 Good at finding low dimensional structure in high dimensional data 
Methods:
Multidimensional scaling (MDS): attempts to find a distance-preserving low-dimensional projection
Preserves information about how points in original dataspace are close to each other


Manifold learning algorithms

*Understanding PCA*. (2020, January). GitHub. Retrieved from [github.com/gskdhiman/Understanding-PCA](https://github.com/gskdhiman/Understanding-PCA) 

University of Michigan - Ann Arbor

This article uses a small dataset to show how PCA works steps by steps, it has the same result with sklearn library.
- Step 1: Standardize the dataset.
- Step 2: Calculate the covariance matrix for the features in the dataset.
- Step 3: Calculate the eigenvalues and eigenvectors for the covariance matrix.
- Step 4: Sort eigenvalues and their corresponding eigenvectors.
- Step 5: Pick k eigenvalues and form a matrix of eigenvectors.
- Step 6: Transform the original matrix.


Steps Involved in the PCA

Pang, Peter. Intuitive Machine Learning. Instagram. Retrieved from [www.instagram.com/machinelearning/](https://www.instagram.com/machinelearning/) 

@machinelearning

Understanding PCA

Singh, Gursewak. *Understanding Principle Component Analysis(PCA) step by step*. (2020, January 7). Medium. Retrieved from [medium.com/analytics-vidhya/understanding-principle-component-analysis-pca-step-by-step-e7a4bb4031d9](https://medium.com/analytics-vidhya/understanding-principle-component-analysis-pca-step-by-step-e7a4bb4031d9) 

Understanding Principle Component Analysis(PCA) step by step.

Eigenvalues and eigenvectors. (2021, February 05). Retrieved February 07, 2021, from https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

Eigenvector and eigenvalues

Eigenvector is the vector whose direction will not change if we apply a linear transformation to it.  To be more specific, if Matrix A times vector v equals to λ times v. Then we can say, v is the eigenvector of matrix A , λ is the eignevalue of v. Given an matrix A, we might have multiple λ v pairs that can complete this equation.

Learn Before

Related

Learn After