A new approach for curvature estimation of sampled data

Despite the high dimensionality of data in machine learning applications, such as facial expression and human activity recognition, the data usually lies in a low dimensional manifold. In order to discover the intrinsic characteristic of the manifold, curvature estimation of the manifold can be helpful. This paper presents a new algorithm for curvature estimation of sampled data by utilizing the local tangent plane and normal vector approximation at each sample point. The proposed algorithm can estimate the curvature by tracking the variations of normal vector around its neighbor points and quantitatively estimate the relative curvature of every data point. Our approach is successful in estimating the curvature of sampled data of known manifolds such as Swiss roll.