# Grassmann Manifold Based State Analysis Method of Traffic Surveillance Video
###### Abstract  
For a contemporary intelligent transport system, congestion state analysis of traffic surveillance video (TSV) is one of the most crucial and intricate research topics because of the rapid development of transportation systems, the sustained growth of surveillance facilities on road, which lead to massive traffic flow data, and the inherent characteristics of our analysis target. Traditional methods on feature extractions are usually operated on Euclidean space in general, which are not accurate for high-dimensional TSV data analysis. This paper proposes a Grassmann manifold based neural network model to analysis TSV data, by mapping the video data from high dimensional Euclidean space to Grassmann manifold space, and considering the inner relation among adjacent cameras. The accuracy of the traffic congestion is improved, compared with several traditional methods. Experimental results are conducted to validate the accuracy of our  
traditional methodologies of the traffic state classifications, such as Sparse Representation (SR), Support Vector Machine (SVM), Neural Networks (NN) and so on. On one hand, SR is based on the principle that a signal can often be represented by a linear sum of a small amount of signals from dictionary. Numerous research has been made to construct the dictionary with specific attributes. Sparse representation model achieves great success in many applications, such as face recognition [4], image denoising [5], and image super-resolution reconstruction [6]. On the other hand, the main idea of SVM can be summarized into two points: (1) It is analyzed for linear separable case. In the case of linear inseparable, in order to make this case linear separable, linear inseparable low-dimensional input space is mapped to high-dimensional feature space through nonlinear mapping algorithm. (2) SVM creates the optimal segmentation hyperplane in the feature space based on the Structural Risk Minimization Theory, so that the learners get global optimization, and the expected risk of the entire sample space can meet a certain upper bound with a certain probability. Compared with the above methods, NN can reflect the relevancy of the TSV data more accurately, so NN is better than the other methods in the classification of traffic TSV. The traditional methods of feature extraction, such as PCA, LDA and LPP, process original data in Euclidean space. However, TSV data is high-dimensional which is operated inaccurately in Euclidean space, thus the result of feature extraction in the Euclidean space is not effective. Scholars demonstrate that high-dimensional Euclidean space can be embedded in manifold space, so if we map the data from high dimensional Euclidean space to manifold space, the operation will be more accurate and the feature extraction will be more effective. At the same time, TSV is difficult to make a consistent length, and it is important to process different lengths of TSV data uniformly. In the manifold, there is a kind named Grassmann manifold, which can process different lengths of TSV data uniformly by unifying data while doing SVD decomposition. In this paper we propose a neural network model based on Grassmann manifold. Our model can directly identify the congestion status without calculating traffic flow parameters such as vehicle speed and number of vehicles. The data processing schematic is shown in Figure 1. Furthermore, the contributions of the paper are as follows:  
* Introducing neural networks model into traffic state classification applications. * Connecting Grassmann manifold with neural networks according to the temporal characteristics of traffic data. * Giving a reliable and efficient algorithm to neural networks model based on Grassmann manifold. Figure 1: The data processing schematic. The rest of the paper is organized as follows. In Section 2, we review the background of neural networks and Grassmann manifold. In Section 3, we introduce the principles and application of Grassmann based neural network method in the traffic state analysis.