In 2005, Vikas Sindwani and the University of Chicago team proposed a new semi-supervised kernel-based SVM algorithm in the paper Beyond the Point Cloud: from Transductive to Semi-supervised Learning. In this algorithm, instead of Euclidean geometry, they utilized the unlabeled data to understand the underlying geometry and construct a Deformed Kernel to encode the information of the deformed geometry. However, the computational time complexity of construction of the Deformed Kernel is cubic. Consequently, the algorithm failed to scale. Our goal is to improve the algorithm and eventually construct a deformed kernel within quadratic computation time complexity.