Detecting dependence between variables is a crucial issue in statistical science. In this paper, we propose a novel metric, named label projection correlation, to measure the dependence between numerical and categorical variables. The proposed correlation does not require any conditions on the numerical variable, and is equal to zero if and only if the two variables are independent. Moreover, when the numerical variable is one-dimensional, we demonstrate that the computational cost of the correlation estimation can be reduced from $\mathrm{O}(n^3)$ to $\mathrm{O}(n \log n)$, where $ n $ is the sample size. Furthermore, if the one-dimensional variable is continuous, the metric can be simplified to a concise rank-based expression. The asymptotic theorem of the estimation is also established. Two simulated experiments are presented to demonstrate the effectiveness of our proposed correlation in feature selection. Furthermore, our approach is applied to feature selection in drivers' facial images and cancer mass-spectrometric data.

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