Probably not make sense to use all d of the princi

probably not make sense to use all D of the princi-
pal components, as that would project the original
D -dimensional data instances right back onto a D -
dimensional subspace, meaning that there would be
no dimensionality reduction at all.
For visualization on a flat 2-D surface such as a
computer screen, selecting K to be 2 or 3 would be
appropriate.
For the purpose of reducing the number of features
in order to reduce the amount of data and improve
the running time of a machine learning training algo-
rithm, the PCA software user must make a choice for
K . On the one hand, a very small K would be de-
sirable because it would reduce the amount of data,
but on the other hand, if too many dimensions are re-
moved, the data may not capture important details.
In the context of PCA, the notion of capturing de-
tails is quantified by the amount of total variance ex-
plained by the selected principal components. Recall
that when the original data points are projected onto
an axis defined by a principal component, the vari-
ance of this projected data can be computed. The
amount of total variance explained is then the sum
of the variances over all K principal components.
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