vector notation, boundaries, kernal trick, features, and shi

Author: Null-Tree

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 - the concept of [[Training with Data (Types of machine learning)|training algorithms using data]]
 - the concepts of model [[overfitting and underfitting]]
 - [[Support Vector Machine|Support vector machines]] (SVM) as margin-maximising linear classifiers, including:
-- the geometric interpretation of applying SVM [[Binary classification|binary classification]] to one- or two-dimensional data
-- the creation of a second feature from one-dimensional data to allow linear classification
+	- the geometric interpretation of applying SVM [[Binary classification|binary classification]] to one- or two-dimensional data
+	- the creation of a second feature from one-dimensional data to allow linear classification
 - Neural Networks, including:
 	- the structure of [[Multi-layer Perceptron|multilayer-perceptron neural networks]]
 	- the evaluation of outputs using [[Forward Propagation]]

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+
+## What are they
+A decision boundary is an abstract boundary that separates input/feature fields into different sections, and thus what output should be given.
+
+In a 2D plane with 2 features, a decision boundary will take the form of a 1d line.
+
+![[Pasted image 20250828194513.png]]
+
+## Notation
+The decision boundary is described by: 
+$$\sum_{i=1}^n(x_{i} w_{i})+b=0$$
+(Note, $b$ is bias)
+
+For 2 features/2 dimensions, it is: $x_{1}w_{1}+x_{2}w_{2}+\text{bias}=0$, which may be rearranged into a linear line.
+
+For vector notation see [[Vector notation for weight and data]]