Decision Tree Classification

A decision tree is a flowchart-like tree structure. The topmost node in a tree is the root node. The each internal node (non-leaf node) denotes a test on an attribute and each branch represents an outcome of the test. The each leaf node (or terminal node) holds a class label.

Decision trees can handle multidimensional data.

Some of the decision tree algorithms are Iterative Dichotomiser (ID3), C4.5 (a successor of ID3), Classification and Regression Trees (CART). Most algorithms for decision tree induction follow a top-down approach.

The tree starts with a training set of tuples and their associated class labels.

The algorithm is called with data partition, attribute list, and attribute selection method, where the data partition is the complete set of training tuples and their associated class labels.

The splitting criterion is determined by attribute selection method which indicates the splitting attribute that may be splitting point or splitting subset.

Attribute selection measures are also known as splitting rules as they determine how the data at a given node are to be split.

The attribute selection measure provides a ranking for each attribute. The attribute having the best score for the measure is chosen as the splitting attribute for the given tuples.

The popular attribute selection measures are information gain, gain ratio and Gini index.

Exercise 2 - Amdahl's Law

A programmer has parallelized 99% of a program, but there is no value in increasing the problem size, i.e., the program will always be run with the same problem size regardless of the number of processors or cores used. What is the expected speedup on 20 processors? Solution As per Amdahl's law, the speedup, N - No of processors = 20 f - % of parallel operation = 99% = 1 / (1 - 0.99) + (0.99 / 20) = 1 / 0.01 + (0.99 / 20) = 16.807 The expected speedup on 20 processors is 16.807

Exercise 1 - Amdahl's Law

A programmer is given the job to write a program on a computer with processor having speedup factor 3.8 on 4 processors. He makes it 95% parallel and goes home dreaming of a big pay raise. Using Amdahl’s law, and assuming the problem size is the same as the serial version, and ignoring communication costs, what is the speedup factor that the programmer will get? Solution Speedup formula as per Amdahl's Law, N - no of processor = 4 f - % of parallel operation = 95% Speedup = 1 / (1 - 0.95) + (0.95/4) = 1 / 0.5 + (0.95/4) Speedup = 3.478 The programmer gets 3.478 as t he speedup factor.

Minor, Cofactor, Determinant, Adjoint & Inverse of a Matrix

Consider a matrix Minor of a Matrix I n the above matrix A, the minor of first element a 11 shall be Cofactor The Cofactor C ij of an element a ij shall be When the sum of row number and column number is even, then Cofactor shall be positive, and for odd, Cofactor shall be negative. The determinant of an n x n matrix can be defined as the sum of multiplication of the first row element and their respective cofactors. Example, For a 2 x 2 matrix Cofactor C 11 = m 11 = | a 22 | = a 22 = 2 Determinant The determinant of A is |A| = (3 x 2) - (1 x 1) = 5 Adjoint or Adjucate The Adjoint matrix of A , adjA is the transpose of its cofactor matrix. Inverse Matrix A matrix should be square matrix to have an inverse matrix and also its determinant should not be zero. The multiplication of matrix and its inverse shall be Identity matrix. The square matrix has no inverse is called Singular. Inv A = adjA / |A| [ adjoint A / determ...

The Data Ilm

Search This Blog