Using random projection, a method to speed up both kernel k-means and centroid initialization with k-means++ is proposed. We approximate the kernel matrix and distances in a lower-dimensional space ${\mathbb{R}}^d$ before the kernel k-means clustering motivated by upper error bounds. With random projections, previous work on bounds for dot products and an improved bound for kernel methods are considered for kernel k-means. The complexities for both kernel k-means with Lloyd’s algorithm and centroid initialization with k-means++ are known to be $O\left(nkD\right)$ and $\Theta \left(nkD\right)$, respectively, with n being the number of data points, the dimensionality of input feature vectors D and the number of clusters k. The proposed method reduces the computational complexity for the kernel computation of kernel k-means from $O\left(n^{2}D\right)$ to $O\left(n^{2}d\right)$ and the subsequent computation for k-means with Lloyd’s algorithm and centroid initialization from $O\left(nkD\right)$ to $O\left(nkd\right)$. Our experiments demonstrate that the speed-up of the clustering method with reduced dimensionality $d=200$ is 2 to 26 times with very little performance degradation (less than one percent) in general.

To monitor road safety, billions of records can be generated by Controller Area Network bus each day on public transportation. Automation to determine whether certain driving behaviour of drivers on public transportation can be considered safe on the road using artificial intelligence or machine learning techniques for big data analytics has become a possibility recently. Due to the high false classification rates of the current methods, our goal is to build a practical and accurate method for road safety predictions that automatically determine if the driving behaviour is safe on public transportation. In this paper, our main contributions include (1) a novel feature extraction method because of the lack of informative features in raw CAN bus data, (2) a novel boosting method for driving behaviour classification (safe or unsafe) to combine advantages of deep learning and shallow learning methods with much improved performance, and (3) an evaluation of our method using a real-world data to provide accurate labels from domain experts in the public transportation industry for the first time. The experiments show that the proposed boosting method with our proposed features outperforms seven other popular methods on the real-world dataset by 5.9% and 5.5%.