Data and its types

The data have been stored in different types in various applications based on the needs. The popular form of the data is in tabular form such as given below.

The tabular data shown above has few rows and columns. The each row represents each record. The each column represents the different attributes of each record.

The record is also referred as Sample, Instance, Case etc.

The attribute of a record is also referred as Variable, Field, Feature etc.

The attribute of the record shall be captured in different types. They are

Nominal - Provides distinguishable information such as Student ID, Gender etc

Ordinal - Provides comparable information such as Score, Grades etc

Interval - Provides interval information such as Dates etc

Ratio - Provides ratio information such as Age, Height etc

The properties of attribute values shall be

Distinctness [ Equal to or Not Equal to ]
Ordering [ Greater than or Less than ]
Addition/Subtraction
Multiplication/Division

The attributes of the record shall possess the properties based on its type.

Nominal - Distinctness

Ordinal - Distinctness & Ordering

Interval - Distinctness, Ordering & Addition/Subtraction

Ratio - Distinctness, Ordering, Addition/Subtraction & Multiplication/Division

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.

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

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. ...

The Data Ilm

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