We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of points. This is in contrast to previous works that obtain these parameters through the minimization of the reconstruction error of individual points. The proposed approach proceeds by finding a linear transformation of the data that effectively reduces the minimization of the pairwise distortions to the minimization of individual reconstruction errors. After such transformation, any of the previously-proposed quantization approaches can be used. Despite the simplicity of this transformation, the experiments demonstrate that it achieves considerable reduction of the pairwise distortions compared to applying quantization directly to the untransformed data.