In this paper, the spectrum sensing problem is investigated under the context of information geometry and a novel clustering algorithm based spectrum sensing scheme is developed to obtain a classifier to estimate the channel state of primary user (PU). In order to enhance the sensing performance at complex environment, the empirical mode decomposition (EMD) algorithm is applied to wipe off the noise component of the received signals from all secondary users (SUs). Subsequently, a signal matrix composed of the reconstructed signals is constructed. Based on the information geometry (IG) theory, the covariance matrix of the signal matrix is mapped into a point on a manifold. Then, the sample points on the manifold are collected as a data set. Moreover, a novel clustering algorithm, namely Riemannian distance based Fuzzy-c means clustering (RDFCM) algorithm, is developed to cluster the samples on manifold for obtaining a classifier, which is employed to decide the PU state. The simulation results show that compared with other spectrum sensing methods, the proposed scheme improves the performance of detection.