Linked Questions

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Correlating variables with eigenvalues in principal components analysis [duplicate]

I have the following problem. I'm performing PCA on a series of correlation matrices (Cm), which result from subsequent rolling windows on data time series, which are my basic variables. That means, ...
0
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0answers
141 views

Does the order of columns matter in PCA for the results? Jumpy factor loadings? [duplicate]

I have six UK inflation time series, starting from Jan 1990 and ending in June 2019. These series as standardized on an expanding window and subsequently forward filled. I use these series to run a ...
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0answers
49 views

Determining the Direction of Eigenvectors in PCA [duplicate]

I'm using R to get the principal components for several datasets. An example result, using prcomp yields: ...
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0answers
19 views

Why are the directions of eigenvectors in SVD and Eigen-Decomposition for PCA opposite? [duplicate]

As you may know, scikit-learn library utilizes singular value decomposition (SVD) of data matrix X to produce eigenvectors for PCA. I decided to code PCA by using ...
456
votes
3answers
306k 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 ...
13
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2answers
5k views

Are PCA solutions unique?

When I run PCA on a certain data set, is the solution given to me unique? I.e., I obtain a set of 2d coordinates, based on interpoint distances. Is it possible to find at least one more arrangement ...
5
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2answers
18k views

Interpreting positive and negative signs of the elements of PCA eigenvectors

If I center my variables and then run a PCA analysis, do I need to interpret negative eigenvectors different than positive eigenvectors? Clarification: In my PCA analysis I have in a component both ...
1
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1answer
2k views

Reverse the sign of PCA [duplicate]

I'm struggling on getting a good explanation for the unexpected signs of Principal Component for months. I tried to replicate a result and I got exactly the opposite signs for all components. While I ...
3
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2answers
2k views

Using the 'U' Matrix of SVD as Feature Reduction [duplicate]

This is a follow-up to the question asked regarding SVD and dimensionality reduction (question). In that question I asked how to use SVD for dimensionality reduction. Although not stated, the ...
2
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2answers
1k views

How does pca() function in Matlab fix the sign of principal components? [duplicate]

PCA gives me loadings with different signs. I understand that I may simply revert them (as explained in this thread), but I need an explanation (my boss insists) of why Matlab implementation gives me ...
1
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2answers
684 views

How to compare the outputs of two algorithms computing SVD?

For example we have 2 algorithms from R: SVD and irlba and I want to compare them int terms of speed,memory and precision. But I don't understand how to compare output of algorithms, they must be ...
2
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1answer
1k views

Singular value decomposition procedure in R

I'm trying to follow Prof Strang exercise but I have a problem with the signs of the resultant matrix. He also had a problem with the signs during the exercise, so I have no way to find what is the ...
1
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0answers
356 views

Is it possible to reverse the sign of factor loadings for one factor? [duplicate]

I just want to confirm if it is possible to reverse the sign (+/-) on the factor loadings of one factor. I run a PAF with Oblimin rotation. I obtained 6 factors but in one of them the items that load ...
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0answers
159 views

Does it mean anything when all items load negatively on one factor? [duplicate]

note: A few people have marked this question as duplicate - But my question here is not answered in the other question. Though a fine distinction, what I was asking about here was not whether the ...
1
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0answers
125 views

How to reverse the sign of factor loadings in factor analysis? [duplicate]

I'm doing a factor analysis and using the resulting factors in a regression. I'm using SAS. A number of the variables load positively on a factor. In order to make it easier to interpret in the final ...

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