The Engineering Design Primer by Richards K. L.;

Author:Richards, K. L.;
Language: eng
Format: epub
Publisher: CRC Press LLC
Published: 2020-01-24T00:00:00+00:00

W1

Sunny

Yes

Rich

Cinema

W2

Sunny

No

Rich

Tennis

W3

Windy

Yes

Rich

Cinema

W4

Rainy

Yes

Poor

Cinema

W5

Rainy

No

Rich

Stay in

W6

Rainy

Yes

Poor

Cinema

W7

Windy

No

Poor

Cinema

W8

Windy

No

Rich

Shopping

W9

Windy

Yes

Rich

Cinema

W10

Sunny

No

Rich

Tennis

8.11 Learning Decision Trees Using Iterative Dichotomiser 3 (ID3)

8.11.1 Specifying the Problem

At this point, you now need to look at how you mentally constructed your decision tree when deciding what to do at the weekend. One way would be to use some background information as axioms and deduce what to do. For example, you might know that your parents really like going to the cinema, and that your parents are in town, so therefore (using something like Modus Ponens) you would decide to go to the cinema.

Another way in which you might have made up your mind was by generating from previous experiences. Imagine that you remembered all the times when you had a really good weekend. A few weeks back, it was sunny and your parents were not visiting, you played tennis and it was good. A month ago, it was raining and you were penniless, but a trip to the cinema cheered you up. And so on. This information could have guided your decision-making, and if that was the case, you would have used an inductive, rather than deductive, method to construct your decision tree. In reality, it is likely that human’s reason to take decisions use both inductive and deductive processes combined.

We can state the problem of learning decision trees as follows.

We have a set of examples correctly categorised into categories (decisions). We also have a set of attributes describing the examples and each attribute has a finite set of values which it can possibly take. We want to use the examples to learn the structure of a decision tree which can be used to decide the category of the unseen question.

Assuming that there are no inconstancies in the data (when two examples have exactly the same values for the attributes, but are categorised differently), it is obvious that we can always construct a decision tree to correctly decide for the training cases with 100% accuracy. All we have to do is to make sure every situation is catered for down some branch of the decision tree. Of course, 100% accuracy may indicate over-fitting.

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