Let’s reiterate the learnings of the past two sessions:
- You understood the concept of basis vectors and how they’re helpful in the representation of data points.
- You then learnt about how you can use different basis vectors to represent the same information.
- Using the previous knowledge, you came to know that when represented under some ‘ideal basis vectors’, it becomes easier for us to do dimensionality reduction. However, you didn’t exactly know how to find those ideal basis vectors.
- Then you learnt about the concept of variance and how more variance meant more information.
- Then you derived that the more important columns in a dataset are the ones which capture more variance than the others.
- Subsequently, you deduced that the most important directions, rather than just columns, are those that capture maximum variance. The ideal basis vectors that we talked about in the previous case are in fact those that do the same.
- These basis vectors or directions that capture the maximum variance are essentially the Principal Components for the dataset.
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