1 A Priori MaxEnt H ( S ) independent class analysis ( ica ) vs

Two mirror symmetric versions of the maximum entropy (MaxEnt) methodology are introduced and compared: (1) A posteriori MaxEnt Independent Component Analysis (ICA) H(V) was proposed by Bell, Sejnowski, Amari, Oja (BSAO) (early by Jutten & Herault, Comon and Cardoso (JHCC) in France). It is ambitious to factorize the unknown joint-probability density function (j-pdf) using the post processing algorithm involving the sigmoid-threshold neurons' output V(x,y)= σ([W]X(x,y)) of all image locations (x,y) in order to apply the pixelensemble averaged synaptic weight matrix [W] learning, ∂[W]/∂t=<∂H(V)/∂[W]>. The pixel ensemble average may be necessary to factorize the unknown joint-pdf from multi-channel data vector X(x,y). (2) A priori MaxEnt H(S) for independent class analysis (ica) is a compliment first step to the ambitious joint-pdf factorization based on a-posteriori MaxEnt H(V) ICA. Since ica is less ambitious to ICA in finding independent classes alone without their underlying pdf, we can derive from Gibb's statistics mechanics of independent classes of irradiation sources Sj by a priori MaxEnt H(S), which would be a flat equal class distribution if each were not constrained by the measurements by means of Lagrangian multipliers of force vector λi and energy scalar (λo -1) for each pixel: ∑ ∑ ∑∑ = = = = − − − − − − = N