I have two quesitons about the Principal Component Analysis (PCA) videos and labs.

- What are some real-life use cases of PCA? I understand that it can help with visualization, but once you visualize the data in fewer dimensions using the new primary components as axes, what does that mean for the data and next steps?
- For example, in the lab we went from 1000 dimensions to 2 and then 3, and this shows that the data is clustered. But what does this clustering mean?
- Do we then use k-means clustering to understand what the clusters are, and then using the PCA transformation know how much each of the 1000 dimensions contribute to the cluster?
- It seems like we removed a bunch of data until we are able to find a pattern. It feels like a hack, like â€śif we prune the data using this systematic approach we end up with a pattern which is goodâ€ť, but what about all the information that is lost? Does that mean that the extra data is not useful for finding patterns?
**My point is that it feels like there is a missing video explaining the significance, usefulness and real-life examples of PCA.**- We used PCA in the Math for ML Specialization to compress an image (which was pretty cool TBH), but this specialization says thatâ€™s an antiquated use case.

- In the lab for PCA (see screenshots below), the
`explained_variance_ratio_`

says that we were able to preserve about 15% of the variance using 2D and about 20% of the variance if we use 3D.- Is this a good percentage? I know we are going down from 1000 to 2 or 3 dimensions, so it seems good that only 3 dimensions have 20% of the information.
- But 15% or 20% seems little, no? Whatâ€™s the significance of finding these 8 to 10 clusters if they are missing most of the information in the original data?

Thanks in advance for any suggestions and clarifications!