Attrasoft DecisionMaker 2.5/Chap. 3

We will generate the data as follows: assume initially that (x1, x2, x3) is in state (1 0 0), then it will generate (1 1 0). Now we will use (x1, x2, x3) = (1 1 0) as an question, then it will generate an answer (2 1 1), ... ...

The parameters of this problem are:

6 variables (3 input: x1, x2, x3; and 3 output: y1, y2, y3);
69 instances;
245 classes

The Math-Database is:

1 0 0 1 1 0

1 1 0 2 1 1

2 1 1 4 2 1

4 2 1 0 4 2

0 4 2 6 0 4

6 0 4 3 6 0

3 6 0 2 3 1

2 3 1 6 2 3

6 2 3 4 6 2

4 6 2 5 4 1

5 4 1 3 5 4

3 5 4 5 3 0

5 3 0 1 5 3

1 5 3 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 6 4 1

6 4 1 4 6 4

4 6 4 0 4 1

0 4 1 5 0 4

5 0 4 2 5 0

2 5 0 0 2 0

0 2 0 2 0 2

2 0 2 4 2 0

4 2 0 6 4 2

6 4 2 5 6 4

5 6 4 1 5 1

1 5 1 0 1 0

0 1 0 1 0 1

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 6 4 1

6 4 1 4 6 4

4 6 4 0 4 1

0 4 1 5 0 4

5 0 4 2 5 0

2 5 0 0 2 0

0 2 0 2 0 2

2 0 2 4 2 0

4 2 0 6 4 2

6 4 2 5 6 4

5 6 4 1 5 1

1 5 1 0 1 0

0 1 0 1 0 1

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 6 4 1

6 4 1 4 6 4

4 6 4 0 4 1

0 4 1 5 0 4

5 0 4 2 5 0

2 5 0 0 2 0

0 2 0 2 0 2

2 0 2 4 2 0

4 2 0 6 4 2

6 4 2 5 6 4

5 6 4 1 5 1

1 5 1 0 1 0

0 1 0 1 0 1

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

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 0 0 0

The 69 rows of data are divided into two parts:

The first 64 rows will be used as the Problem-Database; and
the last 5 rows will be used to test the DecisionMaker's accuracy.

The last 5 rows are further divided into 2 groups

Question Answer

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 0 0 0

The first group,

Question

1 0 1

2 1 0

3 2 1

6 3 2

4 6 3

forms the "Question file" for the DecisionMaker and the DecisionMaker is expected to take this "Question file" and provide the following Answer file:

Question Answer

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 0 0 0

3.1.2 Operation

Step 1. Math-Database file and Question file

The first file is the Math-Database file, which is used to educate the DecisionMaker. Let the file name be "mathex1a.txt" and it looks like this:

=================== Beginning =====================

Let a system be defined by:

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

1 0 0 1 1 0

1 1 0 2 1 1

2 1 1 4 2 1

4 2 1 0 4 2

0 4 2 6 0 4

... ...

4 2 0 6 4 2

6 4 2 5 6 4

5 6 4 1 5 1

1 5 1 0 1 0

0 1 0 1 0 1

=================== End ==========================

This Problem-Database file has three sections:

Remark section: * . . . *: this section will be ignored by the DecisionMaker
Number of variables/attributes: 6
Data

The second file is the Question file, which contains the questions you have. The goal is to use input, (x1, x2, x3), to generate output, (y1, y2, y3), located in the last 5 rows. Let the file be "mathex1b.txt" and it looks like this:

=================== Beginning =====================

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

1 0 1

2 1 0

3 2 1

6 3 2

4 6 3

=================== End ==========================

This Question file has three sections:

Remark section: * . . . *: this section will be ignored by the DecisionMaker
Number of variables/attributes: 3
Data

Step 2. Link the 2 files to the DecisionMaker

Save the above two files in the same directory where the DecisionMaker is located. Click "Data/Link" (see Figure 4; first of 2 clicks) and the dialog box asks for the following:

1. Problem-Database File Name;

2. Question File Name;

3. Answer File Name;

4. Precision level of the prediction;

To link the data files (Figure 5), enter

mathex1a.txt
Mathex1b.txt

into the first 2 textboxes, and the linking is completed. These two files are in your software.

