Genetic Algorithm - Fitness function and Rule optimization - machine-learning

Question

Let's say I have a set of training examples where A_i is an attribute and the output is Iris-setosa
The values in the dataset are
A1, A2, A3, A4 outcome
3 5 2 2 Iris-­setosa
3 4 2 2 Iris­-setosa
2 4 2 2 Iris­-setosa
3 6 2 2 Iris­-setosa
2 5 3 2 Iris­-setosa
3 5 2 2 Iris­-setosa
3 5 2 3 Iris­-setosa
4 6 2 2 Iris­-setosa
3 7 2 2 Iris­-setosa
from analysis the range of attribute are:
A1 ----> [2,3,4]
A2 ----> [4,5,6,7]
A3 ----> [2,3]
A4 ----> [2,3]
I have defined:
A1 ----> [Low(2),Medium(3),High(4)]
A2 ----> [Low(4,5),Medium(6),High(7)]
A3 ----> [Low(<2),Medium(2),High(3)]
A4 ----> [Low(<2),Medium(2),High(3)]
I have set like below:
A1, A2, A3, A4 outcome
Medium Low Medium Medium Iris-setosa
Medium Low Medium Medium Iris-setosa
Low Low Medium Medium Iris-setosa
Medium Medium Medium Medium Iris-setosa
Low Low High Medium Iris-setosa
Medium Low Medium Medium Iris-setosa
Medium Low Medium High Iris-setosa
High Medium Medium Medium Iris-setosa
Medium High Medium Medium Iris-setosa
I know I have to define the fitness function. What is it for this problem? In my actual problem there are 50 training examples but this is a similar problem.
How can I optimize rule by using GA? How can I encode?
Suppose if I input (4,7,2,3), how optimization can help me classify whether the input is Iris-setosa or not?
Thank You for your patience.

Answer 1

The task you describe is known as one-class classification.
Identifying elements of a specific class amongst all elements, by learning from a training set containing only the objects of that class is
... different from and more difficult than the traditional classification problem, which tries to distinguish between two or more classes with the training set containing objects from all the classes.
A viable approach is to build the outlier class data artificially and train using a two class model but it can be tricky.
When generating artificial outlier data you need a wider range of possible values than the target data (you have to ensure that the target data is surrounded in all attribute directions).
The resulting two-class training data set tends to be unbalanced and
large.
Anyway:
if you want to try Genetic Programming for one-class classification take a look at
One-Class Genetic Programming - Robert Curry, Malcolm I. Heywood (presented in EuroGP'10, the 13th European conference on Genetic Programming)
also consider the anomaly detection techniques (a simple introduction is the 9th week of the Coursera Machine Learning class by Andrew Ng; notes here).

Answer 2

Okay, if you just want to know how to program a fitness function... Assume training data is list of tuples as so:
training_data = list((3,6,3,5),(8,3,1,2),(3,5,2,4)...)
Make a reference set for elements of A1, A2, etc. as follows, assuming first tuple tells us length of all the others (that way you can have any number of tuples in your training data):
A=[]
for x in training_data[0]:
res_list = set()
res_list.update(x[index] for x in training_data)
A.append(res_list)
index+=1
Now all your reference data is easily referred to (sets of A[0], A[1] etc). Let's make a fitness function that takes a tuple and return a fitness score that will help a GA converge on a right answer (1-4 if right elements, 5+ if in training_data). Play around with the scoring but these should work fine.
def fitness_function(target):
# Assume target is a tuple of same length as reference data
global A, training_data
score = 0
# Give a point for each element that is in the data set
index = 0
for t in target:
if t in A[index]:
score+=1
index += 1
# Give 5 points if entire tuple is exact match
if target in training_data:
score+=5
return score

Answer 3

What you have here is a multi-class classification problem that can be solved with Genetic Programming and related techniques.
I suppose that data are those from the well-known Iris data set: https://en.wikipedia.org/wiki/Iris_flower_data_set
If you need a quick start, you can use the source code of my method: Multi Expression Programming (which is based on Genetic Programming) which can be downloaded from here: https://github.com/mepx/mep-basic-src
There is a C++ source name mep_multi_class.cpp in the src folder which can "solve" iris dataset. Just call the read_training_data function with iris.txt file (which can also be downloaded from dataset folder from github).
Or, if you are not familiar with C++, you can try directly MEPX software which has a simple user-interface: http://www.mepx.org. A project with iris dataset can also be downloaded from github.