Perceptron
Perceptron linear classifier Model for the second category classification, which is an example of the input feature vector, the output of the class instances, taking values of +1 and -1 two.
Perceptron Model
Assume that the input space (feature space) is X⊆R n- , the output space is the y = {+ 1, -1} denotes the input feature vector x∈X example, the input space corresponding to a point (feature space); and output y∈ Y represents a class instance.
Is a linear perceptron model classification, discriminant model belongs. Perceptron model hypothesis space is defined in the feature space classification model all linear or linear classifier.
Perceptron learning strategies
Linear separability data set
Perceptron learning strategies
Suppose the training data set is linearly separable, perceptual learning target is able to find a set of positive training examples and negative examples of point-point can be completely separated hyperplane. It is how to find w and b, need to identify a learning strategy, namely the definition of (experience) loss function and loss function minimization.
Perceptron learning loss function defined as
the perception of the policy machine learning really constituency hypothesis space to minimize the loss of function of the model parameters w, b, that is, Perceptron model.
Perceptron learning algorithm
The method for optimizing stochastic gradient descent method so that,
Perceptron learning algorithm original form
Perceptron learning algorithm is misclassified driven, having random gradient descent
Convergence of the algorithm
For linear separable data sets Perceptron learning algorithm converges original form, that is, after a finite number of iterations can get the training data set entirely correct division separating hyperplane and Perceptron model.
Perceptron learning algorithm dual form
The w and b represent examples of the form of a linear combination of the xi and yi, and is obtained by solving the coefficients w and b, without loss of generality
