# 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