General Equation
Generally the equation for a linear model will have two inputs(but can have any number of inputs) and be written as:
x1*w1 + x2*w2 +b
The goal of the ANN is to find the minimal errored equation which, when given a new input can predict accurate outputs compared to outputs that have been classified or calculated by previous inputs.
Two well known models are:
Linear Regression Model– derives a linear relation between the dependent variable and independent(input) variable.
Linear Classification Model-approximates and maps the probabilty that the (input) independent variable is a class of the dependent variable.
How Does the Linear model succeed in minimizing the error?
The Linear model algorithm starts a compilation of iterations/epochs with a random line equation and gradually descends the error to its minimum value.
This error descendence is achieved by using pre-labeled data points(in case of linear supervised model) or in-time-labels data points(in case of linear unsupervised model) and checking each iteration’s/epoch’s error for each data point according to them.
Each data point’s error is calculated and when the minimum error in all data points converges to a minimum, we stop the iteration and are left the linear equation.
We can then determine which weights have the most effect on the model.