Can the mean squared error be used for classification?

I know the mean squared error formula and how to compute it. When we talk about a regression we can compute the mean squared error. However can we talk about a MSE for a classification problem and how to compute it?

Answer

Many classifiers can predict continuous scores. Often, continuous scores are intermediate results that are only converted to class labels (usually by threshold) as the very last step of the classification. In other cases, e.g. posterior probabilities for the class membership can be calculated (e.g. discriminant analysis, logistic regression).
You can calculate the MSE using these continuous scores rather than the class labels. The advantage of that is that you avoid the loss of information due to the dichotomization.
When the continuous score is a probability, the MSE metric is called Brier’s score.

However, there are also classification problems that are rather regression problems in disguise. In my field that could e.g. be classifying cases according to whether the concentration of some substance exceeds a legal limit or not (which is a binary/discriminative two-class problem). Here, MSE is a natural choice due to the underlying regression nature of the task.

In this paper we explain it as part of a more general framework:
C. Beleites, R. Salzer and V. Sergo:
Validation of Soft Classification Models using Partial Class Memberships: An Extended Concept of Sensitivity & Co. applied to Grading of Astrocytoma Tissues
Chemom. Intell. Lab. Syst., 122 (2013), 12 – 22.

How to compute it: if you work in R, one implementation is in package “softclassval”, http:/softclassval.r-forge.r-project.org.

Attribution
Source : Link , Question Author : kamaci , Answer Author : cbeleites unhappy with SX

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