Abstract : This paper addresses the problem of dimension reduction of noisy data, more precisely the challenge of determining the dimension of the subspace where the signal lives in. Based on results from random matrix theory, a novel estimator of the signal dimension is developed. Consistency of the estimator is proved in the modern asymptotic regime, where the number of parameters grows proportionally with the sample size. Experimental results show that the novel estimator is robust to noise and, moreover, it gives highly accurate results in settings where standard methods fail. The application of the new dimension estimator on several biomedical data sets in the context of classification illustrates the improvements achieved by the new method compared to the state of the art.