it it possible to use the same alogorithm in two different publication? Currently, I am conducting a social media analysis research and have implemented a training algorithm where it combines various features of set to show that specific classifier works better than others. 

The question is, can I use this algorithm in further work? Is it possible to use the proposed algorithm in other research ideas (I am using it now at twitter dataset)-if I apply it to FB dataset will it be considered new contribution?
Generally, yes.

It would be expected that there is some novel aspect in the second article, but the novel aspect does not need to be the algorithm.

It can be a different type of data (e.g., "bla algorithm applied to detect liver tumors" and "bla algorithm applied to detect stroke"), or a substantially larger dataset (e.g., "preliminary results of bla on 9 patients" and "results of bla on 500 patients"), etc.