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Perceptron
- Popularized by Frank Rosenblatt (1960s)
- Used for tasks with very big vectors of features
Decision Unit: Binary trheshold neuron.
Bias can be learned like weights, it's weight with value 1.
Perceptron convergence
- If output correct ⇒ no weight changes
- If output unit incorrectly outputs 0 ⇒ add input vector to weight vector.
- If output unit incorrectly outputs 1 ⇒ substract input vector from the weight vector.
This generates set of weights that gets the right answer for all training cases, if such a set exists. ⇒ Deciding the features is the important distinction
Geometrical Interpretation
Weight-Space view
- 1 dimension for each weight
- Point represents a setting of all weights
- Leaving the threshold out, each training case can be represented as a hyperplane through the origin. Inputs represent planes (or Constraints)
- For a particular training case: Weights must lie on one side of this hyper-plane to get the answer correct.
Plane goes through origin, is perpendicular to the input vector (with correct answer = 1 (or 0)). Good weight vector needs to be on the same side of the hyperplane. Scalar product of wight vector and input vector positiv (angle < 90°).
Cone of feasable solutions
- Hypercone - Weight vectors don't need to exist - Convex hypercone