A decision tree is a graph that uses a branching method to illustrate every possible outcome of a decision. Informally, decision trees are useful for focusing discussion when a group must make a decision. A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements.

Decision tree is the most powerful and popular tool for classification and prediction. A Decision tree is a flowchart like tree structure, where each internal node denotes a test on an attribute, each branch represents an outcome of the test, and each leaf node (terminal node) holds a class label.

A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test, and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represent classification rules.

In decision analysis, a decision tree and the closely related influence diagram are used as a visual and analytical decision support tool, where the expected values (or expected utility) of competing alternatives are calculated.

A decision tree consists of three types of nodes:

1. Decision nodes – typically represented by squares
2. Chance nodes – typically represented by circles
3. End nodes – typically represented by triangles

Decision trees are commonly used in operations research and operations management. If, in practice, decisions have to be taken online with no recall under incomplete knowledge, a decision tree should be paralleled by a probability model as a best choice model or online selection model algorithm. Another use of decision trees is as a descriptive means for calculating conditional probabilities.

Decision trees, influence diagrams, utility functions, and other decision analysis tools and methods are taught to undergraduate students in schools of business, health economics, and public health, and are examples of operations research or management science methods.

Decision rules

The decision tree can be linearized into decision rules, where the outcome is the contents of the leaf node, and the conditions along the path form a conjunction in the if clause. In general, the rules have the form:

       *if* condition1 *and* condition2 *and* condition3 *then* outcome.

Decision rules can be generated by constructing association rules with the target variable on the right. They can also denote temporal or causal relations.

Decision tree using flowchart symbols

Commonly a decision tree is drawn using flowchart symbols as it is easier for many to read and understand.

Construction of Decision Tree :

A tree can be “learned” by splitting the source set into subsets based on an attribute value test. This process is repeated on each derived subset in a recursive manner called recursive partitioning. The recursion is completed when the subset at a node all has the same value of the target variable, or when splitting no longer adds value to the predictions. The construction of decision tree classifier does not require any domain knowledge or parameter setting, and therefore is appropriate for exploratory knowledge discovery. Decision trees can handle high dimensional data. In general decision tree classifier has good accuracy. Decision tree induction is a typical inductive approach to learn knowledge on classification.

Decision Tree Representation :

Decision trees classify instances by sorting them down the tree from the root to some leaf node, which provides the classification of the instance. An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute as shown in the above figure. This process is then repeated for the subtree rooted at the new node.

The decision tree in above figure classifies a particular morning according to whether it is suitable for playing tennis and returning the classification associated with the particular leaf. (in this case Yes or No).

For example,the instance

(Outlook = Rain, Temperature = Hot, Humidity = High, Wind = Strong )

would be sorted down the leftmost branch of this decision tree and would therefore be classified as a negative instance.

In other words we can say that decision tree represent a disjunction of conjunctions of constraints on the attribute values of instances. (Outlook = Sunny ^ Humidity = Normal) v (Outllok = Overcast) v (Outlook = Rain ^ Wind = Weak)

Here’s a simple example: An email management decision tree might begin with a box labeled “Receive new message.” From that, one branch leading off might lead to “Requires immediate response.” From there, a “Yes” box leads to a single decision: “Respond.” A “No” box leads to “Will take less than three minutes to answer” or “Will take more than three minutes to answer.” From the first box, a box leads to “Respond” and from the second box, a branch leads to “Mark as task and assign priority.” The branches might converge after that to “Email responded to? File or delete message.”

Advantages and disadvantages

Among decision support tools, decision trees (and influence diagrams) have several advantages. Decision trees:

• Decision trees are able to generate understandable rules. They are simple to understand and interpret.
• Decision trees perform classification without requiring much computation.
• Decision trees are able to handle both continuous and categorical variables.
• Decision trees provide a clear indication of which fields are most important for prediction or classification.
• Have value even with little hard data. Important insights can be generated based on experts describing a situation (its alternatives, probabilities, and costs) and their preferences for outcomes.
• Help determine worst, best and expected values for different scenarios.
• Use a white box model. If a given result is provided by a model.
• Can be combined with other decision techniques.

Disadvantages of decision trees:

• They are unstable, meaning that a small change in the data can lead to a large change in the structure of the optimal decision tree.
• They are often relatively inaccurate. Many other predictors perform better with similar data. This can be remedied by replacing a single decision tree with a random forest of decision trees, but a random forest is not as easy to interpret as a single decision tree.
• For data including categorical variables with different number of levels, information gain in decision trees is biased in favor of those attributes with more levels.
• Calculations can get very complex, particularly if many values are uncertain and/or if many outcomes are linked.
• Decision trees are less appropriate for estimation tasks where the goal is to predict the value of a continuous attribute.
• Decision trees are prone to errors in classification problems with many class and relatively small number of training examples.
• Decision tree can be computationally expensive to train. The process of growing a decision tree is computationally expensive. At each node, each candidate splitting field must be sorted before its best split can be found. In some algorithms, combinations of fields are used and a search must be made for optimal combining weights. Pruning algorithms can also be expensive since many candidate sub-trees must be formed and compared.