-*- Mode: Text -*-

;;; File:  AutoClass:doc;reports-math.text
;;;--------------------------------------------------------------------------;;;
;;;  AUTOCLASS 3.0  Released 5/11/90    contact:  Taylor@pluto.arc.nasa.gov  ;;;
;;;  by P. Cheeseman, J. Stutz, R. Hanson, W. Taylor 			     ;;;
;;;  NASA Ames Research Center, MS 244-17, Moffett Field, CA 94035           ;;;
;;;                                                                          ;;;
;;;  Copyright (C) 1990 Research Institute for Advanced Computer Science.    ;;;
;;;  All rights reserved.  The RIACS Software Policy contains specific       ;;;
;;;  terms and conditions on the use of this software, and must be           ;;;
;;;  distributed with any copies.  THIS FILE MAY BE REDISTRIBUTED.  This     ;;;
;;;  copyright and notice must be preserved in all copies made of this file. ;;;
;;;--------------------------------------------------------------------------;;;


-------------------  3.1 Influence Values Equations  --------------------------  
                                    
The influence values report generated by AUTOCLASS-REPORTS-FROM-RESULTS-FILE or
AUTOCLASS-REPORTS-FROM-CLSF uses the following equations:
                                           
Influence value for discrete valued attributes:

        I  = - Sum [P   ln (P  / P )]
         jk      l  jkl     jkl   kl

Influence value for real (continuous) valued attributes: 

                                2    2     2            2
        I  = ln (s / s ) + 1/2 s   [s   - s  + (m  - m ) ]
         jk       k  jk         k   jk    k     jk    k

     where:

       j     class index

       k     attribute index

       l     discrete attribute value index

       I     influence value of k'th attribute of j'th class
        jk

       P     probability value of l'th value of k'th attribute for j'th class
	jkl

       P     global probability value of l'th value of k'th attribute
        kl

       s     global standard deviation of k'th attribute 
        k

       m     global mean of k'th attribute 
        k

       s     standard deviation of k'th attribute of j'th class
        jk

       m    mean of k'th attribute of j'th class
        jk

		------------------------------

Class Strength:

	This is a measure of information density given by:

  	   (class-$-log-A<w.S/H.pi.theta> cl)
	   ----------------------------------
     		   (class-$-w_j cl)

	where:

	  cl 	class number

	  class-$-log-A<w.S/H.pi.theta>
	        log approximate liklehood of class statistics
		with respect to the class hypothesis and
		parameters.

	  class-$-w_j
		sum of the attribute weights for this class

-------------------------------------------------------------------------------
