## 4 Clustering and Classification
### Classification  
A traditional technique for RLR detection and classification is the Support Vector Machine (SVM) [28,29]. SVM is a technique that classifies into two classes by obtaining a decision boundary that separates several sample points. The decision boundary separates two classes of clusters, and the sample closest to the boundary becomes the support vector. SVM classifies the binary classes by finding the decision boundary that maximizes the margin between the support vector and the decision boundary. Multi-class SVM for multi-class classification obtains sub-SVMs for classifying each class, and performs multi-class classification based on this idea [30,31]. Recently, deep learning models with higher classification accuracy than SVM have been proposed [32]. A representative deep learning model is the Convolutional Neural Network (CNN). In general, CNN consists of a convolutional layer, Rectified Linear Unit (ReLU) layer, pooling layer, and fully-connected layer [33]. The convolutional layer extracts the features of the input, while the ReLU layer increases the non-linearity properties of the convolutional layer. The pooling layer prevents overfitting through down-sampling. Finally, scores are calculated for each class of output in the fully connected layer. However, the general CNN  
Figure 3: Comparison of driving profiles from two different Red Light Runner (RLR) clusters. (**a**) Speed maintenance pattern; (**b**) Acceleration after deceleration by the preceding vehicle pattern.  
is an image-based model but not for the time-series data. Therefore, a deep learning model using time-series data as input is needed.  
We use the Multi-Channel Deep Convolutional Neural Network (MC-DCNN), a signal data-based model for time-series classification [34; 35]. MC-DCNN is a model that uses time-series data of each sensor as the input of multi-channels. The proposed MC-DCNN model uses the speed, acceleration, headway, and DTI as input signals. Since the driving pattern obtained from the speed profile of the vehicle is affected by various driving conditions, the headway and DTI are also selected as inputs to consider the front vehicle and the distance to the intersection. In addition, speed and acceleration are selected to analyze the driving pattern of the RLR. Since the input signal used for MC-DCNN is time-series data, a window length and a prediction time after yellow onset are also required to determine the time interval of traffic data measurement and also to determine when to perform the classification. Prediction time after yellow initiation refers to the point at which RLR is predicted after the start of the yellow signal. If the window length is 2 s and the prediction time after the onset of yellow is 3 s, 2 s of data are collected from 1 to 3 s after the yellow onset.  
The proposed network structure consists of two convolutional, ReLU, pooling layers and the last fully connected layer. The convolution layer is composed of a 1D convolution because the driving pattern is identified through the feature over time [36]. The last layer is a softmax, which outputs a distribution over classes. The classes are defined in five categories: Non-RLR, Type A RLR, Type B RLR, Type C RLR, and Type D RLR.