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I am new to classification, but not to regression. I already used regression to fit a linear combination of time varying signals to match two constant signals, -1 and 1, representing their classes.

In order to decide which class the result belongs to, a standard way is to test if the average is positive or negative.

I found a classifier that gives better results, which is computed by comparing the MSE between the prediction and the two constant signals -1 and 1. The smaller MSE decides the class. I am 100% sure other people have used this before (it seems pretty intuitive), but I can't find it anywhere (most likely, I'm not searching for the right words).

Can any of you help me with the name of this classifier and/or where it was used?

Thanks in advance.

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  • $\begingroup$ First of all: why would you use a suboptimal method where there are lots of better ways of doing this? Second, how exactly MSE would work here? "The smaller MSE decides the class" does not make sense since MSE is a single value that describes the overall errors of the model, so it us unusable for the purpose. $\endgroup$
    – Tim
    Commented Oct 27, 2017 at 18:13
  • $\begingroup$ I am not talking about the MSE describing the overall performance of the algorithm, but an MSE computed for every time varying prediction (so for every input-output pair), in order to decide the class it belongs to. I hope this is a bit clearer. $\endgroup$
    – Dorian Florescu
    Commented Oct 27, 2017 at 18:27
  • $\begingroup$ So you are not talking about MSE, but about smaller squared distances. Still, I don't get it, since squared difference between predicted value and -1 will be smaller if the value is < 0 and and it will be smaller to +1 when the value is > 0, so it is the same as if you just took the sign of the value... $\endgroup$
    – Tim
    Commented Oct 27, 2017 at 19:03
  • $\begingroup$ Linear regression with dichotomous dependent variable is equivalent to Fisher's linear discriminant analysis, a classifier. $\endgroup$
    – ttnphns
    Commented Oct 27, 2017 at 19:05
  • $\begingroup$ Could you walk through an example of how the MSE is computed and compared between the prediction and the two constant signals? $\endgroup$
    – Juho Kokkala
    Commented Oct 27, 2017 at 19:27

1 Answer 1

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Thanks to ttnphns, I learnt this problem is equivalent to Fisher's linear discriminant analysis, a classifier. I realised it's just a matter of choice whether you use MSE or a simple average for class prediction, depending on the application.

Thanks to everyone for their time.

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  • $\begingroup$ Fisher's linear discriminant analysis is not based on MSE of class membership predictions. Its loss function is based on the distance between the two covariance matrices of predictor values for group 1 subjects and predictor values for group 2 subjects. Your original thoughts about this problem are not based on good statistical principles. $\endgroup$
    – Frank Harrell
    Commented Nov 2, 2017 at 12:08

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