2.5 Linear Separability

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Linear Separability

  • The training data must be linearly separable. This means there exists a hyperplane that can separate the positive and negative examples without any errors.

  1.  Linearly Separable data: It refers to a set of data points can be perfectly divided into two distinct classes using a straight line (in two dimensions), a plane (in three dimensions), or a hyperplane (in higher dimensions). This means that there exists a linear boundary that can clearly separate all the data points of one class from those of the other class without any overlap.

2. Non-linearly separable data: It refers to a set of data points cannot be divided into two distinct classes using a straight line (in two dimensions), a plane (in three dimensions), or a hyperplane (in higher dimensions). In other words, no single linear boundary can perfectly separate the two classes.





Limitations of perceptron: -

  • Linearly separable data: Perceptrons can only classify data that is linearly separable, meaning it can be separated by a straight line. 
  • Binary output: Perceptrons can only produce a binary output of 0 or 1. 
  • Limited memory: Single-layer perceptrons have limited memory and can only process a limited amount of information at a time. 
  • Sensitive to initial conditions: The performance of a perceptron depends on how the weights are initialized. 
  • Convergence issues: Perceptrons may not converge if the data is not linearly separable. 
  • Simple tasks only: Single-layer perceptrons are limited to simple tasks like classification or regression. 














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