I know that Linear Discrimination Analysis (LDA) is used for classification and Multiple Linear Regression (MLR) is for regression. Lets say I have a matrix X (independent variables) and Y(dependent variables)  if the Y is continues and I make a regression , it becomes MLR if the Y is categories (like 1111122222) and I do MLR to make a relation , it becomes LDA?  can one explain it in simple words and illustrations ?
Is there a relationship between regression and linear discriminant analysis (LDA)? What are their similarities and differences? Does it make any difference if there are two classes or more than two classes?
I am working with dimensionality reduction algorithms. Linear Discriminant Analysis (LDA) is a supervised algorithm that takes into account the class label (which is not the case of PCA for example). I am using Python to do a comparative study between some algorithms.  Why with two classes (k = 2), regardless of the data dimensionality, LDA gives one dimension, i.e. the new subspace is composed of only one dimension? For example if I try to project my dataset (of 100 attributes and 2 classes) to 10-dimensional space by using LDA(n_components=10) I only obtain 1 dimension?  For k&gt;2 I can obtain the number of discriminant vectors that I specified as n_components. How can I get n_components dimensions for k=2?