"Machine learning basics" from the perceptual machine model

Perception Machine (Perceptron)

The Perceptron (Perceptron) was proposed by Rosenblatt in 1957 and is the basis of neural networks and support vector machines. Perceptron is a linear classification model of class Two classification, its input is the characteristic vector of the instance, the output is the class of the instance, and the value of +1 and 12 is taken. The perceptual machine corresponds to the separation of the instances into positive and negative two classes in the input space (feature space), which belongs to the discriminant model. Perceptual machine learning is designed to find out the discrete hyper plane that divides the training data linearly.

Separation of hyper-planar taxonomy

The process of separating the hyper-plane for classification is to construct a linear judgment boundary, and try to display the data to different classes as well as possible.

The theorem of super plane separation

The Super plane separation theorem is an important result of applying convex set to optimization theory, which has important position in optimization theory. The so-called two convex set separation, visually refers to the two convex sets do not intersect and coincident parts, so you can use a super-plane to separate the two on both sides.

Perceptual Machine Definition
Perceptual Machine Geometry Interpretation

Perceptual Machine Learning Algorithm (Perception learning algorithm)

The following image shows the original learning process of the Perceptron:

Pla_process

As can be seen, if the 2D plane in the vector w and vector x is an obtuse angle, and X is a positive example, which means that W x is too large, so that the W is adjusted to W+y X, the W to x rotation, close to the x vector, similarly, if the separation of the super-plane error will be divided into negative case data (2D plane, Vector W and vector x are at a sharp angle), then the W is adjusted to W+y x, actually the vector w-x, then W is away from X.

A demonstration of the learning algorithm of the sensing machine

Initially, the classifier thinks all the data is wrong, so any data can be found to be corrected.

Step_initial

Here, W is the normal vector for the separation plane, and the separation plane is perpendicular to the normal vector.

Step1

XG is the data that is divided, so the original normal vector and the vector of the data are added to get a normal vector after rotation.

Step2

So, go on, keep revising until all the data is sorted correctly.

Step3
Step4
Step5
Step6
Step7
Step8
Step9
Step_final

Finally, we found the line of the "perfect" category.

Will the PLA stop.

Under linear conditions, how can we ensure that the PLA algorithm is able to stop? We can use the Nebilai of WF and WT to indicate whether they are getting closer.
We can see that the inner product of WF and WT increases with the update, which to some extent shows that WF and WT are more and more similar, but because the length of the vector is not taken into account, it is not complete.

Next, WT increases the length of xn each time.

Finally, we formalize WF and WT to get a product that is actually the cosine value of the angle between WF and WT. This means that each update, the angle of WF and WT is close to a little bit, and cannot grow indefinitely, because this value cannot be greater than 1. So this proves that the PLA algorithm will stop.

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GitHub home page (http://jasonding1354.github.io/)
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"Machine learning basics" from the perceptual machine model