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204.5.4 Issue with Non Linear Decision Boundary

In previous post we just tried solving a non linear data using linear boundary. We can use multiple linear boundaries to separate classes in this kind of datasets.

However, this will cause some issues which we will understand bu visualizing the problem and think about a possible solution too.

Non-Linear Decision Boundaries-Issue

Logistic Regression line doesn’t seam to be a good option when we have non-linear decision boundaries

Non-Linear Decision Boundaries

We can try to build two different models and have two difference linear decision boundaries. These two models will give us intermediate outputs and combining both will give us the final output.

Non-Linear Decision Boundaries-Solution

Intermediate Output1 Intermediate Output2
out(x)= \(g(\sum w_kx_k)\) say h1 out(x)= \(g(\sum w_kx_k)\) say h2

The Intermediate output

  • Using the x’s directly; predicting y is challenging.
  • We can predict h, the intermediate output, which will indeed predict Y

Finding the Weights for Intermediate Outputs

If we increase the number of intermediate outputs and add a few layers of intermediate models, we end up with a basic neural network.

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