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In order to perform successful diagnosis and treatment of cancer, discovering, and classifying cancer types correctly is essential. One of the challenging properties of class discovery from cancer data sets is that cancer gene expression profiles not only include a large number of genes, but also contains a lot of noisy genes. In order to reduce the effect of noisy genes in cancer gene expression profiles, we propose two new consensus clustering frameworks, named as triple spectral clustering-based consensus clustering (SC3) and double spectral clustering-based consensus clustering (SC2 Ncut) in this paper, for cancer discovery from gene expression profiles. SC3 integrates the spectral clustering (SC) algorithm multiple times into the ensemble framework to process gene expression profiles. Specifically, spectral clustering is applied to perform clustering on the gene dimension and the cancer sample dimension, and also used as the consensus function to partition the consensus matrix constructed from multiple clustering solutions. Compared with SC3, SC2 Ncut adopts the normalized cut algorithm, instead of spectral clustering, as the consensus function. Experiments on both synthetic data sets and real cancer gene expression profiles illustrate that the proposed approaches not only achieve good performance on gene expression profiles, but also outperforms most of the existing approaches in the process of class discovery from these profiles.