I am working on a project that takes some features of audio signals and classify them with a neural network. However, the audio signals are added with their own echo with the environment. What would be some of the processing techniques that can be applied on the features, including chroma stft and Mfcc.
well, while applying a room impulse response to audio (which is what echoes are) is a linear operation on the time-domain signal, it's generally not on features.
So, you're looking to find a non-linear mapping of a somewhat high-dimensional feature vector space to a "cleaned up" feature vector space with some well-known metric on how well that mapping performs as cleanup....
That sounds exactly like the kind of job that neural networks are good at. And that's not a coincidence: When you look under the mathematical hood of all your ML algorithms, there's the Universal Approximation Theorem that says that a NN that's sufficiently large can represent any non-linear mapping.
So, really, that's a hard problem to do analytically, and it's thoroughly reasonable to assume that "echo removal on MFCC features" can most sensibly be done with a Neural network, most likely even the same that you directly train to classify your audio signals.