D2.0 General Nature of the Three Level, Nested, Adaptive Mechanism

      Figure D-2 presents a flow diagram of the proposed three level, nested, adaptive mechanism that will implement the pattern recognition methodology presented in Figure D-1.

      For each of the three adaptive loops in Figure D-2, there is a search process over a multidimensional parameter space.

      For LOOP I it is important to understand that for each geocentric planetary configuration there is one f(). Each f() is comprised of a sum of nine exponential functions, with two parameters x_i and y_i determining the amplitude and "width", respectively, of each exponential function. So, for a given iteration of this loop, there will be 60 f()s, one for each of the 60 geocentric planetary configurations in the 60-Item Perdurabo/TAARP Data Base, and 540 exponential functions, where 60 x 9 = 540. Thus, for each iteration of this loop there will be 60 X's and 60 Y's, where:

=

x1 . . . x9

and

=

y1 . . . y9

      There is one and one for each geocentric planetary configuration. Furthermore, each x_i and each y_i of each individual and is a function of a number of parameters (p₁,...,p_q) that define how a set of factors, such as the diurnal position of a planet, the cosmic (i.e., zodiacal) position of a planet, and the very fact that a planet is unique (e.g., Mars is Mars and is not Jupiter) are to be treated.

      The space over which an adaptive search for LOOP I is carried out is the space defined by this set of parameters. Therefore, one iteration of LOOP I will correspond to one point in the q dimensional space defined by parameters p₁,...,p_q, which comprise vector . One point in P space will define exactly how the set of factors are to be transformed into the numerical values x_i, y_i. So, for each geocentric planetary configuration, there are nine planets (i=1,...9), and each planet exists within the realm of the set of factors. Each of the factors is manipulated in a certain way, depending on the particular point in P space that the current iteration of LOOP I has determined, and these factors are conglomerated together to give a value for x_i and a value for y_i for a given planet. The particular form of the manipulation for a given factor is the same for each geocentric planetary configuration for each iteration of LOOP I.

      Consider the following example. One factor of importance is the position of a planet relative to the eastern horizon. Assume that the way it has been determined to handle this factor is to model it with an exponential function:

Ae^B(_H-_i)2

Therefore, three of the parameters of would be assigned to this factor: one parameter for A specifying the amplitude, one parameter for B specifying the "width," and one parameter for _H specifying where relative to the horizon the exponential function is centered. Therefore, since every planet in each of the 60 geocentric planetary configurations has a distinct location, _i, every planet will have a unique value for this exponential function for any given iteration of LOOP I based on the particular values of the three parameters A, B, _H that the LOOP I search process has determined. For each planet of each geocentric planetary configuration, the unique exponential function value will be conglomerated together with all the other factors to determine one value for x_i and one value for y_i. (Note that the exponential functions discussed here will help determine the x_i and y_i for the exponential functions in the 2nd Transformation of Figure D-1. In other words, two different sets of exponential functions are under discussion.)

      Section E6.0 of Appendix E discusses this subject in more detail. For now, suffice it to say that for LOOP I there is an adaptive search process over a q-dimensional space, where the parameters defining the space are p₁, p₂, ..., p_q.

      For LOOP II, the search space is of dimension 2n, and the parameters of the search space are c_i, d_i, where:

=

c1 . . . cn

and

=

d1 . . . dn

are the parameter vectors. n is to be determined by the judgment of the analyst. The objective here is to partition the axis of Figure D-1, Part "e" into n windows, each of which with a center point, c_i, and a width, d_i.

      Each point in the 2n dimensional parameter space of LOOP II will define a specific sampling of the amplitude and phase of the Fourier transform space of Figure D-1, Part "e." Thus the amplitude features, fa_i, and the phase features, fp_i, of Figure D-1, Part "f" are determined by a single point in the 2n dimensional parameter space of LOOP II. So, for each iteration of LOOP II, for each of the 60 geocentric planetary configurations, there will be n Fourier amplitude features and n Fourier phase features. It will be the job of LOOP III to operate upon the 60 feature vector pairs , from LOOP II to see if it is possible to produce a correct separation of the 60 pairs into the three classes of High PHENOMENON, Medium PHENOMENON, and Low PHENOMENON.

