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We present the stellar populations of 138 compact elliptical galaxies (cEs) in the redshift range of $z < 0.05$ using the Sloan Digital Sky Survey (SDSS) DR12. Our cEs are divided into those with [cE(w)] and without [cE(w/o)] a bright ($M_{r} < -21$ mag) host galaxy. We investigated the stellar population properties of cEs based on the Lick line indices extracted from SDSS spectra. cE(w)s show [Z/H] and \afe\ distributions skewed toward higher values compared to those of the cE(w/o)s. No statistically significant difference in age distribution was found between the cE(w)s and cE(w/o)s. In the mass-metallicity distribution, cE(w)s deviate from the relation observed for early-type galaxies at a given stellar mass, whereas cE(w/o)s conform to the relation. Based on the different features in the stellar populations of cE(w)s and cE(w/o)s, we can propose two different cE formation channels tracing different original masses of the progenitors. cE(w)s would be the remnant cores of the massive progenitor galaxies whose outer parts are tidally stripped by a massive neighboring galaxy (i.e., nurture origin). In contrast, cE(w/o)s are likely the faint end of early-type galaxies maintaining in-situ evolution in an isolated environment with no massive galaxy nearby (i.e., nature origin). Our results reinforce the propositions that cEs comprise a mixture of galaxies with two types of origins depending on their local environment.