# How to interpret the classification boundary?

I am beginner to neural network and machine learning. I am working neural network with 1 hidden layer. I took spiral data set and I am trying to overfit the data.

I applied neural network to it and I am getting a 98% accuracy. But, I am getting the of classification boundary in 2nd figure. I mean why am I getting read color on yellow side and blue color on red side!

I should get boundary like the right figure.

Is there a reason why I am not getting such boundary even though I am achieving high accuracy. Or can you tell what precautions I should take to avoid such problems.

The reason is that you are NOT asking model to provide "a desired boundary", BUT simply ask the model to correctly classify your data.

There are infinite decision boundaries exist, that achieve same classification task with same accuracy.

When we use neural network, the model can chose whatever it wants. In addition, the model does not know the shape of the data (the groundtruth / generative model / spiral shape in your example). The model will just select one "working" decision boundary, but not "really optimal to the true distribution" (as indicated in your figure 3)

If you want to do something with decision boundary, please check support vector machine. In fact, even you use SVM, decision boundary may not be what you expected, because it will max the "margin", but still have no idea about true distribution (spiral or other shape).

As mentioned in the comment, different types of the model have different decision boundaries. For example, logistic regression and linear discriminant analysis (LDA) will have a line (or hyperplane in high dimensional space), and quadratic discriminant analysis (QDA) will have a quadratic curve as division boundary.

pic source

Finally, My answer for another question gives some examples on the different model's decision boundaries.

Do all machine learning algorithms separate data linearly?

• So, this means we can't control such things with neural network? – Shubham Sharma Dec 30 '16 at 5:18
• short answer is know, But I bet you can design an "objective function" that describes the boundary, note this is totally different from the "correctly classify all data points" objective. And use NN to optimize such objective – Haitao Du Dec 30 '16 at 5:31
• Is SVM really intrinsically better here? I think it would depend completely on the features/kernel? I remember playing here and for their (2-class) spiral, a deeper network was needed. (Particularly if only $x$ and $y$ were input as "features"). Probably regularization would also be important? – GeoMatt22 Dec 30 '16 at 5:56
• @GeoMatt22 I was trying to say NN has little thing to do with the boundary, and SVM has something to do with boundary, but may not get what the "true boundary" – Haitao Du Dec 30 '16 at 6:18
• The OP mentioned overfitting. Isn't this a problem that affects all techniques? I know more about discriminant analysis. Should I tell the OP that discriminant analysis will cure the problem? (rhetorical question). – Michael Chernick Dec 30 '16 at 14:37