Decision Boundary

In machine learning and statistics, a decision boundary is a surface that separates different classes in the feature space. For a classification algorithm, the decision boundary is the demarcation where the algorithm assigns a data point to one class or another. The complexity and shape of the decision boundary depend on the model and the feature space.

For instance, linear models like logistic regression or linear SVMs will have linear (straight-line) decision boundaries in the input feature space, whereas more complex models like neural networks with hidden layers can learn non-linear decision boundaries, allowing for more intricate separations of classes. The decision boundary is not always explicitly defined but is a result of the model's learned parameters during the training process.

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In a binary classification problem where the task is to classify emails as either 'spam' or 'not spam', the decision boundary would be the set of conditions defined by the model that determines whether a new email falls into the 'spam' category or the 'not spam' category. For a simple linear classifier, this might be a single line in a two-dimensional feature space (such as word frequency), where emails on one side of the line are classified as 'spam' and those on the other side as 'not spam'.

For more complex models, like neural networks, the decision boundary could be a complex curve that more accurately separates the 'spam' emails from the 'not spam' based on multiple features.

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