Principal Component Analysis

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>

• Also download these 3 CSV files and bring them on your computer:
  • Peas dataset: http://datasets.connectmv.com/info/peas
  • Food texture dataset: http://datasets.connectmv.com/info/food-texture
  • Food consumption dataset: http://datasets.connectmv.com/info/food-consumption

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

• Reading on cross validation