The equation 10.37a shown above uses the coordinates zdn for the original data point xn. The limits used for the summation are from d = 1 to D. Also, It is concluded in one of the points (on Page no 328 - 329) that coordinates of original data point x and projected data point x̃ are identical for limits only from m = 1 to M as shown below
where equations 10.26 and 10.27 are shown below
So, why are we using the coordinates zdn for the original data point xn in 10.37a for the limit from d = 1 to D?
isn't it should be only from d = 1 to M?
Location
version 29-7-2021
Chapter 10
page 330
equation number 10.37a
Proposed solution
The equation 10.37a can be modified as
Here, from the limit d = 1 to M, we have used the coordinates identical to the ones used in projected points while from p = M+1 to D, some suitable coordinates ζ pn are used.
The equation 10.37a shown above uses the coordinates zdn for the original data point xn. The limits used for the summation are from d = 1 to D. Also, It is concluded in one of the points (on Page no 328 - 329) that coordinates of original data point x and projected data point x̃ are identical for limits only from m = 1 to M as shown below
So, why are we using the coordinates zdn for the original data point xn in 10.37a for the limit from d = 1 to D? isn't it should be only from d = 1 to M?
Location
Proposed solution The equation 10.37a can be modified as
Here, from the limit d = 1 to M, we have used the coordinates identical to the ones used in projected points while from p = M+1 to D, some suitable coordinates ζ pn are used.
Please clarify.