Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.
Questions tagged [principal-component-analysis]
142 questions
3
votes
1 answer
Principal Component Analysis of variables $x$, $x^2$, $x^3$?
I know the working of PCA, but was baffled by question asked in the interview that:
Principal Component Analysis of variables $x$, $x^2$, $x^3$. How can
we derive it mathematically?
Do we need to create matrix of it and then calculate covariance…
MAC
- 143
- 4
2
votes
1 answer
What is the correct formula for the covariance matrix?
I am solving about principal component analysis (PCA) and I stumbled upon a place where I need to calculate the covariance matrix, I am seeing varieties of formula. Here are some that I have found:
The $n$ or $n-1$ is confusing me. What is the…
Team B.I
- 199
1
vote
0 answers
Relation of principal component analysis between a matrix and its transopose
With a matrix $X_{n\times p}$ ($n>p$), we perform a principal component analysis:
$T_{n\times p}=X_{n\times p}W_{p\times p}$
where $W$ is the loadings matrix while $T$ is the scores matrix for $X$. Now, we can also perform a PCA for the transpose…
bluepole
- 153
1
vote
1 answer
Clarifying the constraints used in deriving the Principal Components of PCA
In studying principal components analysis, I am confused by one point.
For a set of $N$ (zero-centered) data points of dimension $m$, projected to a dimension $k < m$, we want a set of vectors of dimension $m$, say $w_{i}$, that maximises the…
IntegrateThis
- 3,778
1
vote
0 answers
How to create separation of "sides"/signs in PCA / eigenvector "directionality of data" analysis?
How to create separation of "sides"/signs in PCA / eigenvector "directionality of data" analysis?
Since PCA will only give eigenvectors that show the principal axes, but it does not specify, whether the data is skewed more towards the "plus side" of…
mavavilj
- 7,270
0
votes
0 answers
Proving the relationship between mean-squared error of 1D projection of PCA and the largest eigenvalue of the covariance matrix
I was studying the topic of principal component analysis and came across this problem that I was not able to prove.
Consider a data matrix, X and its covariance matrix, S. I know that taking the eigenvector of S that corresponds to the largest…
0
votes
0 answers
Principal Component Analysis - How do these two representations not contradict each other?
enter image description here
The representation here basically says each observation in a data set is a sum of products of some Zs and loadings. By Zs, I mean the component scores. Loadings are the weights given to the individual features in a…
