I am running a PCA against two datasets of biological data (gene expression data).
The first has 20K genes (dimensions) x 450 samples, while the second has 11K genes (dimensions) x 185 samples.
Running PCA on these two datasets I get a very low amount of explained variance by the first principal components. Specifically, in the case of the first dataset I get
PC1 PC2 PC3 PC4 PC5 Standard deviation 1.175e+05 1.132e+05 9.022e+04 8.412e+04 7.002e+04 Proportion of Variance 1.396e-01 1.296e-01 8.236e-02 7.161e-02 4.961e-02 Cumulative Proportion 1.396e-01 2.692e-01 3.516e-01 4.232e-01 4.728e-01 PC6 PC7 PC8 PC9 PC10 Standard deviation 6.857e+04 6.816e+04 6.147e+04 5.796e+04 4.940e+04 Proportion of Variance 4.758e-02 4.701e-02 3.823e-02 3.399e-02 2.470e-02 Cumulative Proportion 5.204e-01 5.674e-01 6.056e-01 6.396e-01 6.643e-01 PC11 PC12 PC13 PC14 PC15 Standard deviation 4.434e+04 4.196e+04 3.953e+04 3.667e+04 3.374e+04 Proportion of Variance 1.989e-02 1.782e-02 1.581e-02 1.361e-02 1.152e-02 Cumulative Proportion 6.842e-01 7.020e-01 7.178e-01 7.315e-01 7.430e-01 PC16 PC17 PC18 PC19 PC20 Standard deviation 3.324e+04 3.237e+04 3.155e+04 3.080e+04 2.955e+04 Proportion of Variance 1.118e-02 1.060e-02 1.007e-02 9.600e-03 8.830e-03 Cumulative Proportion 7.541e-01 7.648e-01 7.748e-01 7.844e-01 7.933e-01
In this case, the first principal component amounts for the $13.96$% of total variance.
For the second dataset, which is smaller in size, the first principal component amount for the $41.71$% of total variance, the second for the $10.56$%.
- in the first dataset, cumulative explained variance for the first $10$ principal component is $66.43$%
- in the second dataset, cumulative explained variance for the first $10$ principal component is $78.43$%
I have two questions:
- Could it be that the amount of explained variance is this low because of the high number of dimensions?
- Could the result of this PCAs be used for subsequent analysis, even if the amount of variance is very low?