Most of cover song identification algorithms are based on the pairwise (dis)similarity between two songs which are represented by harmonic features such as chroma, and therefore the choice of a distance measure and a feature has a significant impact on performance. Furthermore, since the similarity measure is query-dependent, it cannot represent an absolute distance measure. In this paper, we present a novel approach to tackle the cover song identification problem from a new perspective. We first construct a set of core songs, and represent each song in a high-dimensional space where each dimension indicates the pairwise distance between the given song and the other in the pre-defined core set. There are several advantages to this. First, using a number of reference songs in the core set, we make the most of relative distances to many other songs. Second, as all songs are transformed into the same high-dimensional space, kernel methods and metric learning are exploited for distance computation. Third, our approach does not depend on the computation method for the pairwise distance, and thus can use any existing algorithms. Experimental results confirm that the proposed approach achieved a large performance gain compared to the state-of-the-art methods.