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Voice activity detection has attracted significant research efforts in the last two decades. Despite much progress in designing voice activity detectors, voice activity detection (VAD) in presence of transient noise is a challenging problem. In this paper, we develop a novel VAD algorithm based on spectral clustering methods. We propose a VAD technique which is a supervised learning algorithm. This algorithm divides the input signal into two separate clusters (i.e., speech presence and speech absence frames). We use labeled data in order to adjust the parameters of the kernel used in spectral clustering methods for computing the similarity matrix. The parameters obtained in the training stage together with the eigenvectors of the normalized Laplacian of the similarity matrix and Gaussian mixture model (GMM) are utilized to compute the likelihood ratio needed for voice activity detection. Simulation results demonstrate the advantage of the proposed method compared to conventional statistical model-based VAD algorithms in presence of transient noise.