I'm trying to understand PCA, but I don't have a machine learning background. I come from software engineering, but the literature I've tried to read so far is hard for me to digest.
As far as I understand PCA, it will take a set of datapoints from an N dimensional space and translate them to an M dimensional space, where N > M. I don't yet understand what the actual output of PCA is.
For example, take this 5 dimensional input data with values in the range [0,10):
// dimensions: // a b c d e [[ 4, 1, 2, 8, 8], // component 1 [ 3, 0, 2, 9, 8], [ 4, 0, 0, 9, 1], ... [ 7, 9, 1, 2, 3], // component 2 [ 9, 9, 0, 2, 7], [ 7, 8, 1, 0, 0]]
My assumption is that PCA could be used to reduce the data from 5 dimensions to, say, 1 dimension.
There are two "components" in the data.
- One component has mid
d, and nondeterministic
- The other component has high
dlevels, and nondeterministic
This means that the two components are most differentiated by
d, somewhat differentiated by
a, and negligibly differentiated by
I'm making this up, but say the (non-normalized) linear combination with the highest differentiating power is something like
5*a + 10*b + 0*c + 10*d + 0*e
The above input data translated along that single axis is:
[, , , ...etc
Is that linear combination (or a vector describing it) the output of PCA? Or is the output the actual reduced dataset? Or something else entirely?