Principal component analysis (PCA) with small number of observations

Click For Summary
SUMMARY

Principal Component Analysis (PCA) can be applied to hyperspectral data with 200 observations and 1000 bands, despite the singularity of the estimated variance-covariance matrix. The maximum number of meaningful principal components is indeed limited to 199, as it is defined by the number of observations minus one. This limitation arises because PCA requires a sufficient number of observations to accurately capture the variance in high-dimensional data.

PREREQUISITES
  • Understanding of Principal Component Analysis (PCA)
  • Familiarity with hyperspectral data analysis
  • Knowledge of variance-covariance matrices
  • Experience with dimensionality reduction techniques
NEXT STEPS
  • Research "PCA in cluster analysis" for applications in dimension reduction
  • Explore "Singular Value Decomposition (SVD)" as an alternative to PCA
  • Study "Regularization techniques for PCA" to handle singular matrices
  • Investigate "Hyperspectral imaging data preprocessing methods" for improved analysis
USEFUL FOR

Data scientists, statisticians, and researchers working with high-dimensional datasets, particularly in the fields of remote sensing and hyperspectral imaging.

miguelcc
Messages
1
Reaction score
0
Dear all,
I'd like to apply principal component analysis (PCA) to hyperspectral data (~1000 bands). The number of observations is 200.
The estimated variance covarance matrix is singular because the number of observations is smaller than the number of variables.

My questions are,

Can I still perform PCA (number of variables is < number of observations)?

Is the maximum number of meaninful principal components equal to 199?

Could you also provide me with references, please?

Thanks a lot in advance.

MiguelCC
 
Physics news on Phys.org
I am not sure but I would search for: "PCA in cluster analysis" since this is a method for dimension reduction of the phase space. Wikipedia has a good overview on PCA.
 

Similar threads

Graduate Is There a Linear Transformation to Map Data Set X to Y in PCA?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Principal component analysis (PCA) coefficients
  • · Replies 29 ·
Replies
29
Views
7K
Undergrad Using PCA for variable reduction
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Mean centering of the covariance matrix in PCA
  • · Replies 2 ·
Replies
2
Views
9K
Graduate Is Calculating Variance Reduction in PCA Accurate?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Principal Component Analysis vs Factor Analysis vs regression
  • · Replies 1 ·
Replies
1
Views
23K
Undergrad Principal Component Analysis: eigenvectors?
  • · Replies 1 ·
Replies
1
Views
6K
Undergrad Progress In Calculating The HLbL Contribution To Muon g-2
  • · Replies 0 ·
Replies
0
Views
3K
Programs How good is this applied math program?
  • · Replies 13 ·
Replies
13
Views
4K
How do these statistics courses compare to other schools?
  • · Replies 2 ·
Replies
2
Views
3K