Predicting Cardiovascular Risks using Pattern Recognition and Data ...

3.4.1. Linear ModelsDefinition: A linear model is a model defined using a linear function. A linear function can berepresented in an n-dimensional space as follows:y = w 1 x 1 + w 2 x 2 + … + w n x n +bwhere x = (x 1 , x 2 , .., x n ) is a vector of a pattern in an n-dimensional space,w = (w 1 , w 2 , .., w n ) is a parameter vector of x in the data spaceThe weights are used to define the decision boundary for the classification problem. For simplicity, ycan be presented as:y = w T x +b ; or y = x T w +bExample 3.3x 2 High risk++ ++ ++ +++++ ++ ++ ++ ++ +Possibleboundariesy=wx +bLow riskDecisionx 1Figure 3.5: An example of a linear classification problem.Assume that the data distributions can be represented in the graph in Figure 3.5. Data is classified intotwo classes of “High risk” and “Low risk” areas. Obviously, this is a linear classification problem in a2-dimensional space, because its decision boundaries, to separate the output classes, can be representedas linear functions.29