Effects of Lambda Changes

The image collection that is combined in Figure $[*]$ shows 4 ROC curves. This comparison shows how varying the number of eigenvalues (organised in descending order) affects the results. The weakness of this experiment is that it treats random examples that are not the same and given the size of the sets used for plotting, there is plenty of room for dependency on the stochastically-chosen set. That having been argued, it does not appear as though there is remarkable merit in limiting the number of greatest eigenvalues. The next experiment will look at how changing the value of delta affects performance, where the number of eigenvalues will be set high for obvious reasons (it is negligible when only high eigenvalues are accounted for).

**Figure:** The result - in terms of performance - of varying in $\lambda_{1<i<n}$

While the choice of $\delta$ may heavily depend on the number

in $\lambda_{1<i<n}$ (the further we go down the list of eigenvalues, the smaller their value is and the more impact $\delta$ has), Figure $[*]$ shows the effect of altering the value of $\delta$ on overall recognition performance (still just a small set with facial expressions varying).

**Figure:** The effect of changing the value of $\delta$ on the overall recognition performance

Based on the above results, we are from obtaining the published results by Mian et al. The idea we had in mind is to obtain similar results by re-implementing their exact methods and then introduce modifications using either R-PCA or GMDS, and investigate if and how we improve. The recognition rates (including expressions) are at a completely different scale than those reported even for early NIST/FRGC tests.

The scale of the experiments is vastly different because UWA trains a model on thousands of instances (some proprietary ones), which require one to sort pairs. In comparison, we build a model with just a couple of hundreds of examples and in order to speed things up we rescale the images.

Additionally, we could train on images without expressions and then apply the algorithm to the whole NIST/FRGC set, which comprises a vast number of neutrals. The main caveat is the need to prepare more data. It should be possible to invest some hours expanding the size of the training sets and auditing the results. There are many ways to make the recognition problem easier, e.g. by selecting particular types of images rather than edge cases we currently deal with. From a general point of view, performance can be improved later by designing an experiment to also include easier cases.