on the basis of the number of eigen values, for example n eigen values then the dimension should be n.

I am not sure if we understand your question correctly. Are you asking for the right amount of principals components?

An easy, but comprehensive and well visualized tutorial on PCA can be found here http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/112-pca-principal-component-analysis-essentials/ .

You run PCA with a data frame (rows being samples, columns being parameters). With the help of the eigenvalues and the scree plot, you can decide how many principal components to include.

It depends what you are using the result for, and how many dimensions you think should account for the interesting variation in the sample.

As previous commentators note, if you have no thoughts about these two aspects, the eigenvalues of the correlation matrix can offer clues. If you're data are X and you are using R, try

plot(1:ncol(X),eigen(cor(X))$values)

and look up scree test for how to interpret this. But first think about those first two things.

@michael heming

Thanks, but I am not asking for right amount of principal components.

I am asking to reconstruct the input vector, i.e. if I have an input sequence of 2000x1 and I want to apply the PCA over it then to do so I should first convert it into on input vector of dimention n*k which after applying PCA depending upon variation is converted to an output vector of dimention n*s (s being lesser than k).

Then is there any criteria to select n and k or any combination of n*k should be selected randomly ?

Ankit Soni

Maybe it's easiest if we start with a minimal working example.

If we follow this easy tutorial: http://www.sthda.com/english/articles/31-principal-component-methods-in-r-practical-guide/112-pca-principal-component-analysis-essentials/ we can simply do:

library(factoextra)

library(FactoMineR)

data(decathlon2)

decathlon_active print(res)

**Results for the Principal Component Analysis (PCA)**

The analysis was performed on 23 individuals, described by 10 variables

*The results are available in the following objects:

name description

1 "$eig" "eigenvalues"

2 "$var" "results for the variables"

3 "$var$coord" "coord. for the variables"

4 "$var$cor" "correlations variables - dimensions"

5 "$var$cos2" "cos2 for the variables"

6 "$var$contrib" "contributions of the variables"

7 "$ind" "results for the individuals"

8 "$ind$coord" "coord. for the individuals"

9 "$ind$cos2" "cos2 for the individuals"

10 "$ind$contrib" "contributions of the individuals"

11 "$call" "summary statistics"

12 "$call$centre" "mean of the variables"

13 "$call$ecart.type" "standard error of the variables"

14 "$call$row.w" "weights for the individuals"

15 "$call$col.w" "weights for the variables"

If this doesn't answer your question, I would suggest that you provide a minimal working example for your data.

Let me see if I understand. You have a single vector, length 2000, and you want to reduce this in some way. I assume you are expecting some pattern. Are you expecting PCA to find this pattern?