Sos, Lost in a High Dimensional Space

Face recognition methods based on Principle Component Analysis (PCA), known as the eigen face method, were some of the best performing methods for some time and are still often used as base line in comparisons. One of the best known variants is the combination of eigenfaces with the log likelihood ratio distance measure. The last few years no large improvements have been made and the method is outperformed by other methods regularly, despite the fact that the method has been proven to be optimal under certain conditions. One of the characteristics of the eigen face method is that its performance hardly increases if nowadays available higher resolution images are used, while other algorithms perform considerably better with (parts of) this data. An explanation for this has been missing until now. One effect the use of higher resolution images has, is that the data has a higher dimensionality. It has been known for some time that the estimation of Second Order Statistics (SOS), an important part of the eigen face method, becomes increasingly inaccurate with higher dimensionality. This is because the variance maxima are increasingly determined by random structures in the actual data set instead of the data generating process parameters. This is especially noticeable in the eigenvalue estimates: they are biased. The bias of an estimator is not random; therefore, the estimate can be corrected for this bias. A correction method developed by Karoui has the best performance at the moment, but unfortunately it is very difficult to apply the method to facial image data. A significant part of our study therefore focussed on developing a correction method which can be used to correct the eigenvalue estimates in the eigen face method. With the correction of the bias in estimated eigenvalues from facial data we can also study if the distortion in the SOS estimates is the reason why the performance of the eigen face method is not improved compared to other methods if high resolution images are used. The method we developed for this purpose is the fixed point bias correction. This method is better suited for data with the characteristics of facial data compared to the Karoui method, which we proved by tests with synthetic data. The eigenface method focusses mainly on estimating the variations of all the faces. However, for recognition it is more important to find the structures in the face which have a large variation between photos of different persons while they have a low variation between photos of the same person. This involves the estimation of