23-12-2025, 12:55 AM
I am not sure I understand the proposed points for or against PCA analysis.
PCA is only used to find the largest dimensions in a multi-dimensional cloud of points.
The result can be used for visualisation. On a piece of paper or a screen, one can only show two dimensions.
To do statistics (e.g. clustering) one can use all dimensions.
When a multi-dimensional cloud of points is projected onto two dimensions, all coordinates other than these two are set to zero. This means that a lot of data is eliminated or lost.
The problem is that in such projections, points that look very close to each other may be separated in the invisible dimensions.
To avoid or reduce the impact of that, one can show several different projections next to each other. When this becomes more than 3, the human mind isn't really capable of fully grasping it.
However, it still allows to see whether any grouping in each of the projections remains a grouping.
There are other types of non-linear projections, which try to preserve the distances. These cannot preserve the scales of course. (I forget what these are called).
PCA is only used to find the largest dimensions in a multi-dimensional cloud of points.
The result can be used for visualisation. On a piece of paper or a screen, one can only show two dimensions.
To do statistics (e.g. clustering) one can use all dimensions.
When a multi-dimensional cloud of points is projected onto two dimensions, all coordinates other than these two are set to zero. This means that a lot of data is eliminated or lost.
The problem is that in such projections, points that look very close to each other may be separated in the invisible dimensions.
To avoid or reduce the impact of that, one can show several different projections next to each other. When this becomes more than 3, the human mind isn't really capable of fully grasping it.
However, it still allows to see whether any grouping in each of the projections remains a grouping.
There are other types of non-linear projections, which try to preserve the distances. These cannot preserve the scales of course. (I forget what these are called).