Example of A Typical Concept Identification Experiment

The typical concept identification experiment involves:

  • defining an n dimensional space;
  • defining the concept within this space;
  • presenting the learner a sequence of positive and negative examples;

The example concept experiment developed here involves 4 dimensions, each of which has two values. The dimensions are:

  • Shape: Square(sq) or Circle(¬sq);
  • Size: Large(l) or Small(¬l);
  • Color: White(w) or Black(¬w);
  • Position of Shape on Field: Right(r) or Left(¬r);

where the letters in parentheses indicate the abbreviation that will be used in the figures when we describe the concept instance as a conjunction of propositions. Note that with 4 dimensions each of which can take on one of two values there are 2 to the 4th or 16 possible concept instances. Clicking on the example figure on the right will open a window in which these 16 concept instances are displayed.

     A concept definition will partition these 16 possibilities into two spaces that correspond to the positive examples and the negative examples of the concept.

     Consider the example shown to the right. Assume that this example is an instance of the concept that is to be learned. In this example a white small square is shown on the left of the field. The description of this example as a conjunctive description is shown beneath the figure. If this is the only instance, that is the concept is exactly this conjunction of features, then all of the other possibilities lie in the other element of the partition. If the concept is 'white and square', then the space is partitioned into two sets of 4 and 12 elements.

 
     In order to gain some experience with this type of task, there are two different examples of a concept identification experiment provided below. For each of them, you can present examples of a concept that you are to learn by sequentially clicking on the 'Example #' links provided. Clicking on the 'Example link' will take you to a page which contains an example from the concept space. As you look at each example sequentially, try to identify the definition of the concept. If you scroll down the page where an example is presented, you will see either a '+' or a '-' indicating whether the example is a positive or negative example of the concept. Determine whether you think that an example is positive or negative prior to scrolling to check the answer.
Experiment 1.
The first experiment provides only four examples. They are given below:
 

Example 1

Example 10

 
 

Example 4

Example 13

 
Make a note of the concept definition that you arrived at after these few examples. You may have noticed that in this experiment you were shown only positive examples of the concept. What kind of learning strategy is required to learn from positive examples only?
Experiment 2.
The next experiment uses all 16 instances from the concept space and includes positive and negative examples of the concept.
 

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Example 7

 
 

Example 8

Example 9

Example 10

Example 11

Example 12

Example 13

Example 14

Example 15

Example 16

 

     Did you identify the concept? Was there any point prior to the last example where you could be absolutely certain that you had learned the correct concept?

     Click on Possible Hypotheses to see some hypotheses that could have been considered after Example 1. Did you consider more than one of these at the time?

Possible Hypotheses after One Example

Induction,Concepts, Uncertainty
© Charles F. Schmidt