How wavelet analysis works as a dimension reduction techniques? The approximations coefficients at higher level of decomposition are the fewer retained coefficients from the originial ?Is it correct?
Well, not really. The wavelet transform (the discrete to be precise) ist just a base transformation of a signal. However, it can be used to compress signals (dimension reduction in some sense), due to the fact that the energy of most natural signals is compactified under the wavelet transform. The continuous wavelet transform does even the opposite. It blows up your signal and introduces a lot of redundancy.