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. According to this lesson, what do PCA (Lesson 6) and camera projection (P = K[R|t]) have in common?
Both compute a projection via a dot product between a fixed direction and the input coordinates; they differ only in how that direction was chosen.
. What single operation does the lesson show convolution, the Fourier transform, and a homography all secretly are?
Each output value in all three is a dot product between the input and a fixed row/kernel/basis function, which is exactly what one row of a matrix multiply computes.
. What can a single linear projection classifier never do, regardless of how w and b are chosen?
A single projection can only produce a straight-line (hyperplane) decision boundary, and no straight line can separate a ring from the disk it encloses.
. In the classification example, what determines which side of the decision boundary a point falls on?
Points are classified by thresholding the projected score at zero: positive score means one class, negative means the other.