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Shapes Subsets

The stochastic choice of subsets attempted to speed up the construction of models through simplifiction. The choice of subsets was at first made at every single iteration. At later stages, such a choice was only made once within a set cycle (e.g. 10 or 100 iterations). This intended to allow the objective function and the algorithm to stabilise and deal with a somewhat similar problem repeatedly. When subsets are not reshuffled often, the subset under consideration retains more commonalities.

This idea was expected to result in reduction in run-time. That is because Eigen-analysis is then being simplified and, along with it, the scope of the problem is reduced. When sets are smaller, they are strictly easier to handle.

Figure: A comparison of performances in landmark selection. Shown above is an algorithm which is based on an entire set versus one which is based on a stochastic subset. The latter is quicker and it fluctuates due to the varying selection of a subset (3 shapes out of 10 in total).

Unfortunately, the approach taken above worked badly in terms of time. Its performance, as measured by the entire set of data, was worse as well. The first of these is almost a contradiction which is why further work must be considered. It ought to be discovered that handling of subsets should at the least reduce the complexity of model construction. Regarding the performance, results for images prove otherwise as explained below.