page_title: Linear classifier
section_title: Definition
hierarchical_section_title: Linear classifier / Definition
caption_attribution_description: Graphic showing 3 Hyperplanes in 2D. H3 doesn't separate the 2 classes. H1 does, with a small margin and H2 with the maximum margin.
context_page_description: In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class it belongs to. A linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. An object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables, reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.
context_section_description: If the input feature vector to the classifier is a real vector , then the output score is
  where  is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired output. (In other words,  is a one-form or linear functional mapping  onto R.) The weight vector  is learned from a set of labeled training samples. Often f is a threshold function, which maps all values of  above a certain threshold to the first class and all other values to the second class; e.g., 
  A more complex f might give the probability that an item belongs to a certain class.
  For a two-class classification problem, one can visualize the operation of a linear classifier as splitting a high-dimensional input space with a hyperplane: all points on one side of the hyperplane are classified as "yes", while the others are classified as "no".
  A linear classifier is often used in situations where the speed of classification is an issue, since it is often the fastest classifier, especially when  is sparse. Also, linear classifiers often work very well when the number of dimensions in  is large, as in document classification, where each element in  is typically the number of occurrences of a word in a document (see document-term matrix). In such cases, the classifier should be well-regularized.
caption: In this case, the solid and empty dots can be correctly classified by any number of linear classifiers. H1 (blue) classifies them correctly, as does H2 (red). H2 could be considered "better" in the sense that it is also furthest from both groups. H3 (green) fails to correctly classify the dots.
exif: {}