Robust principal components

Croux, C., Filzmoser, P., Oliveira, M. R. Chemom. Intell. Lab. Syst. 87, 2007, 218-225. Algorithms for projection-pursuit robust principal component analysis. 

Hubert, M., Rousseeuw, P. J., Vanden Branden, K. Technometrics 47, 2005, 64-79. ROBPCA A new approach to robust principal components. 

In situations where robust regression cannot be applied (colhnearity, n < 2m) the x-variables could be summarized by robust principal components (Section 3.5). Then the procedure as mentioned above can be applied (see Section 4.6). 

FIGURE 6.26 Cluster validity measures for the glass vessels data (left) and result from model-based clustering for k = 4 (right) as a projection on the first two robust principal components (compare Figure 3.10, right). 

Moreover, the k robust principal components generate a pxp robust scatter matrix of rank k given by... 

Croux, C. and Ruiz-Gazen, A., A fast algorithm for robust principal components based on projection pursuit, in COMPSTAT1996 (Barcelona), Physica, Heidelberg, 1996, pp. 211-217. 

Robust principal component analysis and constrained background bilinearization for quantitative analysis... 

ROBUST PRINCIPAL COMPONENT ANALYSIS BY PROJECTION PURSUIT AND SIMULATED ANNEALING... 

Projection pursuit algorithm for robust principal component analysis... 

Robust principal component analysis by projection pursuit and... 

Principal component analysis (PCA) is frequently the method of choice to compress and visualize the structure of multivariate data [13]. The original experimental data are compressed by representing the total data variance using only a few new variables, called principal components (PCs). These PCs, which are orthogonal to each other, are ranked in a descending order of the variance they model. This means that with PCA, samples are projected onto an optimal direction in the multivariate data space explaining the largest possible variance. As mentioned earlier, the variance of a projection is not robust and the presence of outliers in the data will affect the construction of PCs. A direct way to obtain robust principal components (RPCs) is to replace the classic variance estimator with its robust counterpart. 

The third group of robust approaches to PCA combines the PP idea with the construction of robust covariance. An example of such a hybrid method is robust principal component analysis (ROBPCA) proposed by Hubert et al. [27]. 

Xie YL, Wang JH, Liang Y-Z, Sun LX, Song XH, Yu RQ. Robust principal component analysis by projection pursuit. 1 Chemometr 1993 7 527-41. 

Hubert M, Rousseeuw PJ, Verboven S. A fast method for robust principal components with apphcation to chemometrics. Chemometr Intell Lab Syst 2002 60 101-11. 

Hubert M, Rousseeuw PJ, Vanden Branden K. ROBPCA a new approach to robust principal component analysis. Technometrics 2005 47 64—79. 

Locantore N, Matron JS, Simpson DG, Tripoli N, Zhang JT, Cohen KL. Robust principal components for functional data. Test 1999 8 1-28. 

Croux C, Filzmoser P, Oliveira MR. Algorithms for Projection-Pursuit robust principal component analysis. Chemometr Intell Lab Syst 2007 87 218-25. 

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