Vector Quantizer with Fuzzy Equivalence Relations clustering

The scalar quantizer is often used in many applications due to its simplicity and ease with which it can be implemented. However, whenever we have some constraint in terms of bit rate or distortion, the vector quantizer is almost always a better choice. This is because for a given bit rate or for a given distortion, we can always design a vector quantizer that outperforms the optimal scalar quantizer. There are several algorithms to design a vector quantizer. But, the most popular algorithm is the Linde-Buzo-Gray algorithm which is based on the k-means clustering. For the LBG algorithm, we need to specify the number of clusters as well as the initial reconstruction vectors, which are then updated in successive iterations. Often, choosing the initial reconstruction vectors is not an easy task, especially when we deal with higher dimensions. A better option would be to naturally obtain the initial partitions from the given dataset. In the present article, we describe a hierarchical clustering based vector quantizer design. With our approach, we no longer need to choose the initial reconstruction vectors, but we naturally obtain the partitions for the given bit rate. Moreover, once we obtain the partitions, we simply place our reconstruction vectors at the centroid of the partitions and hence we avoid performing successive iterations and updating the clusters.