Perceptron on "centered data"

Perceptron on "centered data"

by Ghali Chraibi -
Number of replies: 2

Hi,

In the lectures and exercices, it is said that if the data are centered and linearly separable, perceptron will always find a decision boundary without using bias.

However in this situation I don't understand how the perceptron will do :

Indeed the data seems centered to me and also linearly separable, but we can't find a decision boundary that works well without bias ... or am I wrong somewhere ?

Thanks in advance for the attention.

In reply to Ghali Chraibi

Re: Perceptron on "centered data"

by Jan Bednarík -

Hi Ghalil,

the term "centered" is used somewhat vaguely in both the lecture and the perceptron exercise. In this case, "centered" does not refer to data with zero mean, but rather to data shifted so that a linear decision boundary coincides with the origin [0, 0]. Of course, since we do not know the decision boundary, we cannot really center the data before training the perceptron. The reason the notion of "centering the data" was introduced in this context was to demonstrate the importance of the bias term. As for the exercise 3, we worked with a dataset where shifting the data by subtracting the mean of the centroids of both classes happened to shift the dataset so that the decision boundary without a bias term could be found. In practice, though, you have no guarantee that such a strategy would work so it is necessary to use the bias term. If it is not needed, its weight w0 will be found to be (close to) zero.

Best,

Jan