# Logistic Regression

I just finished the code for a Logistic Regression classification model. I worked on a Card transaction processing system and there was a requirement for identifying whether a card transaction is fradulent or not. We did not use any classification model but if we had had a training set of historical data we could have used this learning algorithm.
Most of the time it is the lack of skills that affects software projects that I have been involved with.

### Cost function for Logistic Regression

$J(\theta) = 1/m \sum_{i=1}^{m}[-y^{(i)} log( h_\theta(x^{(i)}) - (1-y^{(i)})log( 1 - h_\theta(x^{(i)}))] ;$

### Gradient of the cost

$(\partial J(\theta)/\partial \theta_j ) = 1/m \sum_{i=1}^{m} ( h_\theta(x^{(i)}) - y^{(i)}) x^{(i)}_j$

This is the plot generated by the course material based on my code. The line is a decision boundary that shows which exam scores ensure admittance. We can use historical card transaction data in place of this.

This classificatio model can predict which card transactions could be fradulent based on a probability calculated by the algorithm. So here instead of plotting exam scores on the axes we can plot card transaction data.