      For LOOP III, the search space is of dimension 2m, and the parameters of the search space are wa_i, wp_i, where

=

wa1 . . . wam

and

=

wp1 . . . wpm

are the parameter vectors. m is to be determined by the judgment of the analyst, and is dependent upon the kind and degree of the polynomial operator that serves to define the discriminant function of the 6^th Transformation of Figure D-1. (See Section D3.0 for a discussion of an example of a polynomial discriminant function.)

      Note that for each of the three adaptive loops in Figure D-2, there is a performance measure, PM, which plays two roles.

• LOOP I
• ROLE 1
• Guidance of the search process for adjusting the exponential functions for f().


• ROLE 2
• Decision to:
• Stop the entire adaptive mechanism because progress in terms of establishing correct classifications in LOOP III is proceeding too slowly.
• Maybe some other basic function type than exponential should be tried.


• Or, to continue with adjustment of the exponential functions.


• LOOP II
• ROLE 1
• Guidance of the search process for adjusting the Fourier amplitude and phase features.


• ROLE 2
• Decision to:
• Continue with adjustment of the Fourier features (i.e., try another specific sampling of the amplitude and phase of the existing 60 Fourier transforms.)
• Note that there is one Fourier transform for each f(), and there is one f() for each of the 60 geocentric planetary configurations in the 60-Item Perdurabo/TAARP Data Base.


• Or, pass control to LOOP I because it is time to try a new set of exponential functions and construct a new set of 60 f()s from them.


• LOOP III
• ROLE 1
• Guidance of the search process for adjusting the weights of the discriminant function.


• ROLE 2
• Decision to:
• Stop the entire adaptive mechanism because classification has been accomplished to an acceptably accurate degree.


• Or, continue with weight adjustment.


• Or, pass control to LOOP II because it is time to try a new set of Fourier amplitude and phase features.

      One option for the PMs vis-a-vis ROLE I is:

• LOOP I
• Let PMI = PMII = PMIII.


• Use a specific guided, accelerated, random search for adjusting the parameters that determine the amplitude coefficients (i.e., the x_is) and the exponential coefficient parameters (i.e., the y_is) of the exponential functions that comprise the f()s based on the values of PMI.
• See Appendix C for a specific example of a guided, accelerated, random search.


• LOOP II
  • Let PMII = PMIII.
  
  
  • Use a specific, guided, accelerated, random search for adjusting the frequency sampling parameters (i.e., the c_is and d_is) based on the values of PMII.
  
  
• LOOP III
• Regardless of how PMIII is calculated (see Section D3.0 for a specific example of how to calculate a PMIII), use a specific guided, accelerated, random search for adjusting the discriminant functions weights based on the values of PMIII.

      One option for the PMs vis-a-vis ROLE 2 is:

• LOOP I
• Let PMI = PMII = PMIII.


• If PMI has not increased by 30% in the last 10,000 iterations, then stop the entire adaptive mechanism and consider replacing the exponential functions with functions of another kind.
• Otherwise, try another 10,000 iterations of LOOP I.


• LOOP II
• Let PMII = PMIII.


• If PMII has not increased by 20% in the last 10,000 iterations, then break out of LOOP II and go to LOOP I.
• Otherwise, try another 10,000 iterations of LOOP II.


• LOOP III
• If PMIII is greater than or equal to some predetermined threshold, then classification is good enough. So, stop the entire adaptive mechanism.


• If PMIII is less than the threshold, then:
• If PMIII has not increased by 10% in the last 10,000 iterations, then break out of LOOP III and go to LOOP II.


• Otherwise, try another 10,000 iterations of LOOP III.

      Note that all of these ideas are simply meant to serve as food for thought for the execution of Task 2 in Section 7.2.

      Figures E-5 through E-9 in Appendix E are a continuation of the vein of thought presented above.