how can I analize music as spotify/musixmath/shazam does?
The general idea for the algorithm is well presented in the linked paper. As is the case with applied machine learning and related fields, the secret sauce (which features to select, how to tweak your algorithms, etc.) is found by trial and error by people who know things about audio/audio signal processing (see for example, Julius O. Smith III's page at CCRMA @ Stanford) and by just trying a ton of things. Unfortunately, to become (and stay) the state of the art, the secret sauce has to be kept, well, secret. 

That being said, the wikipedia article on acoustic fingerprinting is a decent place to look for some alternatives (and some links to some open source ones like Acoustid).