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Galactic cosmic rays are mostly made up of energetic nuclei, with less than $1\%$ of electrons (and positrons). Precise measurement of the electron and positron component requires a very efficient method to reject the nuclei background, mainly protons. In this work, we develop an unsupervised machine learning method to identify electrons and positrons from cosmic ray protons for the Dark Matter Particle Explorer (DAMPE) experiment. Compared with the supervised learning method used in the DAMPE experiment, this unsupervised method relies solely on real data except for the background estimation process. As a result, it could effectively reduce the uncertainties from simulations. For three energy ranges of electrons and positrons, 80--128 GeV, 350--700 GeV, and 2--5 TeV, the residual background fractions in the electron sample are found to be about (0.45 $\pm$ 0.02)$\%$, (0.52 $\pm$ 0.04)$\%$, and (10.55 $\pm$ 1.80)$\%$, and the background rejection power is about (6.21 $\pm$ 0.03) $\times$ $10^4$, (9.03 $\pm$ 0.05) $\times$ $10^4$, and (3.06 $\pm$ 0.32) $\times$ $10^4$, respectively. This method gives a higher background rejection power in all energy ranges than the traditional morphological parameterization method and reaches comparable background rejection performance compared with supervised machine learning~methods.