According to me in logistic regression, we just try to get a line (polynomial) and then based on which side the point is from that line the sigmoid gives ans>=0.5 or <0.5, which we then interpret as 1 (if ans>=0.5) and 0 if (ans < 0.5). Here is a simple plot what I mean.
This is just a random line not a line predicted by any logistic regression model. Here we are only having one feature i.e., x. y is the output(0 or 1). The decision boundary here is x = -3 and x = 3.
So when we have 1 feature we try to get a good line to predict the values.
What if we have 2 features we try to get a plane instead?
This is a 3-d plot of a normal sigmoid.
So if we have 2 features say x and y. For these we are trying to get a plane in z axis which separate the points? which is in turn the decision boundary. I am really confused.? Is this what we are doing?
If yes, can someone plot a 3d plot (of sigmoid/decision boundary) for a circle. For eg:
This is also a random plot. Suppose that our points are like this and our model has given us a circle to differentiate between 0 and 1. So can anyone plot a decision boundary of something like this (which is is 3-D).