Linked Questions

10
votes
1answer
28k views

Calculating PCA variance explained [duplicate]

I've read through this explanation here regarding calculating the variance explained from PCA output. I think I got it right but might be off in my interpretation of R output. In the example below, I ...
12
votes
1answer
44k views

What is percentage of variance in PCA? [duplicate]

I am trying to understand Principal Component Analysis (PCA). I found a webpage on PCA that introduces it and the concept of the percentage of variance. However, I am very confused about what "...
-3
votes
1answer
2k views

What is proportion of variance explained in PCA? [duplicate]

Can anyone explain about the proportion of variance explained in PCA and why it is important in the analysis of PCA?
958
votes
28answers
564k 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 ...
213
votes
14answers
222k 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 ...
346
votes
3answers
215k 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 ...
26
votes
5answers
8k views

What can cause PCA to worsen results of a classifier?

I have a classifier that I'm doing cross-validation on, along with a hundred or so features that I'm doing forward selection on to find optimal combinations of features. I also compare this against ...
22
votes
2answers
15k views

Why PCA of data by means of SVD of the data?

This question is about an efficient way to compute principal components. Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ ...
12
votes
2answers
18k views

Why are principal components in PCA (eigenvectors of the covariance matrix) mutually orthogonal? [duplicate]

Why are principal components in PCA mutually orthogonal? I know that PCA can be calculated by eig(cov(X)), where X is centered. ...
8
votes
1answer
9k views

Questions on PCA: when are PCs independent? why is PCA sensitive to scaling? why are PCs constrained to be orthogonal?

I am trying to understand some descriptions of PCA (the first two are from Wikipedia), emphasis added: Principal components are guaranteed to be independent only if the data set is jointly normally ...
7
votes
1answer
9k views

Understanding cluster plot and component variability

I have run k-means clustering. I have also plotted the results using the following code in R: ...
8
votes
1answer
6k views

Proportion of explained variance in PCA and LDA

I have some basic questions regarding PCA (principal component analysis) and LDA (linear discriminant analysis): In PCA there is a way to calculate the proportion of variance explained. Is it also ...
6
votes
2answers
1k views

Why does log-transformation of the RNA-seq data reduce the amount of explained variance in PCA?

I am running a PCA on a dataset with 2k rows and 36k columns. I noticed that when I log-transform the data I need to ask for more principal components during PCA to achieve the same amount of ...
5
votes
3answers
1k views

Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate]

Suppose that you have 1000 features, and a data set made up of say, 50,000 points. Suppose then that we perform PCA, and we extract the top 5 PCs, since they explain 99.99 percent of the variance, and ...
6
votes
1answer
2k views

Does the first principal component differ from simply computing the mean of all variables?

I was just wondering if the first principal component, while I am trying to find it for a dataset of 18 variables, is different from simply adding all variables and finding the mean? I.e. to compute ...

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