Perceptron learning: Difference between revisions
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'''Perceptron learning''' is good for classifying ''linearly separable data'', as seen in figure 1. | [[File:Linearly separable data.png|thumb|Figure 1. Graphical representation of linearly separable data]] | ||
'''Perceptron learning''' is an algorithm for [[binary classification]]. It is good for classifying ''linearly separable data'', as seen in figure 1. | |||
= How it works = | |||
Initially, all attributes are passed into a ''neuron'', each with a randomized weight. | |||
<math>z = \bf{w}\bf{x}</math> | |||
The '''binary step activation function''' takes in z and outputs 1 or 0 depending on a ''threshold''. | |||
The error is computed | |||
<math>E = \frac{1}{2} \sum (y^{(i)} - \hat{y}^{(i)})^2</math> | |||
where the 1/2 is for simplicity of computation after the gradient. We use the gradient of the error function to update the weights of the model | |||
<math>\Delta w_j = \nabla_{w_j} E = \sum (y^{(i)} - \hat{y^{(i)}})(-x_j)</math> | |||
[[Category:Machine Learning]] | [[Category:Machine Learning]] | ||
Revision as of 06:03, 26 April 2024
Perceptron learning is an algorithm for binary classification. It is good for classifying linearly separable data, as seen in figure 1.
How it works
Initially, all attributes are passed into a neuron, each with a randomized weight.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z = \bf{w}\bf{x}}
The binary step activation function takes in z and outputs 1 or 0 depending on a threshold.
The error is computed
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E = \frac{1}{2} \sum (y^{(i)} - \hat{y}^{(i)})^2}
where the 1/2 is for simplicity of computation after the gradient. We use the gradient of the error function to update the weights of the model
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta w_j = \nabla_{w_j} E = \sum (y^{(i)} - \hat{y^{(i)}})(-x_j)}
