# very low variance explained after applying pca

I applied PCA on MNIST data and found that the first 64 components are able to retain 86% of variance.

Is there any problem while applying pca to a big dataset like MNIST. Because in most of the papers I have read to take the components which can explain upto 99% of variance. But it would be pointless to apply pca if such variance comes at 120 pca components.

It is entirely correct to apply PCA to a dataset like MNIST. Intuitively, corner pixels should almost never contain any information as to what digit is contained in the center of the image. So we should disregard them. You should expect similar results as with other datasets. PCA lowers the dimensionality of your data, thus allowing for a less complex model, however, this is at the cost of some information that is rejected when retaining only $n$ components.