Linear Classification Function

A Linear Classification Function is a Classification Function based on a Linear Function.

• AKA: Linear Classifier.
• Context:
  • It can be associated with a Linear Statistical Model.
  • It can be produced by a Linear Classification Algorithm.
  • It can range from being a Discriminative Linear Classification Function to being a Generative Linear Classification Function.
  • …
• Example(s):
  • [math]\displaystyle{ C(x) = sign\left(\beta_0 +\beta^T x\right) }[/math],
  • …
• Counter-Example(s):
  • a Linear Regression Function.
• See: Non-Linear Function, Linear Decision Function.

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References

2004

• (Hastie et al., 2004) ⇒ Trevor Hastie, Saharon Rosset, Robert Tibshirani, and Ji Zhu. (2004). “The Entire Regularization Path for the Support Vector Machine.” In: The Journal of Machine Learning Research, 5.
  • QUOTE: We have a set of [math]\displaystyle{ n }[/math] training pairs [math]\displaystyle{ x_i,\; y_i }[/math] , where [math]\displaystyle{ x_i \in \mathbb{R}^p }[/math] is a p-vector of real valued predictors (attributes) for the ith observation, [math]\displaystyle{ y_i \in \{−1, +1\} }[/math] codes its binary response. We start off with the simple case of a linear classifier, where our goal is to estimate a linear decision function

    [math]\displaystyle{ f(x) = \beta_0 +\beta^T x,\quad }[/math](1)

    and its associated classifier

    [math]\displaystyle{ C(x) = sign[f(x)]\quad }[/math](2)

    There are many ways to fit such a linear classifier, including linear regression, Fisher’s linear discriminant analysis, and logistic regression [Hastie et al., 2001, Chapter 4].

1995

• (Li, 1995) ⇒ Stan Z. Li. (1995). “Markov Random Field Modeling in Computer Vision.” Springer-Verlag. ISBN:4431701451
  • 7.2.3 Linear Classification Function http://www.cbsr.ia.ac.cn/users/szli/mrf_book/Chapter_7/node120.html

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