Linked Questions

25
votes
2answers
24k views

Reversing PCA back to the original variables [duplicate]

I have a set of data that has $n$ samples described by $m$ variables. I do a PCA to reduce it to just 2 dimensions so I can make a nice 2D plot of the data. I understand that the $x,y$ coordinates (i....
1
vote
1answer
2k views

How to remove technical noise by discarding several leading PCA components? [duplicate]

I have a large metabolomics dataset, 6000 samples and 3300 features. For the samples the only thing that differentiates each sample from the rest is that one gene was knocked out, which will not ...
4
votes
0answers
1k views

How do I remove the first principal component from a data set, while keeping it in the original coordinates? [duplicate]

I would like to remove the first principal component from a data set, but keep that data set in its original coordinates. I have taken a stab at this by taking PCA, zeroing the first PC, and then ...
1
vote
1answer
993 views

Reconstruction of original dataset through loadings in PCA [duplicate]

I am very new to PCA and I was trying, just as excercize, to reconstruct original dataset from loadings. Let's suppose I have a matrix A corresponding to the original dataset and C that is the z-...
1
vote
1answer
523 views

Reversing SVD back to the original variables [duplicate]

I have a data matrix $M$ that has $n$ samples (rows) described by $m$ variables (columns) $X_1,X_2,\ldots X_m$. I do a SVD to reduce the $m$ dimensions to just 3 dimensions. I understand that the $x,y,...
1
vote
1answer
265 views

SVD PCA reconstruction of data [duplicate]

I have some data about the $\{noise,~ size,~ speed,~ length,~ width\}$ of cars. I have performed SVD, and I want to reconstruct my data using only the first 2 principal components. I subtracted mean ...
2
votes
0answers
156 views

Reconstruct the data using first principal component [duplicate]

I would like to know how do I reconstruct the data using only the first principal component of the PCA?
0
votes
1answer
89 views

How to recreate a particular image from PCA from a database of images? [duplicate]

Please forgive if this is a repeat but I couldn't find a similar question (at least as it pertains to me). I have a database of 30,000 images of digits (0-9). Every image is 28*28. So, every image is ...
999
votes
28answers
595k views

Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
215
votes
14answers
230k views

What are the differences between Factor Analysis and Principal Component Analysis?

It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...
361
votes
3answers
232k views

Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
157
votes
7answers
120k views

PCA on correlation or covariance?

What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
30
votes
4answers
34k views

How to perform dimensionality reduction with PCA in R

I have a big dataset and I want to perform a dimensionality reduction. Now everywhere I read that I can use PCA for this. However, I still don't seem to get what to do after calculating/performing ...
20
votes
2answers
28k views

PCA in numpy and sklearn produces different results

Am i misunderstanding something. This is my code using sklearn ...
13
votes
3answers
14k views

Step by step implementation of PCA in R using Lindsay Smith's tutorial

I'm working in R through an excellent PCA tutorial by Lindsay I Smith and am getting stuck in the last stage. The R script below takes us up to the stage (on p.19) where the original data is being ...

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