Principal Component Analysis problem formulation

  |   Source
Principal Component Analysis problem formulation
  • PCA the most popular for DR

  • This is the graph  that we know how to make the projection line.
  • PCA try to visualize where input should project to line, hows the length of error of each element, and minimialized it
  • Second line in magenta is much worse
  • PCA should more prefer red over magenta

  • find the direction of ui (either positive or negative) and see if the projection line has the same direction, and try to minimalized the error
  • Find pair of vector that project 2D-graph(plane)   of data to visualize it
  • Try to minimalized the error between 3d position of the input and the 2D plane projection

  • Similar to linear regression? No.
  • Linear regression try to minimalized the vector between element and the projection line
  • PCA try to minimalized the MAGNITUDE between element and projection line
  • As we can see, the PCA can be diagonal (any straight line that closer to projectioin line, with angle
  • aparameters considered evenly
  • Linear regression trying to "predict y" based on x
  • There's no special variable (ie LR has "y"). All parameters treated equally

  • So PCA is trying to find a generalized 2D plane that project all the data. And also find the error and minimalize it from each point
  • Next, what it's actually does