Smart Vision Image Processing: A Priori MaxEnt H(S) ICA vs a Posteriori MaxEnt H(V) ICA
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, Cornon and Cardoso (JHCC) in France). It wishes to factorize the unknown joint probability density function (pdf) using the multi-channel data vector X(x,y), coined by Comon as ICA by means of a post processing algorithm of output V(x,y)=σ(WX(x,y)) at each pixel location (x,y) via the unsupervised learning algorithm,(e)W/(e)t=<(e)H(V)/(e)W>. The pixel-ensemble average denoted by the angular brackets is necessary to estimate the underlying pdf, which is complete but over-ambitious for a simple classification task. The latter task may be referred to as independent class analysis (ica) in tower case, in contrast to ICA in upper case intended for obtaining the detailed pdf description. (2) A priori MaxEnt H(S) for ica of S could be a complimentary first step to ICA of their underlying pdf, namely an areaintegral of pdf within class boundaries. Since ica is a single realization of the ensemble, we can derive directly from Gibbs statistics mechanics of independent classes of irradiation sources S by the a priori MaxEnt H(S), which would be equally flat if each were not constrained by measurements by means of the Lagrangian multipliers of force vector λi and energy scalar (λo -1) per pixel:H(Sj)=-(N)/(Σ)/(j=1)Sj ln(Sj)-(N)/(Σ)/(i=1)(N)/(Σ)/(j=1)λi(AijSj-Xi(known))-(λo-1((N)/(Σ)/(j=1)Sj-1))Geometric optics speaking, the long distance propagation by the speed of the light insures the Linear and instantaneous characteristic and the line-of-sight validity of withm-pixel mixture of the ground irradiant sources in the remote sensing using optical spectra. This fact should be independent of any algorithm. Without the pixel ensemble average computational limitation, however,the a priori MaxEnt H(S) ica can handle large dimensional and large size imageries such as hyperspectral image data basis (200 spectral channels; 200x200 pixels each) by the pixel-by-pixel divide-and-conquer strategy. This is possible because the ground irradiation source S(Xo,yo) per pixel contributes locally to die corresponding image pixel X(Xo,yo)=- AS(Xo,yo), i.e. the spectral energy collected within me ground footprint of the pixel (Xo,yo)n will not be mixed with odier neighborhood sources due to the optics imaging lens. Although this is basically true for any processing algorithm, for the BSAO algorithm attempting comprehensively the underlying pdf ICA. all pixel ensemble WX(x,y) are utilized in sweeping through a randomly permuted batch mode that makes it limited to a lower dimension image-size (upto 7 spectral channels of 200x200 pixels each). Being less comprehensive, the a priori MaxEnt H(S) ica can compute S-decomposition, namely the area-integral of pdf under die class boundaries, pixel by pixel, in real tune.Furthermore, as a byproduct, the ab initio derivations of sigmoid threshold logic S =σ(λ.A) and Hebbian learning rule △Aij=λiSj makes one wonder for compression efficiency reasons why such a general communication of data X= AS by means of linear independent classes leads to the sigmoid transfer logic under the constraint of unit class decomposition Σj Sj=1. We conclude in passing the Lagrangian Constraint Neural Network (LCNN) is developed since 1997 and that allow nonlinear data generalization and conjugate gradient ascents of mirror symmetric MaxEnts.
Smart Vision Image Processing Unsupervised Learning Remote Sensing Hyperspectral Lagrangian Constraints Neural Net A Priori Maximum Entropy A Posteriori Maximum Entropy ICA ica.
Harold Szu
Digital Media RF Lab, Tompkins Rm308, 725 23rd St., Dept. ECE, George Wash. U., Wash. DC 20052
国际会议
8th International Conference on Neural Information Processing(ICONIP 2001)(第八届国际神经信息处理大会)
上海
英文
14-23
2001-11-14（万方平台首次上网日期，不代表论文的发表时间）