Principal component analysis

aka Principal Component Analysis (PCA)

Unsupervised Learning §

• Find the direction in which the data varies the most and use it as the base axis.

• Find the direction in which the data varies the most with respect to that axis and use it as the second axis.

  • Repeat this process for a total of {number of dimensions} times.

• This will result in new axes arranged in order of variability.

• By plotting the data in a 2D plot using the first and second axes of highest variability, the cancer example looks like this.

  • This is based on the hypothesis that the most variable feature is the most meaningful feature.
    • If the hypothesis is correct, the data will be well classified.

• Think of it as sorting the dimensions by importance.

• Applications: feature extraction, visualizing data in a single graph.

  • Feature extraction: Data can have a form that is more suitable for visualization than its original form.

• 

• Challenge: Humans cannot understand the meaning of the transformed axes.