Lloyd Max Quantization and Clustering : Part 1 The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case
of a vector quantizer (VQ) designed with the Linde Buzo
Gray (LBG) algorithm.

In k-means clustering, we are given a set of n data points in d-dimensional space  and an integer k and the problem is to determine a set of k points in $R^d$, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm.

Confusion :

Is the Lloyd-Max algorithm alternatively in short called the Lloyd's algorithm ? Or are they completely different? 

I am very confused, please help. Thank you.
Different.


Lloyd-Max is a special type of scalar quantizer design which is optimized (in terms of MSE) to source pdf. Hence the quantizer is generally non-uniform.
Lloyd's algorithm (and the more generalized LBG algorithm) is a scheme to design vector quantization. More information here and here.


That said, one should note that Lloyd's algorithm for VQ is essentially an extension of the scalar Lloyd-Max quantization to higher dimensions (vectorized sources).