Disjoint principal components models

S. Wold, Pattern recognition by means of disjoint principal components models. Pattern Recogn., 8 (1976) 127-139. 

Disjoint principal components modelling [266] and SIMCA (soft independent modelling of class analogy) [261,262,267] are examples of PCR wherein principal components models are developed for individual groups of responses within a data set. For these methods, classification is based on quality of fit of an unknown response pattern to the model developed for a given analyte [268-270]. This approach differs from standard PCR, where principal components are derived from the data matrix as a whole. 

S. Wold, Pattern Recognition, 8, 127 (1976). Pattern Recognition by Means of Disjoint Principal Components Models. 

This approach was originally developed by Wold (1976) under the name disjoint principal components models, later termed simple modelling of class analogy (SIMCA) (see also Wold and Sjostrom, 1977 Wold et al., 1983). While biological applications of SIMCA have been limited (e.g. Wold, 1976 Dahl et al., 1984), the technique exhibits some of the attributes of much more advauced neural-net architectures (see following discussion). Moreover, because of its basis in... 

Kvalheim, O.M. Karstang, T.V. (1992). SIMCA-Classification by means of disjoint cross validated principal component models. In Multivariate Pattern Recognition in Chemometrics, illustrated by case studies, R.G. Brereton (Ed.), 209-245, Elsevier, ISBN 0444897844, Amsterdam, Netherland... 

The large number of TIs, and the fact that many of them are highly correlated, confounds the development of predictive models. Therefore, we attempted to reduce the number of TIs to a smaller set of relatively independent variables. Variable clustering " was used to divide the TIs into disjoint subsets (clusters) that are essentially unidimensional. These clusters form new variables which are the first principal component derived from the members of the cluster. From each cluster of indexes, a single index was selected. The index chosen was the one most correlated with the cluster variable. In some cases, a member of a cluster showed poor group membership relative to the other members of the cluster, i.e., the correlation of an index with the cluster variable was much lower than the other members. Any variable showing poor cluster membership was selected for further studies as well. A correlation of a TI with the cluster variable less than 0.7 was used as the definition of poor cluster membership. 

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