From: xindongw@aisb.ed.ac.uk (Xindong Wu)
Newsgroups: comp.ai,comp.ai.shells,comp.lang.prolog
Subject: HCV: A New Efficient Attribute-Based Induction Algorithm
Keywords: rule induction, extension matrix approach
Date: 29 Jul 92 15:00:52 GMT
Reply-To: xindongw@aisb.ed.ac.uk (Xindong Wu)
Followup-To: ai.msgs,comp.sources.misc
Organization: Dept of AI, University of Edinburgh, Scotland


HCV: A New Efficient Attribute-Based Induction Algorithm
--------------------------------------------------------

1. Introduction

The HCV induction algorithm is invented by Xindong Wu in the Department of
Artificial Intelligence at the University of Edinburgh (UK) and the Department
of Computer and Information Engineering at Hefei University of Technology
(China). It is a representative of the extension matrix approach based family
of attribute-based induction algorithms, originating with J.R. Hong's AE1.

By dividing the positive examples (PE) of a specific concept in a given example
set into intersecting groups and adopting a set of strategies to find a
heuristic conjunctive rule in each group which covers all the group's positive
examples and none of the negative examples (NE), the HCV algorithm can find a
rule in the form of variable-valued logic for the concept based on PE against
NE in low-order polynomial time.  If there exists at least one conjunctive rule
in a given training example set for PE against NE, the rule produced by the HCV
algorithm must be a conjunctive one. The rules in variable-valued logic
generated by the HCV algorithm have been shown empirically to be more compact
than the decision trees or their equivalent decision rules produced by the ID3
algorithm (the best-known induction algorithm to date) and its successors in
terms of the numbers of conjunctive rules and conjunctions.

The term ``HCV'' in this prospectus indicates the current implementation
(Version 1.0) of the HCV algorithm in SICStus Prolog which runs on SUN3 and
SPARC workstations. In this implementation, HCV can classify more than 2
classes of examples by incorporating the AQ technique developed in the
generalization-specialization strategy based family of induction algorithms.
It takes a set of pre-classified training examples (vectors of
attribute-values)
as its input and produces a set of rules as its output classifying the
training
examples. It also allows you to evaluate the rules' accuracy in terms of a
set
of pre-classified testing examples.

2. Inputs

HCV's examples are vectors of attribute-values. Values can be either symbolic
or numeric. Don't Cares (denoted by `*') are permitted.

3. Outputs

The output is an unordered set of rules in the form of the variable-valued
logic
adopted in the generalisation specialisation strategy based AQ family of
induction algorithms.

4. User interaction

To use the program, you must prepare your training and testing examples in
the
form of ASCII files in a fixed format. During the program execution, all you
need to do is provide your file names. All outputs and some intermediate
results
are given on the screen.

5. Application domains

HCV works with any classification problems (such as diagnosis, prediction,
and
decision-making) that fit its input grammar.


6. Example

Input: Cases of T and F

	attrilist(['X1','X2','X3','X4']).
	eg([1,a,*,1],'F').
	eg([1,a,a,0],'F').
	eg([1,b,c,1],'T').
	eg([0,b,b,0],'T').
	eg([0,a,c,1],'T').
	eg([1,b,a,*],'T').
	eg([1,c,c,0],'F').
	eg([1,c,b,1],'F').
	eg([0,c,b,0],'T').
	eg([0,a,a,0],'T').
	eg([0,c,c,1],'F').
	eg([0,c,a,0],'T').
	eg([1,a,b,0],'F').
	eg([0,a,a,1],'T').
	eg([0,b,a,1],'T').

Output: Rules in variable-valued logic

	[ X2=[b] ] 
    v				[ X2=[c,a] ] 
	[ X1=[0] ]		[ X1=[1] ]
	[ X2=[a] ] 	    v 
    v 				[ X2=[c] ]
	[ X1=[0] ]		[ X4=[1] ]
	[ X4=[0] ]	   -->
   -->				The F class. 
	The T class. 

7. Main references

[1] Xindong Wu, Optimization Problems in Extension Matrixes, Science in China
    (Series A),  English edition: 35}(1992), 3: 363--373; Chinese edition: 
    35(1992), 2: 200-207.
[2] Xindong Wu,  HCV: A Heuristic Covering Algorithm for Extension Matrix
    Approach, DAI Research Paper No. 578, Department of Artificial
Intelligence,
    University of Edinburgh, 1992.
[3] Xindong Wu, Inductive Learning:  Algorithms and Frontiers, Artificial
    Intelligence Review}, 6(1992).

8. Availability

HCV (Version 1.0) is available electronically for academic use at no cost,
and
for commercial use by arrangement with the author. It may not be
redistributed.
To obtain a copy, send e-mail to 'xindongw@uk.ac.ed.castle' (the recipient
must
sign a condition-of-use agreement).

For people in the Artificial Intelligence Department at Edinburgh, there are
2
programs, 'HCV_Sun3' and 'HCV_Sparc', in the ~xindongw/HCV directory for SUN
3
and SUN 4 (SPARC) workstations respectively. You can run HCV by simply
entering 
~xindongw/HCV/HCV_Sun3 or ~xindongw/HCV/HCV_Sparc according to the machine
you
are using.

All the files with the suffix _data in the same directory with the HCV
program(s) are example sets which can be used as training and/or testing
examples to run HCV.

9. For further information, please contact

	Xindong Wu
	Department of Artificial Intelligence	Telephone: +44 (0)31 650 2727
	University of Edinburgh			Fax: +44 (0)31 650 6516
	80 South Bridge				Email: xindongw@uk.ac.ed.castle
	Edinburgh EH1 1HN, U.K.