I'm trying to reduce the dimension of a dataset from 8 features to 1 using the principal component analysis (PCA) algorithm. The reduced dataset needs to be in 1 dimension(D) so I can use it for matrix factorization and other algorithms.
However, after applying PCA, the reduced 1D dataset only keeps 45% of the variance so I'm loosing a lot of information. I tried to reduce the dimension keeping 95% of the variance but the resulting dataset has 3D.
I know the variance of each feature in the reduced dataset. Therefore, I was thinking of using the variances as weights and linearly combine them with the reduced values so I'd reduce the dataset further to 1D, for example:
value_1D = variance_f1*value_f1 + variance_f2*value_f2 + variance_f3*value_f3
Would it we correct to do it? Do you know any other alternative?
Thanks in advance