Preliminaries A Simple Linear Regression Least Squares Estimation From Linear Regression to Linear Classification pseudo-inverse Least Squares for Classification1 Least-squares for linear regression had been talked about in ‘Simple Linear Regression’. And in this post, we want to find out whether this powerful algorithm can be used in classification.
Recalling the distinction between the properties of classification and regression, two points need to be emphasized again(‘From Linear Regression to Linear Classification’):...

Priliminaries A Simple Linear Regression the column space Another Example of Linear Regression 1 In the blog A Simple Linear Regression, squares of the difference between the output of a predictor and the target were used as a loss function in a regression problem. And it could be also written as:
\[ \ell(\hat{\mathbf{y}}_i,\mathbf{y}_i)=(\hat{\mathbf{y}}_i-\mathbf{y}_i)^T(\hat{\mathbf{y}}_i-\mathbf{y}_i) \tag{1} \]
The linear regression model in a matrix form is:
\[ y=\mathbf{w}^T\mathbf{x}+\mathbf{b}\tag{2} \]
What we do in this post is analyze the least-squares methods from two different viewpoints...