Decision Tree Pruning

Pruning is a technique in decision tree that reduces the size of trees by removing sections of the tree that are non-critical and redundant to classify instances.

Pruned trees tend to be smaller and less complex. They are usually faster and better in classifying independent test data correctly.

There are two approaches to carry out tree pruning. They are prepruning and postpruning.

The prepruning apporoach is used at the early constrcution stage of decison tree. Hence further split of the tree is stopped at the given node, which become leaf node of the tree. This approach would overcome the overfitting issue.

The postpruning approach is the one in which subtrees are removed from the fully grown tree.

The cost complexity algorithm of CART and pessimistic pruning of C4.5 are example of the postpruning approach.

Gaussian Elimination - Row reduction Algorithm

Gaussian elimination is a method for solving matrix equations of the form, Ax=b. This method is also known as the row reduction algorithm. Back Substitution Solving the last equation for the variable and then work backward into the first equation to solve it. The fundamental idea is to add multiples of one equation to the others in order to eliminate a variable and to continue this process until only one variable is left. Pivot row The row that is used to perform elimination of a variable from other rows is called the pivot row. Example: Solving a linear equation The augmented matrix for the above equation shall be The equation shall be solved using back substitution. The eliminating the first variable (x1) in the first row (Pivot row) by carrying out the row operation. As the second row become zero, the row will be shifted to bottom by carrying out partial pivoting. Now, the second variable (x2) shall be eliminated by carrying out the row operation again. ...

Decision Tree - Gini Index

The Gini index is used in CART. The Gini index measures the impurity of the data set, where p i - probability that data in the data set, D belong to class, C i and pi = |C i,D |/|D| There are 2 v - 2 possible ways to form two partitions of the data set, D based on a binary split on a attribute. Each of the possible binary splits of the attribute is considered. The subset that gives the minimum Gini index is selected as the splitting subset for discrete valued attribute. The degree of Gini index varies between 0 and 1. The value 0 denotes that all elements belong to a certain class or if there exists only one class, and the value 1 denotes that the elements are randomly distributed across various classes. A Gini Index of 0.5 denotes equally distributed elements into some classes. The Gini index is biased toward multivalued attributes and has difficulty when the number of classes is large.

Clustering Analysis

Clustering is the process of grouping a set of data objects into multiple groups so that objects within a group have high similarity, but are very dissimilar to objects in other groups. The clustering would help to discover previously unknown groups within the data. The cluster analysis can be used to gain insight into the distribution of data, to observe the characteristics of each cluster, and to focus on a particular set of clusters for further analysis. The main focus has been given to distance-based cluster analysis . The Cluster analysis tools based on k-means, k-medoids, and several other methods also have been built into many statistical analysis software packages. The clustering is a form of learning by observation, rather than learning by examples. Requirement of Clustering Scalability Ability to deal various types of attributes Discovery of clusters with arbitrary shape Requirement for domain knowledge Ability to deal with noisy data Incremental clustering and insensitivity ...

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