Book Image

Data Science Using Python and R

By : Chantal D. Larose, Daniel T. Larose
Book Image

Data Science Using Python and R

By: Chantal D. Larose, Daniel T. Larose

Overview of this book

Data science is hot. Bloomberg named a data scientist as the ‘hottest job in America’. Python and R are the top two open-source data science tools using which you can produce hands-on solutions to real-world business problems, using state-of-the-art techniques. Each chapter in the book presents step-by-step instructions and walkthroughs for solving data science problems using Python and R. You’ll learn how to prepare data, perform exploratory data analysis, and prepare to model the data. As you progress, you’ll explore what are decision trees and how to use them. You’ll also learn about model evaluation, misclassification costs, naïve Bayes classification, and neural networks. The later chapters provide comprehensive information about clustering, regression modeling, dimension reduction, and association rules mining. The book also throws light on exciting new topics, such as random forests and general linear models. The book emphasizes data-driven error costs to enhance profitability, which avoids the common pitfalls that may cost a company millions of dollars. By the end of this book, you’ll have enough knowledge and confidence to start providing solutions to data science problems using R and Python.
Table of Contents (20 chapters)
Free Chapter
1
ABOUT THE AUTHORS
17
INDEX
18
END USER LICENSE AGREEMENT

9.4 THE SIGMOID ACTIVATION FUNCTION

A common activation function is the sigmoid function

equationy=f(x)=11+ex--

Why use the sigmoid function? Because it combines nearly linear behavior, curvilinear behavior, and nearly constant behavior, depending on the value of the input. Figure 9.4 shows the graph of the sigmoid function for −5 < x < 5. Through much of the center of the domain of the input x (e.g. –1 < x < 1), the behavior of f(x) is nearly linear. As the input moves away from the center, f(x) becomes curvilinear. By the time the input reaches extreme values, f(x) becomes nearly constant.

Image described by caption and surrounding text.

Figure 9.4 Graph of the sigmoid function y = f(x) = 1/(1 + ex).

Moderate increments in the value of x produce varying increments in the value of f(x), depending on the location of x. Near the center, moderate increments in the value of x produce moderate increments in the value of f(x); however...