem of the RBF function and the number of neurons in the hidden layer, [PERSON] et al.