Pattern recognition class membership

The primary purpose of pattern recognition is to determine class membership for a set of numeric input data. The performance of any given approach is ultimately driven by how well an appropriate discriminant can be defined to resolve the numeric data into a label of interest. Because of both the importance of the problem and its many challenges, significant research has been applied to this area, resulting in a large number of techniques and approaches. With this publication, we seek to provide a common framework to discuss the application of these approaches. 

In contras to unsupervised methods, supervised pattern-recognition methods (Section 4.3) use class membership information in the calculations. The goal of these methods is to construct models using analytical measurements to predict class membership of future samples. Class location and sometimes shape are used in the calibration step to construct the models. In prediction, these moddsare applied to the analytical measurements of unknowu samples to predict dsss membership. 

Supervised versus Unsupervised Pattern Recognition In some situations the class membership of the samples is unknown. For example, an analyst may simply want to examine a data set to see what can be learned. Are there any groupings of samples Are there any outliers (i.e., a small number of samples that are not grouped with the majority) Even if class information is known, the analyst may want to identify and display natural groupings in the data without imposing class membership on the samples. For example, assume a series of spectra have been collected and the goal is to... 

The goal of unsupervised techniques is to identify and display natural groupings in the data without imposing any prior class membership. Even when the ultimate goal of the project is to develop a supervised pattern recognition model, we recommend the use of unsupervised techniques to provide an initial view of the data. 

Current methods for supervised pattern recognition are numerous. Typical linear methods are linear discriminant analysis (LDA) based on distance calculation, soft independent modeling of class analogy (SIMCA), which emphasizes similarities within a class, and PLS discriminant analysis (PLS-DA), which performs regression between spectra and class memberships. More advanced methods are based on nonlinear techniques, such as neural networks. Parametric versus nonparametric computations is a further distinction. In parametric techniques such as LDA, statistical parameters of normal sample distribution are used in the decision rules. Such restrictions do not influence nonparametric methods such as SIMCA, which perform more efficiently on NIR data collections. 

To handle multivariate data for which their class membership is determined by means of supervised pattern recognition approaches. 

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). 

The first analytical application of a pattern recognition method dates back to 1969 when classification of mass spectra with respect to certain molecular mass classes was tried with the LLM. The basis for classification with the LLM is a discriminant function that divides the -dimensional space into category regions that can be further used to predict the category membership of a test sample. 

Ann X m matrix can be considered n points in the m-dimensional space (or m points in the n-dimensional space). The points can be projected into a smaller dimensional subspace (smaller than n or m, whichever is the smaller) using proper techniques as PCA. Therefore, PCA is often called as a projection method. Projecting the points, dimension reduction of the data can be achieved. The principal components are often called underlying components their values are the scores. The principal components are, in fact, linear combinations of the original variables. PCA is an unsupervised method of pattern recognition in the sense that no grouping of the data has to be known before the analysis. Still the data structure can be revealed easily and class membership is easy to assiga... 

Supervised pattern recognition methods are the methods that use the class membership information while reveaUng dominant pattern in the data. 

One of the most popular pattern recognition methods in chemistry is SIMCA, an acronym for soft/simple independent modeling of class analogy. The central idea is to represent each class of objects by a separate principal component model. Because a probability can be estimated for belonging to a certain class and because outliers can be detected the method is called soft. Classification methods such as discriminant analysis are called hard if they give a categorical answer about the class membership. 

Pattern recognition can be categorized into parametric and non-parametric methods. Non-parametric methods do not make any assumptions about the underlying statistics of the data. Parametric methods estimate probability densities for class memberships (or a response variable) and then apply a classification rule to classify unknown objects or to predict the response. 

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