Supervised learning linear discriminant analysis

Supervised learning methods - multivariate analysis of variance and discriminant analysis (MVDA) - k nearest neighbors (kNN) - linear learning machine (LLM) - BAYES classification - soft independent modeling of class analogy (SIMCA) - UNEQ classification Quantitative demarcation of a priori classes, relationships between class properties and variables... 

Discriminant analysis is a supervised learning technique which uses classified dependent data. Here, the dependent data (y values) are not on a continuous scale but are divided into distinct classes There are often just two classes (e.g. active/inactive soluble/not soluble yes/no), but more than two is also possible (e.g. high/medium/low, 1/2/3/4). The simplest situation involves two variables and two classes, and the aim is to find a straight line that best separates the data into its classes (Figure 12.37). With more than two variables, the line becomes a hyperplane in the multidimensional variable space. Discriminant analysis is characterised by a discriminant function, which in the particular case of linear discriminant analysis (the most popular variant) is written as a linear combination of the independent variables ... 

If the membership of objects to particular clusters is known in advance, the methods of supervised pattern recognition can be used. In this section, the following methods are explained linear learning machine (LLM), discriminant analysis, A -NN, the soft independent modeling of class analogies (SIMCA) method, and Support Vector Machines (SVMs). 

Statistical pattern recognition is based on the statistical nature of signals and extracted features are represented as probability density functions (Schalkoff, 1992). It therefore requires knowledge of a priori probabilities of measurements and features. Statistical approaches include linear discriminant functions, Bayesian functions and cluster analysis and may be unsupervised or supervised. Supervised classifiers require a set of exemplars for each class to be recognized they are used to train the system. Unsupervised learning, on the other hand, does not require an exemplar set. 

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