While working through the previous two chapters, you may have felt that some of the material was esoteric and abstract. Perhaps you felt that the challenge of learning linear algebra wouldn’t pay off in understanding real-world applications in data science and machine learning.
I hope that this chapter dispels you of these doubts. In this chapter, you will learn how vectors and vector operations are used in data science analyses. And you will be able to extend this knowledge by working through the exercises.
Correlation and Cosine Similarity
Correlation is one of the most fundamental and important analysis methods in statistics and machine learning. A correlation coefficient is a single number that quantifies the linear relationship between two variables. Correlation coefficients range from −1 to +1, with −1 indicating a perfect negative relationship, +1 a perfect positive relationships, and 0 indicating no linear relationship. Figure 4-1 shows a few examples of pairs of variables and their correlation coefficients.
Figure 4-1. Examples of data exhibiting positive correlation, negative correlation, and zero correlation. The lower-right panel illustrates that correlation is a linear measure; nonlinear relationships between variables can exist even if their correlation is zero.
In Chapter 2, I mentioned that the dot product is involved in the correlation ...
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