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Understanding the Covariance Matrix | DataScience+

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This article is showing a geometric and intuitive explanation of the covariance matrix and the way it describes the shape of a data set. We will describe the geometric relationship of the covariance matrix with the use of linear transformations and eigendecomposition. Before we get started, we shall take a quick look at the difference between covariance and variance. Variance measures the variation of a single random variable (like the height of a person in a population), whereas covariance is a measure of how much two random variables vary together (like the height of a person and the weight of a person in a population). The formula for variance is given by σ 2 x = 1 n − 1 n ∑ i = 1 ( x i – ¯ x ) 2 σx2=1n−1∑i=1n(xi–x¯)2 where n n is the number of samples (e.g. the number of people) and ¯ x x¯ is the mean of the random variable x x (represented as a vector). The covariance σ ( x , y ) σ(x,y) of two random variables x x and y y is given by σ ( x , y ) = 1 n − 1 n ∑ i = 1

Understanding the Covariance Matrix August 3, 2018 · 9 min read · 482.5K views · 17 comments Share: This article is showing a geometric and intuitive explanation of the covariance matrix and the way it describes the shape of a data set. We will describe the geometric relationship of the covariance matrix with the use of linear transformations and eigendecomposition. Introduction Before we get started, we shall take a quick look at the difference between covariance and variance. Variance measures the variation of a single random variable (like the height of a person in a population), whereas co

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