5、Understanding Covariance, Correlation, and High-Dimensional Spaces

Understanding Covariance, Correlation, and High-Dimensional Spaces

1. Covariance and Correlation Basics

Variables can be related to one another. For example, the outside temperature and the chance of snow have a negative relationship. As the temperature rises, the chance of snow decreases. Conversely, the temperature and the number of people swimming in a local lake have a positive relationship; on warmer days, there are more swimmers.

Finding and measuring these relationships is useful. When teaching an algorithm to extract information from a dataset, if two values are strongly related, one can be removed as it’s redundant. This can improve training speed and results.

1.1 Covariance

• Definition : When two