Step 3. Click command: "Integer/+ Predict"

Figure 7. The "Integer" commands

Figure 7 shows the "Integer" menu. Click "Integer/+ Predict" (second of 2 clicks) and the following Answer file is opened automatically:

=================== Beginning =====================

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

1 0 1

Possibility Confidence*Probability

1 1 0 2048

2 1 0 24576

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

2 1 0

Possibility Confidence*Probability

1 1 0 1024

2 1 1 2048

3 2 1 32768

1 0 1 3072

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

3 2 1

Possibility Confidence*Probability

1 1 0 32

2 1 1 64

4 2 1 1024

2 1 0 384

3 2 1 1024

6 3 2 32768

2 0 2 384

1 0 1 96

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

6 3 2

Possibility Confidence*Probability

4 2 1 4

0 4 2 128

6 2 3 32

1 5 3 128

3 2 1 4

6 3 2 128

4 6 3 32768

4 2 0 24

6 4 2 96

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

4 6 3

Possibility Confidence*Probability

0 4 2 8

6 0 4 4

2 3 1 32

6 2 3 2

5 4 1 2048

2 1 0 64

6 3 2 8

6 4 1 24576

5 0 4 3

0 2 0 12

6 4 2 6

0 1 0 12

0 0 0 8192

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

5 3 1

Precision of each number:

0.33 0.33 0.22

=================== End ==========================

Step 4. Results

This Answer file has three sections:

Remark section: * . . . * is the remark section, which is borrowed from the Question file.
Distribution: for each question, the DecisionMaker presents you with all possible predictions and how valuable the DecisionMaker thinks that prediction is via a confidence number (the higher that number, the more confidence the DecisionMaker has in that prediction).

Go back to the beginning of the above Answer file, and look at case 1:

1 0 1

Possibility Confidence*Probability

1 1 0 2048

2 1 0 24576

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

2 1 0

Th first line, 1 0 1, is the question.

The possibilities are:

1 1 0 2048

2 1 0 24576

The odds are 24576 to 2048 in favor of pattern 2 1 0, which in this case is the correct answer.

The line "---- ... ----" indicates the end of the distribution.

Average: The last line, 2 1 0, is the weighted average of the prediction.

3.2 Step 1: Problem Database File and Question File

The first step of using the DecisionMaker is to provide two files:

Problem-Database file: this is all the data you have collected about your problem and put it into one big database file. This file teaches the DecisionMaker your problem and the value of your experience.
Question file : this file asks the question(s) you have based on your specific database. You want to use as much information (encoded in your database) as possible to arrive at intelligent answers.

3.2.1 Data set

The data set is all parameters used to define specifics in a problem. These parameters are used to present an instance.

Example: The data set of the cancer database is:

Attribute Domain

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

1. Sample code number id number

__________________________________________

2. Clump Thickness 1 - 10

3. Uniformity of Cell Size 1 - 10

4. Uniformity of Cell Shape 1 - 10

5. Marginal Adhesion 1 - 10

6. Single Epithelial Cell Size 1 - 10

7. Bare Nuclei 1 - 10

8. Bland Chromatin 1 - 10

9. Normal Nucleoli 1 - 10

10. Mitoses 1 - 10

___________________________________________

11. Class: (2 for benign, 4 for malignant)

You also have to determine the precision level of the variables. The default value is set to 10.

As a general rule, the more data you have, the better the outcome will be. The complexity of the prediction grows exponentially with these parameters:

Number of variables in the data set;
Precision level.

You must formulate your problem in such a way that you have enough data to support your prediction. The guideline is 100 instances per class per variable (See next chapter).

Also, do not pass the limit of the Attrasoft neural network, and the limits are:

The number of variables * precision level < 65,000, and

The number of variables < 10,000.

3.2.2. Arranging Variables/Attributes

Once you have selected the data set, they have to be arranged in the following order: input variables first, output variables last.

