Supervised Linear Model-based Classification Algorithm

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A Supervised Linear Model-based Classification Algorithm is a supervised model-based classification algorithm that fits a linear classification function.



References

2024

2024

  • (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Linear_classifier#Generative_models_vs Retrieved:2024-1-15.
    • There are two broad classes of methods for determining the parameters of a linear classifier [math]\displaystyle{ \vec w }[/math] . They can be generative and discriminative models. [1] [2] Methods of the former model joint probability distribution, whereas methods of the latter model conditional density functions [math]\displaystyle{ P({\rm class}|\vec x) }[/math] . Examples of such algorithms include: * Linear Discriminant Analysis (LDA)—assumes Gaussian conditional density models * Naive Bayes classifier with multinomial or multivariate Bernoulli event models. The second set of methods includes discriminative models, which attempt to maximize the quality of the output on a training set. Additional terms in the training cost function can easily perform regularization of the final model. Examples of discriminative training of linear classifiers include: * Logistic regression—maximum likelihood estimation of [math]\displaystyle{ \vec w }[/math] assuming that the observed training set was generated by a binomial model that depends on the output of the classifier.
      • Perceptron—an algorithm that attempts to fix all errors encountered in the training set
      • Fisher's Linear Discriminant Analysis—an algorithm (different than "LDA") that maximizes the ratio of between-class scatter to within-class scatter, without any other assumptions. It is in essence a method of dimensionality reduction for binary classification. [3]
      • Support vector machine—an algorithm that maximizes the margin between the decision hyperplane and the examples in the training set.
    • Note: Despite its name, LDA does not belong to the class of discriminative models in this taxonomy. However, its name makes sense when we compare LDA to the other main linear dimensionality reduction algorithm: principal components analysis (PCA). LDA is a supervised learning algorithm that utilizes the labels of the data, while PCA is an unsupervised learning algorithm that ignores the labels. To summarize, the name is a historical artifact. [4] Discriminative training often yields higher accuracy than modeling the conditional density functions. However, handling missing data is often easier with conditional density models.

      All of the linear classifier algorithms listed above can be converted into non-linear algorithms operating on a different input space [math]\displaystyle{ \varphi(\vec x) }[/math] , using the kernel trick.

2015

2011

  • http://en.wikipedia.org/wiki/Linear_classifier
    • … If the input feature vector to the classifier is a real vector [math]\displaystyle{ \vec x }[/math], then the output score is [math]\displaystyle{ y = f(\vec{w}\cdot\vec{x}) = f\left(\sum_j w_j x_j\right), }[/math] where [math]\displaystyle{ \vec w }[/math] is a real vector of weights and [math]\displaystyle{ f }[/math] is a function that converts the dot product of the two vectors into the desired output. (In other words, [math]\displaystyle{ \vec{w} }[/math] is a one-form or linear functional mapping [math]\displaystyle{ \vec x }[/math] onto R.) The weight vector [math]\displaystyle{ \vec w }[/math] is learned from a set of labeled training samples. Often [math]\displaystyle{ f }[/math] is a simple function that maps all values above a certain threshold to the first class and all other values to the second class. A more complex [math]\displaystyle{ f }[/math] might give the probability that an item belongs to a certain class.

2009

2006

2004

1995


  1. T. Mitchell, Generative and Discriminative Classifiers: Naive Bayes and Logistic Regression. Draft Version, 2005
  2. A. Y. Ng and M. I. Jordan. On Discriminative vs. Generative Classifiers: A comparison of logistic regression and Naive Bayes. in NIPS 14, 2002.
  3. R.O. Duda, P.E. Hart, D.G. Stork, "Pattern Classification", Wiley, (2001).
  4. R.O. Duda, P.E. Hart, D.G. Stork, "Pattern Classification", Wiley, (2001).