AGMDA Course Project Solution

  1. Consider the vector dataset D given in the link https://archive.ics.uci.edu/ml/datasets/Human+Activity+Recognition+Using+Smartphones# with jDj = N such that each v 2 D is embedded in a suitable R D of min-

imum possible dimension D. Construct a suitable subspace S  RD of

ln

p

N

0:05

dimension at most  O

0:01

such that at least 95% of the pairwise

distances between the points in D and their corresponding projections to S do not di er by more than a factor of 0:1. Now produce the best- t of

    ◦ along this S.

  2. Construct the top k-SVD subspace Vk for D such that the ratio of t of

    ◦ along Vk to the t of D along V (the full SVD-subspace) does not fall below 0:1. Having obtained this Vk, compare this t with the t obtained in Part 1 above. Discuss the results.

  3. Generate a dataset D0 which has the same dimensions as the original dataset D such that each v 2 D0 is distributed N (0; ). Choose such that it is non-zero in all its elements. Now nd the probability of the following events:

P

pjDj

1:05 max(

p

) + q

n

max(D0)

tr( )

P

q

pjDj

0:95 min(

)

n

min(D0)

p

tr( )

by repeated generation of such a dataset under your same chosen .