Example Consider:

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

The correct order is:

x1, x2, x3, y1, y2, y3

3.2.3 Two files

There are two files required to run the DecisionMaker:

Problem-Database file: your accumulated data over years which will pass to the DecisionMaker the value of your extensive experience;
Question file: the questions you have.

The Problem-Database and Question files must be prepared in the text file format. You can also use any word processors, like Microsoft Word, or WordPerfect; just make sure you save the data file in the text format.

Here is a Problem-Database file:

Example The following is a complete example:

=================== Beginning =====================

Let a system be defined by:

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

1 0 0 1 1 0

1 1 0 2 1 1

2 1 1 4 2 1

4 2 1 0 4 2

0 4 2 6 0 4

... ...

1 0 1 2 1 0

2 1 0 3 2 1

3 2 1 6 3 2

6 3 2 4 6 3

4 6 3 0 0 0

=================== End ==========================

The Problem-Database data file has three sections:

Comment section
Number of variables section
Data section.

Section 1 starts with a "*" and ends with another "*". The DecisionMaker will ignore this section. The purpose of this section is to document your data:

Give a description of the data;
Specify the prediction commands used;
Specify the beginning and the ending dates of the data
. . .

Section 2 tells the DecisionMaker how many variables you will use.

Section 3 contains Problem Database: one record per row.

The Question file follows the exact same format as the above. The number of variables in the Question file must be smaller than the number of variables in the Problem-Database file.

* * *

For Mathematicians Only: The black box defines the following function:

y1 = f1(x1, x2, ..., xn)

y2 = f2(x1, x2, ..., xn)

...

ym = fm(x1, x2, ..., xn)

The Problem-Database data is a set records of the following variables: x1, x2, ... , xn, y1, y2, ..., ym. The Question data is a set of the records of the following variables: x1, x2, ... , xn. The answer file is: x1, x2, ... , xn (from the Question file),

y1, y2, ..., ym (from the neural computation).

The number of variables in the Problem-Database file is n+m, and the number of variables in the Question file is n, note that, n < n+m.

* * *

3.3 Step 2. Link Data Files To DecisionMaker

Three files are used:

Problem-Database file,
Question file and
Answer file.

The default file names are:

Problem-Database file: example2a.txt

Question file: example2b.txt

Answer file: example2c.txt

These default files are automatically connected to the software.

When you use the DecisionMaker, you have link your data files to DecisionMaker by clicking: "Data|Link", or its button on the toolbar, then type in the data file names.

Assume your files are:

cancer1a.txt

cancer1b.txt

These two files must be in the same directory. Here is how to link:

Method 1:

Save the two files to C:\ Program Files\Attrasoft\decisionmaker 2.5\ (the default directory for the DecisionMaker);
Click command "Data\link" (Figure 4, 5), then enter the two file names.

Method 2:

Save the two files to anywhere, use command "File/Open" to open the two files;
Click command "Data\link" (Figure 4, 5), then enter the two file names.

3.4 Step 3: Run

Definition:

Integer = numbers like 0, 2, 300;

Average = Weighted average.

The weighted average of

5 30%

6 50%

7 20%

is 5*0.30 + 6 * 0.50 + 7 *0.20.

3.4.1 Real Command

Under menu "Real", there are six commands (See Figure 8):

+ Predict
- Predict
0 Predict
+ Enumerative
-- Enumerative
0 Enumerative.

Figure 8. The "Real" commands

These are the primary commands. These commands present you with all possible predictions and how valuable the DecisionMaker thinks that prediction is via a confidence number (the higher that number, the more confidence the DecisionMaker has in that prediction).

