How explainable is Linear Discriminant Analysis? 
In a survey paper on the interpretability of various machine learning algorithms, I didn't find Linear Discriminant Analysis (LDA). I wonder how explainable is LDA to audiences not familiar with machine learning?
The idea behind LDA seems intuitive - finding some linear combinations of the original variables where the two classes are separated the most. So this is similar to extracting "hidden" features and use them for classification. Following this line of thought, would LDA be considered as less explainable on the spectrum?

I would describe Linear Discriminant Analysis (LDA) as a supervised linear transformation technique, rather than an actual model that's attempting to predict something (like the ones labeled in the plot you shared). This is likely why you did not find it in the paper you referenced.
As you mentioned, LDA attempts to reduce dimensionality by identifying linear combinations of the n features which best explain the data. It's quite similar to Principal Component Analysis (PCA), except that LDA explicitly attempts to identify the differences between the classes of data (i.e., can be particularly handy for segmentation/classification exercises).
Often times you will use a dimensionality reduction technique in the preprocessing stages of your model-building process. For example, if you're trying to build a predictive model off of 150 unique features, you may find it helpful to incorporate a technique such as LDA to "shrink" these features down in an attempt to better understand/explain your data.
Regarding explainability, I feel like the depth you went to is more or less appropriate for what should be communicated to a more non-technical audience. I.e., "The results of LDA represent the linear combination of a number of features that our model is taking into account. Some of the most important features include a, b, c, etc."
