How PCA works step by step?

How do you do a PCA?

1. Standardize the range of continuous initial variables.
2. Compute the covariance matrix to identify correlations.
3. Compute the eigenvectors and eigenvalues of the covariance matrix to identify the principal components.
4. Create a feature vector to decide which principal components to keep.

How does PCA standardize data?

There are 6ish steps to PCA:

1. Standardize data.
2. Construct covariance matrix.
3. Extract eigenvectors and eigenvalues from the covariance matrix.
4. Sort the eigenvalues (and their eigenvectors!) in decreasing order.
5. Select a number of components to care about (and keep)
6. Transform your dataset.

How does normalization affect PCA?

Normalization is important in PCA since it is a variance maximizing exercise. It projects your original data onto directions which maximize the variance. The first plot below shows the amount of total variance explained in the different principal components wher we have not normalized the data.

How do you solve PCA?

Mathematics Behind PCA

1. Take the whole dataset consisting of d+1 dimensions and ignore the labels such that our new dataset becomes d dimensional.
2. Compute the mean for every dimension of the whole dataset.
3. Compute the covariance matrix of the whole dataset.
4. Compute eigenvectors and the corresponding eigenvalues.

Does PCA need normalization?

Yes, it is necessary to normalize data before performing PCA. The PCA calculates a new projection of your data set. And the new axis are based on the standard deviation of your variables.

What is normalization and standardization?

Normalization typically means rescales the values into a range of [0,1]. Standardization typically means rescales data to have a mean of 0 and a standard deviation of 1 (unit variance).