Now we will explain these commands:

+ Predict: the DecisionMaker will give you the upper bound of its answer using the best possibilities. This command runs fast if you have a lot of classes, say 1,000 - 100,000 classes.
-- Predict : the DecisionMaker will give you the lower bound of its answer using the best possibilities. This command runs fast if you have a lot of classes, say 1,000 - 100,000 classes.
0 Predict: the DecisionMaker will give you the answer using the best possibilities. This command runs fast if you have a lot of classes, say 1,000 - 100,000 classes.
+ Enumerative: the DecisionMaker will give you the upper bound of its answer using all possibilities. This command runs slow if you have a lot of classes, say 100,000 - 1,000,000 classes.
-- Enumerative: the DecisionMaker will give you the lower bound of its answer using all possibilities. This command runs slow if you have a lot of classes, say 100,000 - 1,000,000 classes.
0 Enumerative: the DecisionMaker will give you the answer using all possibilities. This command runs slow if you have a lot of classes, say 100,000 - 1,000,000 classes.

If you only have a few classes, say 100 - 1,000, the two commands run at the same speed. The Enumerative-commands are the preferred choices because it checks all possibilities. On the other hand, if you have 100,000 - 1,000,000 classes, the Predict-commands are the preferred choices because it arrives at a conclusion very fast and only misses some unimportant possibilities. The limit on the standard version is 10,000 classes. Beyond 10,000 classes, a customized version can easily be ordered.

In the above commands:

"Enumerative" commands will take care of all situations.
"Predict" commands will take care of the best situations, and leave out some unimportant states for increased computation speed.
'+', '--', and '0' commands are upper bound, lower bound and correct prediction, respectively. They work like this; assuming a predicted value is:

x = 5.6 ^{+ 0.3} _{- 0.2} ,

i.e. the result is likely to be 5.6, but could be in the range [5.4, 5.9], then :

the 0 prediction will be 5.6;
the + prediction will be 5.9;
the - prediction will be 5.4.

If the '0' command works, it will always be more reliable than '+' and '--' commands. Please keep that in mind. Because of its accuracy, when ambiguity exists, it will not offer any answers.

Please replace numbers like, .234, by 0.234.

3.4.2 Integer Command

From time to time, the numbers in your database will be all integers. A pure integer presentation will look better than real number presentation. Therefore, integer commands are provided for your convenience. Under menu "Integer", there are six commands:

+ Predict
- Predict
0 Predict
+ Enumerative
-- Enumerative
0 Enumerative.

3.4.3 Answer File

The default Answer file name is example2c.txt. You can change the file name by clicking: "Data|Link", or its button on the toolbar, and type in your new data file name.

A Confidence & Probability number will be to the right of each answer prediction. The number indicates how valuable the DecisionMaker thinks that prediction is. The higher that that number, the more confidence the DecisionMaker has in that prediction

Here is an answer file generated by clicking "Integer/+ Predict":

=================== Beginning =====================

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5;

1 0 1

Possibility Confidence*Probability

1 1 0 2048

2 1 0 24576

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

2 1 0

Possibility Confidence*Probability

1 1 0 1024

2 1 1 2048

3 2 1 32768

1 0 1 3072

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

3 2 1

Possibility Confidence*Probability

1 1 0 32

2 1 1 64

4 2 1 1024

2 1 0 384

3 2 1 1024

6 3 2 32768

2 0 2 384

1 0 1 96

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

6 3 2

Possibility Confidence*Probability

4 2 1 4

0 4 2 128

6 2 3 32

1 5 3 128

3 2 1 4

6 3 2 128

4 6 3 32768

4 2 0 24

6 4 2 96

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

4 6 3

Possibility Confidence*Probability

0 4 2 8

6 0 4 4

2 3 1 32

6 2 3 2

5 4 1 2048

2 1 0 64

6 3 2 8

6 4 1 24576

5 0 4 3

0 2 0 12

6 4 2 6

0 1 0 12

0 0 0 8192

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

5 3 1

Precision of each number:

0.33 0.33 0.22

=================== End ==========================

This answer file has three sections:

Remark section: * . . . *, which is borrowed from the Question file.
Distribution: For each Question, DecisionMaker presents you with all possible predictions and how valuable the DecisionMaker thinks that prediction is via a confidence number (the higher that number, the more confidence the DecisionMaker has in that prediction)

Go back to the beginning of the above answer file, the first of the 5 cases is:

1 0 1

Possibility Confidence*Probability

1 1 0 2048

2 1 0 24576

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

2 1 0

Th first line, 1 0 1, is the question.

