Prashant,

It all depends on what you are trying to achieve with the learning algorithm.

For example, the difference between Art and Art2 is the use of discrete vs continuous values respectively. The decision to encode into continuous values vs. discrete depends on your systems setting and the effort you want to spend in encoding( which you should consider doing).

The question on using ART2 vs ARTMAP also depends on your goal and dataset. If you read the paper "ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network " by Carpenter , G rossberg and R eynolds it states on page 567 that "Both ARTMAP and Back Propagation are supervised learning systems" .ART on the other hand is an unsupervised learning algorithm.

In this sense, the selection of whether to use ARTMAP or ART(1 or 2) depends on your dataset and if it has labelled data for supervised learning or not.

Implementations of ART and its variants vary a lot between implementations. The original implementation by Grossberg is quite complicated and I have seen that some people have made simplificating assumptions to the algorithm. If you are beginning, I would suggest that you first get a grasp on ART which is the simplest and the progress to the other ones. I would recommend as reference the book "Pattern Recognition with Neural Networks in C++" by Abhijit S. Pandya and Robert B.Macy. It provides both the theory by Grossberg and translates it into code in the same book( which is one big advantage). From there you can progress to the more complex architectures without much trouble by possibly modifying the initial code by Pandya and Macy.

Hope this helps