An automatic unsupervised classification of 1318 light curves of variable stars, including eclipsing binaries along with some possible pulsating stars, has been performed using k-medoids clustering method. This separates the stars according to their geometrical configuration in a more scientific way compared to the subjective traditional classification scheme. The light curves in the Galaxy, subjectively grouped in four categories (EA, EB, EW, PUL) in Miller et al. (2010), have been found to consist of two optimum groups containing primarily eclipsing binaries corresponding to bright, massive systems and fainter, less massive systems. Our technique has been assessed in terms of clustering accuracy measure the Average Silhouette Width, which shows the resulting clustering pattern is quite good.