The answers are:

Possibility Confidence*Probability

1 1 0 2048

2 1 0 24576

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

Their probabilities are:

2048/(2048 + 24576) and

24576/(2048 + 24576),

respectively. The odds are 10 to 1 in favor of pattern 2 1 0, which in this case is the correct answer. The line "---- ... ----" indicates the end of the distribution.

Average: The last line, 2 1 0, is the weighted average of the prediction.

* * * For Mathematicians Only: As we have stated earlier: the black box converts the following question to the following answer: Question: (x1, x2, ... , xn)

Answer: (y1, y2, ..., ym).

Let a set of possibilities be

(y1, y2, ..., ym)1,

(y1, y2, ..., ym)2,

(y1, y2, ..., ym)3,

. . . ,

(y1, y2, ..., ym)l

and a set of relative probabilities be:

(p1, p2, p3, . . . , pl ), These probabilities are relative probabilities. Relative probabilities are proportional to probabilities. For example, let the relative probabilities be (3 5), then they represent the probabilities (3/8, 5/8) = (37.5%, 62,5%).

The Answer file looks like this

The remark section from the Question file

(y1, y2, ..., ym)1, p1

(y1, y2, ..., ym)2, p2

(y1, y2, ..., ym)3, p3

. . . ,

(y1, y2, ..., ym)l , pl

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

(a1, a2, ... , am )

Error:

(e1, e2, ... , em)

where

(a1, a2, ... , am ) is the weighted average calculated from the distribution; and
(e1, e2, ... , em) is the error associated with each number. Increasing the precision number can reduce the error.

* * *
3.4.4 "Average" Commands

We have discussed 12 commands; each one gives a distribution. Sometimes, you might not be interested in the distribution, but only in a simple answer. The "Average" commands give you one simple answer: the weighted-average. There are 12 average commands.

If you want one simple answer, which is the one with the highest probability, a customized version has to be ordered from Attrasoft ($1000).

3.4.5 Confidence of a Prediction

A Confidence & Probability number will be to the right of each answer prediction. Among all the numbers in a prediction, the highest number is called the Confidence Number. The higher this number is, the more reliable the result is. For each prediction, one Confidence Number is produced. This number is similar to the number in an Internet Search Engine: the higher that number, the more confidence the DecisionMaker has in that prediction. Unfortunately, no quantitative description can be made for the Confidence Number. You can get a feel for this Confidence Number from experience.

3.5 Prediction Parameters

The parameters of the prediction are:

Precision: determines the precision of each variable. You can change this variable by clicking "Predict|Link". The default value is 10. The larger this number is, the higher the precision is. It is mathematically easier for the DecisionMaker to predict a less accurate prediction than a more accurate prediction.
Data volume: more data will produce more accurate results than less data. The rule of thumb is 100 instances per class per attribute.
Data set: it is mathematically easier for the DecisionMaker to predict fewer variables at a time than more variables at a time;

If you run the DecisionMaker, and get too much information, you can do one or more of the following:

Reduce the data volume;
Increase the number of variables;
Increase the precision of the prediction.

If you run the DecisionMaker, and get no results, you can do one or more of the following:

Increase the data volume;
Reduce the number of variables;
Reduce the precision of the prediction.

3.6 Mathematics Probability

3.6.1 Problem Database

All files used in this section are in your software package. Let a mapping be defined by:

y1 = ( x1 + x2 + x3 ) Mod 7;
y2 = x1;
y3 = x2 Mod 5; 60%
y3 = ( x2 + 1 ) Mod 5; 40%
y4 = ( x4 + 1 ) Mod 5; 60%
y4 = ( x4 + 2 ) Mod 5; 40%
y5 = x4 Mod 3.

Note that by design, each question can have 4 different answers. All four answers are correct and each answer has certain probability to appear. The parameters of this problem are:

10 variables (5 input; and 5 output);
9999 instances;
3675 classes.

