# Interpreting the new dimensions after PCA

I have telecom data with large number of dimentions. Now if I apply dimentionality reduction like PCA then from resulting dimention say PC1, PC2 I would loose the meaning or would not understand what they represent.

Are their any techniques other than PCA which can provide any meaning or intution about the new dimentions. Also suggest if there are any research papers in this.

• Can you provide the PCA output sample for interpretation ? You need to provide a Loading plot too so can be understood the positive or negative association in order to provide the explanation of PCA in context if your data. – n1tk Sep 27 '19 at 20:49

To give meaning to the Axis of the PCA, you can study the scalar product between the two new axes and all your original axes (you have to normalise the vectors before doing that).

Those axes with a high scalar product will be highly associated the with the new axes and viceversa. This may help you interpret them.

• Could you guide me the steps or share some resources to exactly do that...thanks for the info......also do you suggest any better method than PCA since my data has lot of categorical data – shrish123 kumar Sep 26 '19 at 2:44

You could also check t-SNE which is a dimensionality reduction technique based on the probability distribution

• t-SNE is a useful tool, but isn't well-suited to the OP's task - t-SNE dimensions have no consistent meaning whatsoever that can be mapped into the original feature space. PCA dimensions can easily be interpreted in the context of the original features, t-SNE dimensions cannot. – Nuclear Hoagie Oct 20 '20 at 18:28

One way to explore the mapping between the original dimensions and and PCA dimensions is to look at something called the factor loadings. These are essentially projections of your original dimensions into your PCA space. From this, you can see which of your original features are aligned with your new dimensions, or are aligned with one another.

An example of how to generate a PCA plot with factor loadings in R can be found here, to generate a plot like the one shown below:

Here, we can see that the PC1 axis is aligned with the Petal Length and Width, indicating that higher PC1 value is strongly associated with longer/wider petals. Sepal length is also in a similar direction, so PC1 captures a good bit of Sepal length variability as well. Sepal width, on the other hand, is related to both PC1 and PC2.