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In recent years, a variety of nonlinear dimensionality reduction techniques have been proposed that aim to address the limitations of traditional techniques such as PCA. The paper presents a review and systematic comparison of these techniques. The performances of the nonlinear techniques are investigated on artificial and natural tasks. The results of the experiments reveal that nonlinear techniques perform well on selected artificial tasks, but do not outperform the traditional PCA on real-world tasks. The paper explains these results by identifying weaknesses of current nonlinear techniques, and suggests how the performance of nonlinear dimensionality reduction techniques may be improved.