In exploratory factor analysis, we can clearly see the weightage of the factors on different features. Following this, we can understand the extent to which factors have an influence on the features. I understand this as factor analysis.
In other techniques, be it supervised like PCA or unsupervised like LDA, is the aforesaid possible? For example in PCA, the factors get boiled down to an equal number of features, and depending on the variance explained we extract it out. Similarly for LDA, the number of classes minus one, factor gets extracted. It essentially reduces the dimension, calling it a dimensional reduction process.
So does this mean, dimensional reduction techniques like PCA and LDA lack the explanatory components on determining which features are influencing the factors? If so, do there exist any other techniques which work in a similar way to exploratory factor analysis, rather than just dimensionally reducing the data?