Book Image

Mathematica Data Visualization

By : Nazmus Saquib
Book Image

Mathematica Data Visualization

By: Nazmus Saquib

Overview of this book

Table of Contents (12 chapters)

Chapter 1. Visualization as a Tool to Understand Data

In the last few decades, the quick growth in the volume of information we produce and the capacity of digital information storage have opened a new door for data analytics. We have moved on from the age of terabytes to that of petabytes and exabytes. Traditional data analysis is now augmented with the term big data analysis, and computer scientists are pushing the bounds for analyzing this huge sea of data using statistical, computational, and algorithmic techniques.

Along with the size, the types and categories of data have also evolved. Along with the typical and popular data domain in Computer Science (text, image, and video), graphs and various categorical data that arise from Internet interactions have become increasingly interesting to analyze. With the advances in computational methods and computing speed, scientists nowadays produce an enormous amount of numerical simulation data that has opened up new challenges in the field of Computer Science.

Simulation data tends to be structured and clean, whereas data collected or scraped from websites can be quite unstructured and hard to make sense of. For example, let's say we want to analyze some blog entries in order to find out which blogger gets more follows and referrals from other bloggers. This is not as straightforward as getting some friends' information from social networking sites. Blog entries consist of text and HTML tags; thus, a combination of text analytics and tag parsing, coupled with a careful observation of the results would give us our desired outcome.

Regardless of whether the data is simulated or empirical, the key word here is observation. In order to make intelligent observations, data scientists tend to follow a certain pipeline. The data needs to be acquired and cleaned to make sure that it is ready to be analyzed using existing tools. Analysis may take the route of visualization, statistics, and algorithms, or a combination of any of the three. Inference and refining the analysis methods based on the inference is an iterative process that needs to be carried out several times until we think that a set of hypotheses is formed, or a clear question is asked for further analysis, or a question is answered with enough evidence.

Visualization is a very effective and perceptive method to make sense of our data. While statistics and algorithmic techniques provide good insights about data, an effective visualization makes it easy for anyone with little training to gain beautiful insights about their datasets. The power of visualization resides not only in the ease of interpretation, but it also reveals visual trends and patterns in data, which are often hard to find using statistical or algorithmic techniques. It can be used during any step of the data analysis pipeline—validation, verification, analysis, and inference—to aid the data scientist.

How have you visualized your data recently? If you still have not, it is okay, as this book will teach you exactly that. However, if you had the opportunity to play with any kind of data already, I want you to take a moment and think about the techniques you used to visualize your data so far. Make a list of them.

Done? Do you have 2D and 3D plots, histograms, bar charts, and pie charts in the list? If yes, excellent! We will learn how to style your plots and make them more interactive using Mathematica. Do you have chord diagrams, graph layouts, word cloud, parallel coordinates, isosurfaces, and maps somewhere in that list? If yes, then you are already familiar with some modern visualization techniques, but if you have not had the chance to use Mathematica as a data visualization language before, we will explore how visualization prototypes can be built seamlessly in this software using very little code.

The aim of this book is to teach a Mathematica beginner the data-analysis and visualization powerhouse built into Mathematica, and at the same time, familiarize the reader with some of the modern visualization techniques that can be easily built with Mathematica. We will learn how to load, clean, and dissect different types of data, visualize the data using Mathematica's built-in tools, and then use the Mathematica graphics language and interactivity functions to build prototypes of a modern visualization.

In this chapter, we will look at a few simple examples that demonstrate the importance of data visualization. We will then discuss the types of datasets that we will encounter over the course of this book, and learn about the Mathematica interface to get ourselves warmed up for coding.