We will generate the data as follows: assume initially that (x1, x2, x3, x4, x5) is in state (1 0 0 0 0), then it will generate (1 1 0 1 0). Now we will use (x1, x2, x3, x4, x5) = (1 1 0 1 0) as a question, then it will generate an answer (2 1 2 3 1), ...

9999 rows can generated in this way:

1 0 0 0 0 1 1 0 1 0

1 1 0 1 0 2 1 2 3 1

2 1 2 3 1 5 2 1 0 0

5 2 1 0 0 1 5 3 2 0

1 5 3 2 0 2 1 0 4 2

2 1 0 4 2 3 2 2 1 1

3 2 2 1 1 0 3 3 2 1

The 9999 rows of data are divided into two parts:

The first 9994 rows will be used for the problem Database file; and
The last five rows will be used as questions for the DecisionMaker, as well as providing us correct answers against which to measure the accuracy of the DecisionMaker.

The last 5 rows are:

Question Answer

6 6 1 3 1 6 6 1 4 0

6 6 1 4 0 6 6 1 0 1

6 6 1 0 1 6 6 1 1 0

6 6 1 1 0 6 6 1 3 1

6 6 1 3 1 6 6 1 4 0

They are further divided into 2 groups, as indicated above. The first group,

Question

6 6 1 3 1

6 6 1 4 0

6 6 1 0 1

6 6 1 1 0

6 6 1 3 1

forms the Question file for the DecisionMaker and the DecisionMaker is expected to take the question file and to arrive at the following Answer file:

Question Answer

6 6 1 3 1 6 6 1 4 0

6 6 1 4 0 6 6 1 0 1

6 6 1 0 1 6 6 1 1 0

6 6 1 1 0 6 6 1 3 1

6 6 1 3 1 6 6 1 4 0

3.6.2 Operation

Step 1. Problem Database file and Question file

The first file is the Problem-Database file, which is used to educate the DecisionMaker. Let the file be "mathex2a.txt" and it looks like this:

=================== Beginning =====================

Let a system be defined by:

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5; 60%

y3 = ( x2 + 1 ) Mod 5; 40%

y4 = ( x4 + 1 ) Mod 5; 60%

y4 = ( x4 + 2 ) Mod 5; 40%

y5 = x4 Mod 3.

We will generate the data as follows: assume initially that (x1, x2, x3, x4, x5) is in state (1 0 0 0 0), then it will generate (1 1 0 1 0). Now we will use (x1, x2, x3, x4, x5) = (1 1 0 1 0) as an question, then it will generate an answer (2 1 2 3 1), ...

1 0 0 0 0 1 1 0 1 0

1 1 0 1 0 2 1 2 3 1

2 1 2 3 1 5 2 1 0 0

5 2 1 0 0 1 5 3 2 0

1 5 3 2 0 2 1 0 4 2

2 1 0 4 2 3 2 2 1 1

3 2 2 1 1 0 3 3 2 1

... ...

=================== End ==========================

This Problem-Database file has three sections:

Remark section: * . . . *: this section will be ignored by the DecisionMaker
Number of variables/attributes: 10
Data

The second file is the Question file, which contains the question you have. The goal is to use a question, (x1, x2, x3, x4, x5), to generate an answer: (y1, y2, y3, y4, y5). Let the file be "mathex2b.txt" and it looks like this:

=================== Beginning =====================

...

6 6 1 3 1

6 6 1 4 0

6 6 1 0 1

6 6 1 1 0

6 6 1 3 1

=================== End ==========================

This Question file has three sections:

Remark section: * . . . *: this section will be ignored by the DecisionMaker
Number of variables/attributes: 5
Data

Step 2. Link the data to the DecisionMaker

Save the above two files in the same directory where the DecisionMaker is located. Click "Data/Link" (see Figure 4, first of 2 clicks) and the dialog box asks for the following:

1. Problem-Database File Name;

2. Question File Name;

3. Answer File Name;

4. Precision level of the prediction;

To link the data files, in the first 2 textboxes, enter

Mathex2a.txt
Mathex2b.txt

And the linking is completed.

