Lecture 8

• Lecture 8
  • Video
  • Topics
  • PCA

Video

link

Topics

• dimensionality reduction
  • Principal Component Analysis - PCA
  • Singular Valued Decomposition - SVD

PCA

• to reduce number of dimensions
• why?
  • we might not have enough computational power

• the cameras placed are arbitrary oriented

• so how do we remove unwanted data

• I have to fidure out from these 3 figures ki movement is along x-axis

• red and green lines depict a line along which I am projecting
• red line me bahut error
• data points ke term me variance is more in red line
• green is the best fit line
• so find best fit line
• aagr 3d data hai, best fit plane nikal
• agar n-d space hai find n-1 dimensional hyperplane
• so pca ko kisi bhi dimensions pe laga sakte
• I want to reduce one dimension out of the two, the new dimension need not be either of these axes
• say x ya y ko remove karna, toh project kar x and y pe, yaha pe I will choose x (one having largest variance)
• but x axis does not have largest variance
• so we need to find a new dimension, which I should keep
• What PCA does?
  • I will rotate x axis, to get max variance
  • and orthogonal
• PCA allows to order dimensions wrt variance ind ecreasing order