Principal Component Analysis

From Latent Variable Methods in Engineering
Jump to navigation Jump to search
Video material
Download video: Link (plays in Google Chrome) [290.1Mb]

Video timing

  • 00:00 to 21:37 Recap and overview of this class
  • 21:38 to 42:01 Preprocessing: centering and scaling
  • 42:02 to 57:07 Geometric view of PCA

Class notes

<pdfreflow> class_date = 16 September 2011 [1.65 Mb] button_label = Create my projector slides! show_page_layout = 1 show_frame_option = 1 pdf_file = lvm-class-2.pdf </pdfreflow>

Class preparation

Class 2 (16 September)

  • Reading for class 2
  • Linear algebra topics you should be familiar with before class 2:
    • matrix multiplication
    • that matrix multiplication of a vector by a matrix is a transformation from one coordinate system to another (we will review this in class)
    • linear combinations (read the first section of that website: we will review this in class)
    • the dot product of 2 vectors, and that they are related by the cosine of the angle between them (see the geometric interpretation section)

Class 3 (23 September)

  • Least squares:
    • what is the objective function of least squares
    • how to calculate the two regression coefficients \(b_0\) and \(b_1\) for \(y = b_0 + b_1x + e\)
    • understand that the residuals in least squares are orthogonal to \(x\)
  • Some optimization theory:
    • how an optimization problem is written with equality constraints
    • the Lagrange multiplier principle for solving simple, equality constrained optimization problems

Update

This illustration should help better explain what I trying to get across in class 2B

Geometric-interpretation-of-PCA-xhat-residuals.png