typos in pca

2020-01-03 11:12:22 +01:00
parent 011f787528
commit 59d4b6253d
10 changed files with 24 additions and 24 deletions
@@ -829,7 +829,7 @@ specific case.

 === Compute the sample covariance ===

-Now we are going to use the mean centered data to compute the sample covariance of the data. 
+Now we are going to use the mean centered data to compute the sample covariance of the data by using the following equation
 !bt
 \begin{equation*}
 \Sigma_n = \frac{1}{n-1} \sum_{i=1}^n \bar{x}_i^T \bar{x}_i = \frac{1}{n-1} \sum_{i=1}^n (x_i - \mu_n)^T (x_i - \mu_n)
@@ -841,8 +841,8 @@ We can write our own code or simply use either the functionaly of _numpy_ or tha
 print(df.cov())
 print(np.cov(X_centered.T))
 !ec
-Note that the way we define the covariance matrix here has a factor $n-1$ instead of $n$.
-Our own code here is not very elegant and asks for improvements. 
+Note that the way we define the covariance matrix here has a factor $n-1$ instead of $n$. This is included in the _cov()_ function by _numpy_ and _pandas_. 
+Our own code here is not very elegant and asks for obvious improvements. It is tailored to this specific $2\times 2$ covariance matrix. 
 !bc pycod
 # extract the relevant columns from the centered design matrix of dim n x 2
 x = X_centered[:,0]