Predicting Cardiovascular Risks using Pattern Recognition and Data ...

3.4.2. Nonlinear ModelsDefinition: Any model that can not be defined using a linear model can be seen as a nonlinear model. Itis defined using nonlinear functions. Nonlinear functions are represented as:y= f(w, x), where w=(w 1 , w 2 ,..., w n ) is not linear; or f is a nonlinear function.Example 3.4Assume that a Gaussian distribution of data as seen in Figure 3.6. This Gaussian function, in a 3-dimensional space, can be seen as1 x2 ( )2 y f ( x,, ) f ( x1 , x2,, ) e;where µ= 0; and δ=0.5.Figure 3.6: Gaussian distributions of data in a 3-dimensional space.The graph can be redrawn into a 2-dimensional space as seen in Figure 3.7. It is clear that this is anexample of a nonlinear classification problem, because the decision boundary between “High risk” and“Low risk” classes is a curve.30