Appendix B. Mathematical Formulas
Throughout the book I have introduced a number of mathematical concepts. This appendix covers selected concepts and gives a description, relevant formulas, and code for each of them.
Euclidean distance finds the distance between two points in multidimensional space, which is the kind of distance you measure with a ruler. If the points are written as (p1, p2, p3, p4, ...) and (q1, q2, q3, q4, ...), then the formula for Euclidean distance can be expressed as shown in Figure B-1.
Figure B-1. Euclidean distance
A clear implementation of this formula is shown here:
def euclidean(p,q): sumSq=0.0 # add up the squared differences for i in range(len(p)): sumSq+=(p[i]-q[i])**2 # take the square root return (sumSq**0.5)
Euclidean distance is used in several places in this book to determine how similar two items are.
Pearson Correlation Coefficient
The Pearson correlation coefficient is a measure of how highly correlated two variables are. It is a value between 1 and −1, where 1 indicates that the variables are perfectly correlated, 0 indicates no correlation, and −1 means they are perfectly inversely correlated.
Figure B-2 shows the Pearson correlation coefficient.
Figure B-2. Pearson correlation coefficient
This can be implemented with the following code: ...