Data visualization is a general term that describes any effort to help people understand the significance of data by placing it in a visual context. Patterns, trends and correlations that might go undetected in text-based data can be exposed and recognized easier with data visualization.
With interactive visualization, we can take the concept a step further by using technology to drill down into charts and graphs for more detail, interactively changing what data we see and how it’s processed.
Python provides a module to plot and visualize data called matplotlib.Together with numpy module, you can perform analysis, calculate numbers and represent data as models.
Let us go through each of the models one by one
Note: I have taken random values to create graphs or plot data below.
A bar chart represents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally.Below is a bar chart that shows the performance of students when put under Prof B and Prof G. Clearly Prof B is a better teacher.
When we represent two or more plots that share the same x or y axis, they are called sub plots.Below we have two graph representations sin and cos that share the same x axis.
A histogram is a graphical display of data using bars of different heights. In a histogram, each bar groups numbers into ranges. Taller bars show that more data falls in that range.They more or less follow the normal distribution.
Normal Distribution
There are cases where the data tends to be around a central value with no bias left or right, and it gets close to what is called 'Normal Distribution' like below.
Many things closely follow a Normal Distribution such as heights of people, blood pressure etc. Below is a histogram that follows Normal Distribution.
A pie chart is a circular statistical graph which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice, is proportional to the quantity it represents. Below is a pie chart that represents my monthly expenses and how much I am able to save every month.Clearly I am able to save only 23% of my pocket money.Gotta start saving more!
A box plot is a standardized way of displaying the distribution of data based on the five number summary.
Five number Summary
Five number summary consists of the following parameters: minimum, first quartile, median, third quartile, and maximum. Any data can be represented by a Five number summary that gives an overall view of the data.
Below is a box plot that gives information about the five parameters.
Clearly looking at it, we can derive the following information
min: 0.93
Q1: (0.9 - 16.9)
median: 17.24
Q3: (68.91 - 98.04)
max: 98.04
A line plot is a graph that shows the frequency of data occuring along a number line.Below is a line plot where the sin(x) and cos(x) finctions are plotted on the number line.
A Scatter (XY) Plot has points that show the relationship between two sets of data.Below is a scatter plot that shows the relationship (X, Y) for the two sets of data X and Y.
A quiver plot displays velocity vector as arrows with components (u, v) at the points (x, y).
x, y: The coordinate for the point u, v: The displacement for eg x has moved by u and y has moved by v
quiver(x, y, u, v) plots vectors as arrows at the coordinates specified in each pair of elements in x and y
Below is a quiver plot for x and y axis each of (-10, 10).
It can be used for example to plot ocean currents.
It displays a three-dimensional plot of a set of data points.Below is a quiver plot that generates a 3D plot for given points along X, Y and Z axis.
It is a three-dimensional surface plot that plots the values in matrix Z as heights above a grid in the x-y plane defined by X and Y.
Below is a 3D surface plot that generates a surface for given points along X, Y and Z axis.Here z is a function of x and y where for each value of x and y, z is the sum of square of x and y.
Now let us do some real world analysis of data.I have implemented a scatter plot to display word frequency for a given word in a book.
The book is titled 'The Art of Public Speaking' by Dale Carnegie (it is an amazing book by the way!) available for free from the website www.gutenberg.org.You can use the Linux commad below to download the content of the book and save it to a .txt file.
curl http://www.gutenberg.org/cache/epub/16317/pg16317.txt --output public-speaking.txt
Let us look for the occurence of a word confidence in the book.Below is a scatter plot for the result obtained.
Clearly we can see that the word 'confidence' has a rank of 576 and has occured around 50 times.
Let us do it once again for another word.Let us look for the occurence of a word public
Once again we can see that the word 'public' has a rank of 110 and has occured around 100 times.