Because the decoding function is not necessarily linear. Check kernel PCA.
Read more… (11 words)
Active In
Deep Learning Book
Machine Learning
Artificial Intelligence
Competitive Programming
Featured Contributions
NaN.
discussion
Chapter 2: Linear Algebra
If you're reading Deep Learning Book, feel free to ask questions, discuss the material or share resources.
Below is a video from a book club in San Francisco, ...
Read more…(37 words)
reply in this discussion
NaN.
discussion
Chapter 2: Linear Algebra
If you're reading Deep Learning Book, feel free to ask questions, discuss the material or share resources.
Below is a video from a book club in San Francisco, ...
Read more…(37 words)
reply in this discussion
Here's a bit more detailed proof (the moderator can check for any errors in the proof):
consider this:
x = d_1d_1^Tx + d_2d_2^Tx + ... + d_nd_n^Tx\\
\text{where } d_i \text{ is the }i^{th}\text{ principal compopnent ordered based on:}\\
^{max}_{d_i}\ d_i^TX^TXd_i^T
if we want to use the first l principal components represented by Dl, we have the reconstruction error:
error = x - D_lD_l^Tx = d_{l+1}d_{l+1}^Tx + .. + d_nd_n^Tx
Now if want to use an additional principal component, one good idea to do it is to extract the first PC of the above error, which will follow the same way when extracting the first PC of X.
let:
Read more… (172 words)