Step 3. Click command: "Integer/0 Predict"

Click "Integer/0 Predict"(second of 2 clicks) and the following Answer file is opened automatically:

=================== Beginning =====================

y1 = ( x1 + x2 + x3 ) Mod 7;

y2 = x1;

y3 = x2 Mod 5; 60%

y3 = ( x2 + 1 ) Mod 5; 40%

y4 = ( x4 + 1 ) Mod 5; 60%

y4 = ( x4 + 2 ) Mod 5; 40%

y5 = x4 Mod 3.

6 6 1 3 1

Possibility Confidence*Probability

6 6 1 4 0 65536

6 6 1 0 0 65536

6 6 2 4 0 163840

6 6 2 0 0 32768

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

6 6 2 3 0

6 6 1 4 0

Possibility Confidence*Probability

6 6 1 0 1 229376

6 6 2 1 1 163840

6 6 1 1 1 32768

6 6 2 0 1 65536

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

6 6 1 0 1

Possibility Confidence*Probability

6 6 1 1 0 294912

6 6 2 1 0 98304

6 6 1 2 0 65536

6 6 2 2 0 32768

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

6 6 1 1 0

Possibility Confidence*Probability

6 6 1 2 1 262144

6 6 2 3 1 131072

6 6 1 3 1 98304

6 6 2 2 1 65536

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

6 6 1 2 1

6 6 1 3 1

Possibility Confidence*Probability

6 6 1 4 0 65536

6 6 1 0 0 65536

6 6 2 4 0 163840

6 6 2 0 0 32768

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

6 6 2 3 0

Precision of each number:

0.33 0.33 0.22 0.22 0.11

=================== End ==========================

4. Results

This Answer file has three sections:

Remark section: * . . . *, which is borrowed from the Question file.
Distribution: for each Question, the DecisionMaker presents you with all possible predictions and how valuable the DecisionMaker thinks that prediction is via a confidence number (the higher that number, the more confidence the DecisionMaker has in that prediction)

Go to the beginning of the Answer file and look at case 1:

6 6 1 3 1

Possibility Confidence*Probability

6 6 1 4 0 65536

6 6 1 0 0 65536

6 6 2 4 0 163840

6 6 2 0 0 32768

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

6 6 2 3 0

Th first line, 6 6 1 3 1, is the Question.

The possibilities are:

6 6 1 4 0 65536

6 6 1 0 0 65536

6 6 2 4 0 163840

6 6 2 0 0 32768

The line "---- ... ----" indicates the end of the distribution. These are indeed the correct outcomes based on the formula given at the beginning of this section (1 question, 4 answers).

Average: The last line, 6 6 2 3 0, is the weighted average of the prediction.

3.7 Customized Software

Customized software can be ordered from Attrasoft upon your request for the following reasons:

Worded Data: the worded data has to be customized in the current version. It might be supported in our future version. Example: very good, good, OK, bad, very bad.

Worded data can be converted into numerical data easily via a tool like Microsoft Excel. When you convert the worded data, please convert then in order.

Example: Assume X1 and X2 contribute a classification in a similar fashion, then

Correct conversion:

Attribute Value

X1 good(1), ok(2), bad(3)

X2 good(1), ok(2), bad(3)

Wrong conversion:

Attribute Value

X1 good(1), ok(2), bad(3)

X2 good(3), ok(2), bad(1)

Missing Data: Attrasoft neural net, by design, can handle missing information easily, however, the interface for the DecisionMaker cannot handle the missing information. If your data contains many records with missing numbers, it has to be customized.
Larger Networks: The current version supports up to 65,000 external neurons, and 10,000 classes. If you want a larger one, it has to be customized. The current version supports up to 650 MB for storing compressed weights. If you want more space, it has to be customized.
Special Data Interface: If you need to interface the DecisionMaker with your application data, customized software can be ordered.

To make a customized order, go to:

http://attrasoft.com

and click the email button.

We encourage all comments from our prospective customers. These comments are delivered directly to our new product development department. Your comments directly affect our future products ....... , we aim to please you.

To make a comment, go to:

http://attrasoft.com

and click the email button.