This paper addresses the problem of dimension reduction of noisy data, more precisely the challenge to determine the dimension of the subspace where the observed signal lives in. Based on results from random matrix theory, two novel estimators of the signal dimension are proposed in this paper. Consistency of the estimators is proved in the modern asymptotic regime, where the number of parameters grows proportionally with the sample size. Experimental results show that the novel estimators are robust to noise and, moreover, they give highly accurate results in settings where standard methods fail. We apply the novel dimension estimators to several life sciences benchmarks in the context of classification, and illustrate the improvements achieved by the new methods compared to the state-of-the-art approaches.